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Import pdf-to-markdown converter and shorten hosted image suffixes.

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Bring the local project into the remote repository and reduce generated image object suffixes to six characters for shorter URLs.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
qz 2026-04-19 14:37:42 +08:00
parent 7f69426fb5
commit 22165a3c26
16 changed files with 2568 additions and 162 deletions
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.env.example Normal file
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MINERU_API_TOKEN=your_mineru_api_token
R2_BASE_URL=https://r2.118229.xyz
R2_BEARER_TOKEN=r2img-bed-2026-secure-key-huang
R2_PREFIX=
R2_PUBLIC_BASE_URL=https://r2.118229.xyz
POLL_INTERVAL_SECONDS=5
TIMEOUT_SECONDS=1800

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.gitignore vendored
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# ---> Python
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
*$py.class
# C extensions
*.so
# Distribution / packaging
.Python
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
wheels/
share/python-wheels/
*.egg-info/
.installed.cfg
*.egg
MANIFEST
# PyInstaller
# Usually these files are written by a python script from a template
# before PyInstaller builds the exe, so as to inject date/other infos into it.
*.manifest
*.spec
# Installer logs
pip-log.txt
pip-delete-this-directory.txt
# Unit test / coverage reports
htmlcov/
.tox/
.nox/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*.cover
*.py,cover
.hypothesis/
.pytest_cache/
cover/
# Translations
*.mo
*.pot
# Django stuff:
*.log
local_settings.py
db.sqlite3
db.sqlite3-journal
# Flask stuff:
instance/
.webassets-cache
# Scrapy stuff:
.scrapy
# Sphinx documentation
docs/_build/
# PyBuilder
.pybuilder/
target/
# Jupyter Notebook
.ipynb_checkpoints
# IPython
profile_default/
ipython_config.py
# pyenv
# For a library or package, you might want to ignore these files since the code is
# intended to run in multiple environments; otherwise, check them in:
# .python-version
# pipenv
# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
# However, in case of collaboration, if having platform-specific dependencies or dependencies
# having no cross-platform support, pipenv may install dependencies that don't work, or not
# install all needed dependencies.
#Pipfile.lock
# poetry
# Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
# This is especially recommended for binary packages to ensure reproducibility, and is more
# commonly ignored for libraries.
# https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
#poetry.lock
# pdm
# Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
#pdm.lock
# pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
# in version control.
# https://pdm.fming.dev/#use-with-ide
.pdm.toml
# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
__pypackages__/
# Celery stuff
celerybeat-schedule
celerybeat.pid
# SageMath parsed files
*.sage.py
# Environments
.env
.venv
env/
venv/
ENV/
env.bak/
venv.bak/
# Spyder project settings
.spyderproject
.spyproject
# Rope project settings
.ropeproject
# mkdocs documentation
/site
# mypy
.mypy_cache/
.dmypy.json
dmypy.json
# Pyre type checker
.pyre/
# pytype static type analyzer
.pytype/
# Cython debug symbols
cython_debug/
# PyCharm
# JetBrains specific template is maintained in a separate JetBrains.gitignore that can
# be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
# and can be added to the global gitignore or merged into this file. For a more nuclear
# option (not recommended) you can uncomment the following to ignore the entire idea folder.
#.idea/
.venv/
__pycache__/
*.pyc

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README.md
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# pdf2md
# PDF to Markdown
输入学术论文 PDF，调用 MinerU 提取为 Markdown，随后把 Markdown 中引用的本地图片上传到 R2 图床，并输出一个纯 Markdown 文件。
## 1. 安装依赖
```bash
cd /home/qingz/projects/pdf-to-markdown
uv venv
source .venv/bin/activate
uv sync
cp .env.example .env
```
把 `.env` 里的 `MINERU_API_TOKEN` 改成你自己的 MinerU token。
## 2. 运行
```bash
uv run python run.py /path/to/paper.pdf
```
可选参数：
```bash
uv run python run.py /path/to/paper.pdf -o /path/to/output.md --language en
uv run python run.py /path/to/paper.pdf --ocr
uv run python run.py /path/to/paper.pdf --disable-table
uv run python run.py /path/to/paper.pdf --disable-formula
```
## 3. 输出
程序会输出最终生成的 Markdown 文件路径。Markdown 中的图片链接会被替换成绝对地址，上传结构为 `年/月/日/论文名简写/图片文件名`，因此在不同设备上直接打开 Markdown 文件也能看到图片。
## 4. 环境变量
- `MINERU_API_TOKEN`：MinerU API token
- `R2_BASE_URL`：图床上传基础地址
- `R2_BEARER_TOKEN`：图床 Bearer token
- `R2_PREFIX`：上传路径前缀
- `R2_PUBLIC_BASE_URL`：Markdown 中使用的公开访问基础地址
- `POLL_INTERVAL_SECONDS`：轮询间隔
- `TIMEOUT_SECONDS`：最大等待时间

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pyproject.toml Normal file
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[project]
name = "pdf-to-markdown"
version = "0.1.0"
description = "Convert academic paper PDFs to pure Markdown via MinerU and host extracted images on R2"
requires-python = ">=3.10"
dependencies = [
"requests>=2.32.0",
"python-dotenv>=1.0.1",
]
[tool.uv]
package = false

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requirements.txt Normal file
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requests>=2.32.0
python-dotenv>=1.0.1

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run.py Normal file
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#!/usr/bin/env python3
import argparse
import datetime as dt
import mimetypes
import os
import posixpath
import re
import sys
import tempfile
import time
import uuid
import zipfile
from pathlib import Path
from urllib.parse import urlparse
import requests
from dotenv import load_dotenv
MINERU_BASE_URL = "https://mineru.net"
IMAGE_EXTENSIONS = {".png", ".jpg", ".jpeg", ".gif", ".webp", ".bmp", ".tif", ".tiff", ".svg"}
def parse_args() -> argparse.Namespace:
parser = argparse.ArgumentParser(
description="Convert a PDF academic paper to pure Markdown with hosted images via MinerU."
)
parser.add_argument("pdf", help="Path to the input PDF file")
parser.add_argument(
"-o",
"--output",
help="Path to the output Markdown file. Defaults to <pdf_stem>.md next to the PDF.",
)
parser.add_argument(
"--language",
default="en",
help="Document language hint for MinerU, default: en",
)
parser.add_argument(
"--ocr",
action="store_true",
help="Enable OCR mode for scanned PDFs",
)
parser.add_argument(
"--disable-table",
action="store_true",
help="Disable table extraction",
)
parser.add_argument(
"--disable-formula",
action="store_true",
help="Disable formula extraction",
)
parser.add_argument(
"--poll-interval",
type=float,
default=float(os.getenv("POLL_INTERVAL_SECONDS", "5")),
help="Polling interval in seconds",
)
parser.add_argument(
"--timeout",
type=int,
default=int(os.getenv("TIMEOUT_SECONDS", "1800")),
help="Overall timeout in seconds",
)
return parser.parse_args()
def require_env(name: str) -> str:
value = os.getenv(name, "").strip()
if not value:
raise SystemExit(f"Missing required environment variable: {name}")
return value
def mineru_headers(token: str) -> dict[str, str]:
return {
"Authorization": f"Bearer {token}",
"Content-Type": "application/json",
}
def submit_pdf(pdf_path: Path, token: str, language: str, is_ocr: bool, enable_table: bool, enable_formula: bool) -> tuple[str, str]:
data_id = uuid.uuid4().hex
payload = {
"files": [
{
"name": pdf_path.name,
"data_id": data_id,
"is_ocr": is_ocr,
}
],
"model_version": "vlm",
"enable_table": enable_table,
"enable_formula": enable_formula,
"language": language,
}
response = requests.post(
f"{MINERU_BASE_URL}/api/v4/file-urls/batch",
headers=mineru_headers(token),
json=payload,
timeout=60,
)
response.raise_for_status()
body = response.json()
if body.get("code") != 0:
raise RuntimeError(f"MinerU submit failed: {body}")
data = body["data"]
file_urls = data.get("file_urls") or []
if len(file_urls) != 1:
raise RuntimeError(f"Unexpected MinerU file_urls response: {body}")
return data["batch_id"], file_urls[0]
def upload_pdf_to_signed_url(pdf_path: Path, signed_url: str) -> None:
with pdf_path.open("rb") as f:
response = requests.put(signed_url, data=f, timeout=300)
response.raise_for_status()
def wait_for_result(batch_id: str, token: str, timeout_seconds: int, poll_interval: float) -> str:
deadline = time.monotonic() + timeout_seconds
last_state = None
while time.monotonic() < deadline:
response = requests.get(
f"{MINERU_BASE_URL}/api/v4/extract-results/batch/{batch_id}",
headers={"Authorization": f"Bearer {token}"},
timeout=60,
)
response.raise_for_status()
body = response.json()
if body.get("code") != 0:
raise RuntimeError(f"MinerU polling failed: {body}")
results = body.get("data", {}).get("extract_result") or []
if len(results) != 1:
raise RuntimeError(f"Unexpected MinerU extract_result response: {body}")
result = results[0]
state = result.get("state")
if state != last_state:
print(f"MinerU state: {state}", file=sys.stderr)
last_state = state
if state == "done":
full_zip_url = result.get("full_zip_url")
if not full_zip_url:
raise RuntimeError(f"MinerU returned done without full_zip_url: {body}")
return full_zip_url
if state == "failed":
raise RuntimeError(f"MinerU extraction failed: {result.get('err_msg') or body}")
time.sleep(poll_interval)
raise TimeoutError(f"Timed out waiting for MinerU batch {batch_id}")
def download_zip(full_zip_url: str, target_dir: Path) -> Path:
zip_path = target_dir / "result.zip"
with requests.get(full_zip_url, stream=True, timeout=300) as response:
response.raise_for_status()
with zip_path.open("wb") as f:
for chunk in response.iter_content(chunk_size=1024 * 1024):
if chunk:
f.write(chunk)
return zip_path
def extract_zip(zip_path: Path, target_dir: Path) -> Path:
with zipfile.ZipFile(zip_path) as zf:
zf.extractall(target_dir)
return target_dir
def find_full_markdown(extracted_dir: Path) -> Path:
matches = list(extracted_dir.rglob("full.md"))
if not matches:
raise FileNotFoundError("full.md was not found in the MinerU zip output")
return matches[0]
def infer_content_type(path: Path) -> str:
content_type, _ = mimetypes.guess_type(path.name)
return content_type or "application/octet-stream"
def build_r2_url(base_url: str, prefix: str, folder_name: str, object_name: str) -> str:
base = base_url.rstrip("/")
parts = [segment for segment in [prefix.strip("/"), folder_name.strip("/"), object_name] if segment]
return f"{base}/{posixpath.join(*parts)}"
def slugify_paper_name(pdf_stem: str, limit: int = 48) -> str:
slug = re.sub(r"[^a-z0-9]+", "-", pdf_stem.lower()).strip("-")
if not slug:
slug = "paper"
return slug[:limit].rstrip("-") or "paper"
def unique_object_name(local_path: Path) -> str:
stem = re.sub(r"[^a-zA-Z0-9._-]+", "-", local_path.stem).strip("-._") or "image"
suffix = local_path.suffix.lower() or ".bin"
return f"{stem}-{uuid.uuid4().hex[:6]}{suffix}"
def upload_image_to_r2(local_path: Path, target_url: str, bearer_token: str) -> str:
headers = {
"Authorization": f"Bearer {bearer_token}",
"Content-Type": infer_content_type(local_path),
}
with local_path.open("rb") as f:
response = requests.put(target_url, headers=headers, data=f, timeout=300)
response.raise_for_status()
return target_url
def normalize_public_url(uploaded_url: str, public_base_url: str | None) -> str:
if not public_base_url:
return uploaded_url
path = urlparse(uploaded_url).path.lstrip("/")
return f"{public_base_url.rstrip('/')}/{path}"
def upload_images_and_rewrite(markdown_text: str, asset_root: Path, pdf_stem: str) -> str:
r2_base_url = require_env("R2_BASE_URL")
r2_bearer_token = require_env("R2_BEARER_TOKEN")
r2_prefix = os.getenv("R2_PREFIX", "").strip()
r2_public_base_url = os.getenv("R2_PUBLIC_BASE_URL", "").strip() or None
date_prefix = dt.date.today().strftime("%Y/%m/%d")
paper_folder = slugify_paper_name(pdf_stem)
folder_name = posixpath.join(date_prefix, paper_folder)
uploaded: dict[str, str] = {}
def replace(match: re.Match[str]) -> str:
alt_text = match.group(1)
original_path = match.group(2).strip()
if original_path.startswith(("http://", "https://", "data:")):
return match.group(0)
if original_path in uploaded:
hosted_url = uploaded[original_path]
else:
local_path = (asset_root / original_path).resolve()
if not local_path.exists() or not local_path.is_file():
return match.group(0)
if local_path.suffix.lower() not in IMAGE_EXTENSIONS:
return match.group(0)
object_name = unique_object_name(local_path)
upload_url = build_r2_url(r2_base_url, r2_prefix, folder_name, object_name)
uploaded_url = upload_image_to_r2(local_path, upload_url, r2_bearer_token)
hosted_url = normalize_public_url(uploaded_url, r2_public_base_url)
uploaded[original_path] = hosted_url
return f"![{alt_text}]({hosted_url})"
return re.sub(r"!\[([^\]]*)\]\(([^)]+)\)", replace, markdown_text)
def main() -> int:
load_dotenv()
args = parse_args()
token = require_env("MINERU_API_TOKEN")
pdf_path = Path(args.pdf).expanduser().resolve()
if not pdf_path.exists() or not pdf_path.is_file():
raise SystemExit(f"PDF not found: {pdf_path}")
output_path = Path(args.output).expanduser().resolve() if args.output else pdf_path.with_suffix(".md")
enable_table = not args.disable_table
enable_formula = not args.disable_formula
print("Submitting PDF to MinerU...", file=sys.stderr)
batch_id, signed_upload_url = submit_pdf(
pdf_path=pdf_path,
token=token,
language=args.language,
is_ocr=args.ocr,
enable_table=enable_table,
enable_formula=enable_formula,
)
print("Uploading PDF...", file=sys.stderr)
upload_pdf_to_signed_url(pdf_path, signed_upload_url)
print("Waiting for extraction result...", file=sys.stderr)
full_zip_url = wait_for_result(
batch_id=batch_id,
token=token,
timeout_seconds=args.timeout,
poll_interval=args.poll_interval,
)
with tempfile.TemporaryDirectory(prefix="mineru-") as temp_dir:
temp_path = Path(temp_dir)
zip_path = download_zip(full_zip_url, temp_path)
extracted_dir = extract_zip(zip_path, temp_path / "extracted")
markdown_path = find_full_markdown(extracted_dir)
markdown_text = markdown_path.read_text(encoding="utf-8")
rewritten_markdown = upload_images_and_rewrite(
markdown_text=markdown_text,
asset_root=markdown_path.parent,
pdf_stem=pdf_path.stem,
)
output_path.parent.mkdir(parents=True, exist_ok=True)
output_path.write_text(rewritten_markdown, encoding="utf-8", newline="\n")
print(str(output_path))
return 0
if __name__ == "__main__":
raise SystemExit(main())

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skills/pdf-to-markdown-mineru/SKILL.md Normal file
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---
name: pdf-to-markdown-mineru
description: Convert local PDF files, especially academic papers, into Markdown via MinerU and rewrite extracted local image references to hosted URLs on an R2-compatible object store.
---
# PDF to Markdown via MinerU
Use this skill when the user wants a local PDF converted into Markdown and the final Markdown should keep working across machines by replacing extracted local image paths with hosted URLs.
## Included files
- `scripts/convert_pdf_to_markdown.py`: standalone CLI for MinerU submission, polling, download, unzip, image upload, and Markdown rewrite.
- `scripts/requirements.txt`: minimal Python dependencies for the CLI.
- `.env`: bundled MinerU and R2 configuration so the skill can run directly in this workspace.
## Workflow
1. Confirm the source PDF path and choose an output `.md` path.
2. Ensure Python dependencies are installed. Prefer `uv pip install -r <skill-dir>/scripts/requirements.txt` or `python -m pip install -r <skill-dir>/scripts/requirements.txt`.
3. This skill first loads `.env` from the skill root, then falls back to the current working directory or an explicit `--env-file`.
4. Ensure these environment variables are available before running:
- Required: `MINERU_API_TOKEN`, `R2_BASE_URL`, `R2_BEARER_TOKEN`
- Optional: `R2_PREFIX`, `R2_PUBLIC_BASE_URL`, `POLL_INTERVAL_SECONDS`, `TIMEOUT_SECONDS`
5. Run the converter:
```bash
python scripts/convert_pdf_to_markdown.py /path/to/paper.pdf -o /path/to/paper.md
```
6. For scanned PDFs, add `--ocr`. Disable extraction features with `--disable-table` or `--disable-formula` if needed.
## Operational notes
- The script requires outbound network access to MinerU and the R2-compatible object store.
- Progress messages are written to stderr. The final Markdown path is written to stdout.
- Only local image references are uploaded and rewritten. Existing `http`, `https`, and `data:` image URLs are left unchanged.
- If the caller wants Markdown without any image hosting step, this skill is the wrong default; adjust the script first instead of running it as-is.

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skills/pdf-to-markdown-mineru/agents/openai.yaml Normal file
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interface:
display_name: "PDF to Markdown"
short_description: "Convert PDFs to Markdown via MinerU and R2"
default_prompt: "Use $pdf-to-markdown-mineru to turn ./paper.pdf into Markdown and write the result to ./paper.md."

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skills/pdf-to-markdown-mineru/scripts/convert_pdf_to_markdown.py Normal file
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#!/usr/bin/env python3
import argparse
import datetime as dt
import mimetypes
import os
import posixpath
import re
import sys
import tempfile
import time
import uuid
import zipfile
from pathlib import Path
from urllib.parse import urlparse
import requests
from dotenv import load_dotenv
MINERU_BASE_URL = "https://mineru.net"
IMAGE_EXTENSIONS = {".png", ".jpg", ".jpeg", ".gif", ".webp", ".bmp", ".tif", ".tiff", ".svg"}
def parse_args() -> argparse.Namespace:
parser = argparse.ArgumentParser(
description="Convert a PDF academic paper to pure Markdown with hosted images via MinerU."
)
parser.add_argument("pdf", help="Path to the input PDF file")
parser.add_argument(
"-o",
"--output",
help="Path to the output Markdown file. Defaults to <pdf_stem>.md next to the PDF.",
)
parser.add_argument(
"--env-file",
help="Optional path to a dotenv file. If omitted, the script loads .env from the current working directory and the skill directory when present.",
)
parser.add_argument(
"--language",
default="en",
help="Document language hint for MinerU, default: en",
)
parser.add_argument(
"--ocr",
action="store_true",
help="Enable OCR mode for scanned PDFs",
)
parser.add_argument(
"--disable-table",
action="store_true",
help="Disable table extraction",
)
parser.add_argument(
"--disable-formula",
action="store_true",
help="Disable formula extraction",
)
parser.add_argument(
"--poll-interval",
type=float,
default=float(os.getenv("POLL_INTERVAL_SECONDS", "5")),
help="Polling interval in seconds",
)
parser.add_argument(
"--timeout",
type=int,
default=int(os.getenv("TIMEOUT_SECONDS", "1800")),
help="Overall timeout in seconds",
)
return parser.parse_args()
def load_environment(env_file: str | None) -> None:
if env_file:
load_dotenv(Path(env_file).expanduser(), override=False)
return
load_dotenv(override=False)
bundled_env = Path(__file__).resolve().parents[1] / ".env"
if bundled_env.exists():
load_dotenv(bundled_env, override=False)
def require_env(name: str) -> str:
value = os.getenv(name, "").strip()
if not value:
raise SystemExit(f"Missing required environment variable: {name}")
return value
def mineru_headers(token: str) -> dict[str, str]:
return {
"Authorization": f"Bearer {token}",
"Content-Type": "application/json",
}
def submit_pdf(pdf_path: Path, token: str, language: str, is_ocr: bool, enable_table: bool, enable_formula: bool) -> tuple[str, str]:
data_id = uuid.uuid4().hex
payload = {
"files": [
{
"name": pdf_path.name,
"data_id": data_id,
"is_ocr": is_ocr,
}
],
"model_version": "vlm",
"enable_table": enable_table,
"enable_formula": enable_formula,
"language": language,
}
response = requests.post(
f"{MINERU_BASE_URL}/api/v4/file-urls/batch",
headers=mineru_headers(token),
json=payload,
timeout=60,
)
response.raise_for_status()
body = response.json()
if body.get("code") != 0:
raise RuntimeError(f"MinerU submit failed: {body}")
data = body["data"]
file_urls = data.get("file_urls") or []
if len(file_urls) != 1:
raise RuntimeError(f"Unexpected MinerU file_urls response: {body}")
return data["batch_id"], file_urls[0]
def upload_pdf_to_signed_url(pdf_path: Path, signed_url: str) -> None:
with pdf_path.open("rb") as f:
response = requests.put(signed_url, data=f, timeout=300)
response.raise_for_status()
def wait_for_result(batch_id: str, token: str, timeout_seconds: int, poll_interval: float) -> str:
deadline = time.monotonic() + timeout_seconds
last_state = None
while time.monotonic() < deadline:
response = requests.get(
f"{MINERU_BASE_URL}/api/v4/extract-results/batch/{batch_id}",
headers={"Authorization": f"Bearer {token}"},
timeout=60,
)
response.raise_for_status()
body = response.json()
if body.get("code") != 0:
raise RuntimeError(f"MinerU polling failed: {body}")
results = body.get("data", {}).get("extract_result") or []
if len(results) != 1:
raise RuntimeError(f"Unexpected MinerU extract_result response: {body}")
result = results[0]
state = result.get("state")
if state != last_state:
print(f"MinerU state: {state}", file=sys.stderr)
last_state = state
if state == "done":
full_zip_url = result.get("full_zip_url")
if not full_zip_url:
raise RuntimeError(f"MinerU returned done without full_zip_url: {body}")
return full_zip_url
if state == "failed":
raise RuntimeError(f"MinerU extraction failed: {result.get('err_msg') or body}")
time.sleep(poll_interval)
raise TimeoutError(f"Timed out waiting for MinerU batch {batch_id}")
def download_zip(full_zip_url: str, target_dir: Path) -> Path:
zip_path = target_dir / "result.zip"
with requests.get(full_zip_url, stream=True, timeout=300) as response:
response.raise_for_status()
with zip_path.open("wb") as f:
for chunk in response.iter_content(chunk_size=1024 * 1024):
if chunk:
f.write(chunk)
return zip_path
def extract_zip(zip_path: Path, target_dir: Path) -> Path:
with zipfile.ZipFile(zip_path) as zf:
zf.extractall(target_dir)
return target_dir
def find_full_markdown(extracted_dir: Path) -> Path:
matches = list(extracted_dir.rglob("full.md"))
if not matches:
raise FileNotFoundError("full.md was not found in the MinerU zip output")
return matches[0]
def infer_content_type(path: Path) -> str:
content_type, _ = mimetypes.guess_type(path.name)
return content_type or "application/octet-stream"
def build_r2_url(base_url: str, prefix: str, folder_name: str, object_name: str) -> str:
base = base_url.rstrip("/")
parts = [segment for segment in [prefix.strip("/"), folder_name.strip("/"), object_name] if segment]
return f"{base}/{posixpath.join(*parts)}"
def slugify_paper_name(pdf_stem: str, limit: int = 48) -> str:
slug = re.sub(r"[^a-z0-9]+", "-", pdf_stem.lower()).strip("-")
if not slug:
slug = "paper"
return slug[:limit].rstrip("-") or "paper"
def unique_object_name(local_path: Path) -> str:
stem = re.sub(r"[^a-zA-Z0-9._-]+", "-", local_path.stem).strip("-._") or "image"
suffix = local_path.suffix.lower() or ".bin"
return f"{stem}-{uuid.uuid4().hex[:6]}{suffix}"
def upload_image_to_r2(local_path: Path, target_url: str, bearer_token: str) -> str:
headers = {
"Authorization": f"Bearer {bearer_token}",
"Content-Type": infer_content_type(local_path),
}
with local_path.open("rb") as f:
response = requests.put(target_url, headers=headers, data=f, timeout=300)
response.raise_for_status()
return target_url
def normalize_public_url(uploaded_url: str, public_base_url: str | None) -> str:
if not public_base_url:
return uploaded_url
path = urlparse(uploaded_url).path.lstrip("/")
return f"{public_base_url.rstrip('/')}/{path}"
def upload_images_and_rewrite(markdown_text: str, asset_root: Path, pdf_stem: str) -> str:
r2_base_url = require_env("R2_BASE_URL")
r2_bearer_token = require_env("R2_BEARER_TOKEN")
r2_prefix = os.getenv("R2_PREFIX", "").strip()
r2_public_base_url = os.getenv("R2_PUBLIC_BASE_URL", "").strip() or None
date_prefix = dt.date.today().strftime("%Y/%m/%d")
paper_folder = slugify_paper_name(pdf_stem)
folder_name = posixpath.join(date_prefix, paper_folder)
uploaded: dict[str, str] = {}
def replace(match: re.Match[str]) -> str:
alt_text = match.group(1)
original_path = match.group(2).strip()
if original_path.startswith(("http://", "https://", "data:")):
return match.group(0)
if original_path in uploaded:
hosted_url = uploaded[original_path]
else:
local_path = (asset_root / original_path).resolve()
if not local_path.exists() or not local_path.is_file():
return match.group(0)
if local_path.suffix.lower() not in IMAGE_EXTENSIONS:
return match.group(0)
object_name = unique_object_name(local_path)
upload_url = build_r2_url(r2_base_url, r2_prefix, folder_name, object_name)
uploaded_url = upload_image_to_r2(local_path, upload_url, r2_bearer_token)
hosted_url = normalize_public_url(uploaded_url, r2_public_base_url)
uploaded[original_path] = hosted_url
return f"![{alt_text}]({hosted_url})"
return re.sub(r"!\[([^\]]*)\]\(([^)]+)\)", replace, markdown_text)
def main() -> int:
args = parse_args()
load_environment(args.env_file)
token = require_env("MINERU_API_TOKEN")
pdf_path = Path(args.pdf).expanduser().resolve()
if not pdf_path.exists() or not pdf_path.is_file():
raise SystemExit(f"PDF not found: {pdf_path}")
output_path = Path(args.output).expanduser().resolve() if args.output else pdf_path.with_suffix(".md")
enable_table = not args.disable_table
enable_formula = not args.disable_formula
print("Submitting PDF to MinerU...", file=sys.stderr)
batch_id, signed_upload_url = submit_pdf(
pdf_path=pdf_path,
token=token,
language=args.language,
is_ocr=args.ocr,
enable_table=enable_table,
enable_formula=enable_formula,
)
print("Uploading PDF...", file=sys.stderr)
upload_pdf_to_signed_url(pdf_path, signed_upload_url)
print("Waiting for extraction result...", file=sys.stderr)
full_zip_url = wait_for_result(
batch_id=batch_id,
token=token,
timeout_seconds=args.timeout,
poll_interval=args.poll_interval,
)
with tempfile.TemporaryDirectory(prefix="mineru-") as temp_dir:
temp_path = Path(temp_dir)
zip_path = download_zip(full_zip_url, temp_path)
extracted_dir = extract_zip(zip_path, temp_path / "extracted")
markdown_path = find_full_markdown(extracted_dir)
markdown_text = markdown_path.read_text(encoding="utf-8")
rewritten_markdown = upload_images_and_rewrite(
markdown_text=markdown_text,
asset_root=markdown_path.parent,
pdf_stem=pdf_path.stem,
)
output_path.parent.mkdir(parents=True, exist_ok=True)
output_path.write_text(rewritten_markdown, encoding="utf-8", newline="\n")
print(str(output_path))
return 0
if __name__ == "__main__":
raise SystemExit(main())

2
skills/pdf-to-markdown-mineru/scripts/requirements.txt Normal file
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@ -0,0 +1,2 @@
requests>=2.32.0
python-dotenv>=1.0.1

282
test/Resource_Allocation_for_Text_Semantic_Communications.md Normal file
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@ -0,0 +1,282 @@
# Resource Allocation for Text Semantic Communications
Lei $\mathrm { Y a n } ^ { \mathbb { P } }$ , Zhijin $\mathrm { Q i n } ^ { \mathbb { \oplus } }$ , Senior Member, IEEE, Rui Zhang Member, IEEE, Yongzhao Li $\operatorname { L i } ^ { \mathbb { \phi } }$ , Senior Member, IEEE, and Geoffrey Ye Li , Fellow, IEEE
Abstract—Semantic communications have shown its great potential to improve the transmission reliability, especially in the low signal-to-noise regime. However, resource allocation for semantic communications still remains unexplored, which is a critical issue in guaranteeing the semantic transmission reliability and the communication efficiency. To fill this gap, we investigate the spectral efficiency in the semantic domain and rethink the semantic-aware resource allocation issue. Specifically, taking text semantic communication as an example, the semantic spectral efficiency (S-SE) is defined for the first time, and is used to optimize resource allocation in terms of channel assignment and the number of transmitted semantic symbols. Additionally, for fair comparison of semantic and conventional communication systems, a transform method is developed to convert the conventional bit-based spectral efficiency to the S-SE. Simulation results demonstrate the validity and feasibility of the proposed resource allocation method, as well as the superiority of semantic communications in terms of the S-SE.
Index Terms—Semantic communications, semantic spectral efficiency, resource allocation.
# I. INTRODUCTION
W ITH growing wireless applications and increasing datatraffic, wireless communications are facing the bottleneck of spectrum scarcity, which motivates a paradigm shift from conventional to semantic communications [1], [2]. By focusing on transmitting the meaning of the source, semantic communications have shown a great potential to reduce the network traffic and thus alleviate spectrum shortage. Particularly, different types of semantic systems have been studied for different types of sources, including text [3], [4], image [5], [6], speech [7], and video [8], to ensure significant improvement in semantic transmission reliability. In this context, it is vital to investigate the resource allocation issue
Manuscript received March 5, 2022; revised April 13, 2022; accepted April 21, 2022. Date of publication April 27, 2022; date of current version July 11, 2022. This work was supported in part by the National Natural Science Foundation of China under Grant 61901345, Grant 61901333, and Grant 62001358; in part by the Postdoctoral Science Foundation of China under Grant 2019M663630; in part by the Shaanxi Provincial Key Research and Development Program under Grant 2021ZDLGY04-08, Grant 2022ZDLGY05-03, and Grant 2022ZDLGY05-04; in part by the State Key Laboratory of Integrated Services Network under Grant ISN090105; in part by the 111 Project under Grant B08038; in part by the Huawei Technologies Ltd.; and in part by the China Scholarship Council under Grant 202006960013. The associate editor coordinating the review of this article and approving it for publication was D. B. da Costa. (Corresponding authors: Rui Zhang; Yongzhao Li.)
Lei Yan, Rui Zhang, and Yongzhao Li are with the State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China (e-mail: lyan@stu.xidian.edu.cn; $\operatorname { r } Z ^ { ( \varpi ) }$ xidian.edu.cn; yzhli@xidian.edu.cn).
Zhijin Qin is with the School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, U.K. (e-mail: z.qin@qmul.ac.uk).
Geoffrey Ye Li is with the School of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, U.K. (e-mail: geoffrey.li@imperial.ac.uk).
Digital Object Identifier 10.1109/LWC.2022.3170849
for semantic communications to improve the communication efficiency while guaranteeing the transmission reliability [9].
In wireless communications, how to measure the information content as well as the spectral efficiency (SE) is fundamental to the resource allocation issue. Bit is used in the conventional communications. However, it is not applicable in semantic communications as bits are produced based on the statistic knowledge of source symbols rather than the semantic information of the source. Therefore, resource allocation needs to be rethought from the semantic perspective. The research on semantic theory has provided some insights on this issue. Carnap and Bar-Hillel [10] first attempted to measure the semantic information in a sentence based on the logical probability. On this basis, the semantic channel capacity was derived in [11] for the discrete memoryless channel, revealing the existence of the semantic coding strategy for reliable communications. Furthermore, semantic coding, the fundamental limits of semantic transmission, and semantic compression were investigated in [12]. However, the aforementioned works are based on abstract models without any hint of practical implementation and fail to quantify the SE in the semantic domain.
Although a complete theory or a well-developed mathematical model for semantic communications is still missing, the success of semantic system design with the aid of deep learning (DL) makes it possible to define a calculable SE in the semantic domain. Particularly, the DL-enabled semantic communication system (DeepSC) [3] and its several variants [4], [13] can effectively extract the semantic information from text and successfully deliver the meaning to the receiver. In this letter, we use DeepSC as an example to explore the SE issue and the resource allocation problem in such a semanticaware network. The main contributions are as follows:
A novel resource allocation model is proposed for semantic-aware networks. Specifically, the semantic spectral efficiency (S-SE) is first defined to measure the communication efficiency from the semantic perspective. Then a new formulation is proposed and solved to maximize the overall S-SE in terms of channel assignment and the number of transmitted semantic symbols.
• To make a fair comparison between semantic and conventional communication systems, a transform method is developed to convert the bit-based SE to the S-SE.
Simulation results verify the effectiveness of the proposed resource allocation model, as well as the superiority of semantic communication systems in terms of the S-SE.
The rest of this letter is organized as follows. Section II introduces the system model. Semantic-aware resource allocation is formulated and solved in Section III. Section IV introduces a transform method for fair comparison of semantic and conventional communication systems and presents the simulation results. Section V concludes this letter.
Notation: $\mathbb { R } ^ { n \times m }$ represents the set of real matrices of size $n \times m$ . Bold-font variables represent matrices and vectors. $x \sim$
![](https://r2.118229.xyz/2026/04/17/resource-allocation-for-text-semantic-communicat/394f0e8c2f43987b4109d8842fa25e4c0385ca116ec0169de42f163621e39834-51957bc2a37d.jpg)
Fig. 1. The structure of semantic-aware networks.
$\mathcal { C N } ( \mu , \sigma ^ { 2 } )$ means $x$ follows a circularly-symmetric complex Gaussian distribution with mean $\mu$ and covariance $\sigma ^ { 2 }$ .
# II. SYSTEM MODEL
We consider a cellular network consisting of a base station (BS) and a set of users denoted by $\mathcal { N } = \{ 1 , 2 , \dots , n , \dots , N \}$ , n Nas shown in Fig. 1. DeepSC [3] is adopted as the semantic communication model and equipped at each user for text transmission, where the semantics underlying text can be effectively extracted through Transformer. The DeepSC transceiver is assumed to be trained at the BS or cloud platforms. Then the trained semantic transmitter model is broadcast to users. In the following, we will detail the DeepSC transmitter at users, the transmission model, and the DeepSC receiver at the BS.
# A. DeepSC Transmitter
In our model, the $n$ -th user generates a sentence $\begin{array} { r l } { \mathbf { s } _ { n } } & { { } = } \end{array}$ $[ w _ { n , 1 } , w _ { n , 2 } , \ldots , w _ { n , l } , \ldots , w _ { n , L _ { n } } ] ,$ where $w _ { n , l }$ denotes the $l$ -th w wword and $L _ { n }$ w w wis the sentence length at the $n$ -th user. Then Lthe sentence is fed into the DeepSC transmitter and mapped to a semantic symbol vector ${ { \bf { X } } _ { n } } = [ { \bf { x } } _ { n , 1 } , { \bf { x } } _ { n , 2 } , . . . , { \bf { x } } _ { n , k _ { n } L _ { n } } ]$ where $\mathbf { X } _ { n } \in \mathbb { R } ^ { k _ { n } L _ { n } \times 2 }$ and $k _ { n } L _ { n }$ is the length of the semank Ltic symbol vector for a sentence at the $n$ -th user. We notice that the length of ${ \bf X } _ { n }$ varies with $L _ { n }$ to extract the semantic Linformation of sentences with different lengths more effectively [3]. In such a model, $k _ { n }$ denotes the average number kof semantic symbols used for each word at the $n$ -th user, and each semantic symbol can be transmitted over transmission medium directly.
# B. Transmission Model
Let $\mathcal { M } = \{ 1 , 2 , \dotsc , m , \dotsc , M \}$ denote the set of availm Mable channels in the network, where $M$ is the number of channels and each channel is with bandwidth W. The channel assignment vector of the $n$ -th user is denoted as ${ \pmb { \alpha } } _ { n } =$ $\left[ \alpha _ { n , 1 } , \alpha _ { n , 2 } , \ldots , \alpha _ { n , m } , \ldots , \alpha _ { n , M } \right]$ , where $\begin{array} { l l l } { \alpha _ { n , m } } & { \in } & { \{ 0 , 1 \} } \end{array}$ $\alpha _ { n , m } ~ = ~ 1$ when the $m$ -th channel is allocated to the $n$ -th user, and $\alpha _ { n , m } = 0$ , otherwise. Assuming that each channel can only be allocated to at most one user and each user can only occupy at most one channel, we have
$$
\sum_ {n = 1} ^ {N} \alpha_ {n, m} \leq 1, \forall m \in \mathcal {M}; \sum_ {m = 1} ^ {M} \alpha_ {n, m} \leq 1, \forall n \in \mathcal {N}. \tag {1}
$$
In addition, we consider that all channels consist of large-scale fading and small-scale Rayleigh fading. The
signal-to-noise ratio (SNR) of the $n$ -th user over the $m$ -th channel is
$$
\gamma_ {n, m} = \frac {p _ {n} g _ {n} \left| h _ {n , m} \right| ^ {2}}{W N _ {0}}, \tag {2}
$$
where $p _ { n }$ is the transmit power of the $n$ -th user, $g _ { n }$ is the plarge-scale channel gain of the $n$ g-th user including path loss and shadowing, $h _ { n , m } \sim \mathcal { C N } ( 0 , 1 )$ is the Rayleigh fading coefficient for the $n$ h-th user transmitting over the $m$ -th channel, and $N _ { 0 }$ is the noise power spectral density.
# C. DeepSC Receiver
At the BS, the signal from the $n$ -th user can be denoted as ${ \bf Y } _ { n } = \sqrt { g _ { n } } h _ { n , m } { \bf X } _ { n } + { \bf z }$ where z is additive white Gaussian g hnoise (AWGN) and each element of $\mathbf { z }$ follows $\mathscr { C N } ( 0 , N _ { 0 } )$ . The Nreceived signal will be decoded first by the channel decoder and thereby the semantic decoder to estimate sentence $\hat { \mathbf { s } } _ { n }$ .
In order to evaluate the performance of semantic communications for text transmission, we adopt the semantic similarity [3] as the performance metric,
$$
\xi = \frac {\mathbf {B} (s) \mathbf {B} (\hat {s}) ^ {\mathrm {T}}}{\| \mathbf {B} (s) \| \| \mathbf {B} (\hat {s}) \|}, \tag {3}
$$
where B(·) denotes Sentence-Bidirectional Encoder Representations from Transformers (BERT) model. It achieves great improvement over state-of-the-art sentence embedding methods. A pre-trained Sentence-BERT model [14] is adopted. Compared with other semantic metrics, such as bilingual evaluation understudy (BLEU) [15], BERT-level similarity measures the distance of semantic information between two sentences more precisely. From (3), we have $0 \leq \xi \leq 1$ where $\xi = 1$ means that two sentences has the highest similarity and $\xi = 0$ indicates no similarity between them.
# III. SEMANTIC-AWARE RESOURCE ALLOCATION
In this section, the S-SE is first defined as a new metric for semantic-aware networks. Then the semantic-aware resource allocation is formulated as a S-SE maximization problem in terms of channel assignment and the number of transmitted semantic symbols. Finally, the optimal solution of the optimization problem is obtained.
# A. Semantic Spectral Efficiency
In conventional communications, spectral efficiency is measured in bits per second per Hertz $( b i t s / s / H z )$ , which can effectively measure the transmission rate of bit sequences but cannot be used to measure the transmission rate of semantic information. This is because the bit sequences are produced based on the statistical knowledge of the source and are irrelevant to the meaning of the source. Thus new performance metrics need to be investigated at the semantic level.
For the sake of clarity, we assume that semantic information can be measured by the semantic unit (sut), which represents the basic unit of semantic information.1 Based on this, two crucial semantic-based performance metrics can be defined:
Semantic transmission rate (S-R) refers to the effectively transmitted semantic information per second and is measured in suts/s.
1The semantic unit here is just a concept and will not affect the resource optimization solution, the reason of which will be clarified in Section III-C.
• Semantic spectral efficiency (S-SE) refers to the rate at which semantic information can be successfully transmitted over a unit of bandwidth, and is measured in suts/s/Hz.
Then the expressions of S-R and S-SE are derived respectively in the following. Denote $\begin{array} { r l r } { { \mathcal { D } } } & { { } = } & { \{ ( { \bf s } _ { j } } \quad = \end{array}$ $[ w _ { j , 1 } , w _ { j , 2 } , \ldots , w _ { j , l } , \ldots , w _ { j , L _ { j } } ] ) \} _ { j = 1 } ^ { D }$ with size $D$ as the text w wdataset, where ${ \bf s } _ { j }$ is the $j$ w -th sentence with length $L _ { j }$ and $w _ { j , l }$ is the $l .$ L w-th word. Let the amount of semantic information of ${ \bf s } _ { j }$ be $I _ { j }$ . With $p ( \mathbf { s } _ { j } )$ representing the occurrence probability of ${ \bf s } _ { j }$ p, the expected amount of semantic information per sentence can be expressed as $\begin{array} { r } { I = \sum _ { j = 1 } ^ { D } I _ { j } p ( \mathbf { s } _ { j } ) } \end{array}$ , which cor-I I presponds to an expected number of words per sentence as $\begin{array} { r } { L = \sum _ { j = 1 } ^ { D } L _ { j } p ( \mathbf { s } _ { j } ) } \end{array}$ . Note that we focus on the long-term text L L ptransmission rather than the transmission of individual sentences, so the expected values $I$ and $L$ , instead of the random values, should be taken to obtain the representations of S-R and S-SE. Hence, at the $n$ -th user, there are $k _ { n } L$ semantic symk Lbols on average carrying the amount of semantic information of $I .$ , and the average amount of semantic information per semantic symbol is $\bar { I } / ( k _ { n } L )$ . Moreover, since the symbol rate I k Lis equal to the channel bandwidth for passband transmission, the total semantic information transmitted over the channel with bandwidth $W$ is $W I / ( k _ { n } L )$ . Thus the S-R of the $n$ -th user over the $m$ WI k L-th channel can be expressed as
$$
\Gamma_ {n, m} = \frac {W I}{k _ {n} L} \xi_ {\mathrm {n}, \mathrm {m}}, \tag {4}
$$
where $\xi _ { n , m }$ is the semantic similarity of the $n$ -th user over the $m$ -th channel. Note that $\xi _ { n , m }$ relies on the neural network structure of DeepSC and channel conditions. It can be expressed as a function of $k _ { n }$ and $\gamma _ { n , m }$ , i.e., $\xi _ { n , m } = f ( k _ { n } , \mathbf { \bar { \gamma } } _ { n , m } )$ k. From (4), the corresponding S-SE can f kbe expressed as
$$
\Phi_ {n, m} = \frac {\Gamma_ {n , m}}{W} = \frac {I}{k _ {n} L} \xi_ {\mathrm {n}, \mathrm {m}}. \tag {5}
$$
# B. Problem Formulation
In this part, a semantic-aware resource allocation model is proposed to maximize the overall S-SE of all users. By denoting $\Phi$ as the overall S-SE of all users, we have
$$
\Phi = \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \alpha_ {n, m} \frac {\xi_ {n , m} I}{k _ {n} L}. \tag {6}
$$
The channel assignment vector is considered as one of the optimization variables to fully exploit the performance advantage of DeepSC in the low SNR regime. Furthermore, we also optimize the average number of the transmitted semantic symbols for each word, $k _ { n }$ , to enable each symbol to carry kmore semantic information and thus achieve higher S-SE while ensuring the same transmission reliability.
According to the above analysis, the optimization problem can be formulated as
$$
\left(\mathbf {P 0}\right) \max _ {\boldsymbol {\alpha} _ {n}, k _ {n}} \Phi \tag {7}
$$
$$
s. t. \quad C _ {1}: \alpha_ {n, m} \in \{0, 1 \}, \forall n \in \mathcal {N}, \forall m \in \mathcal {M}, \tag {7a}
$$
$$
\mathrm {C} _ {2}: \sum_ {n = 1} ^ {N} \alpha_ {n, m} \leq 1, \forall m \in \mathcal {M}, \tag {7b}
$$
![](https://r2.118229.xyz/2026/04/17/resource-allocation-for-text-semantic-communicat/ce01b773d3b34678c8a12b896d8b0bcffcb7ea494c2bf19ff76b4e283cbfeaef-cdbc39257c44.jpg)
Fig. 2. The semantic similarity for DeepSC.
$$
\mathrm {C} _ {3}: \sum_ {m = 1} ^ {M} \alpha_ {n, m} \leq 1, \forall n \in \mathcal {N}, \tag {7c}
$$
$$
\mathrm {C} _ {4}: k _ {n} \in \{1, 2, \dots , K \}, \tag {7d}
$$
$$
\mathrm {C} _ {5}: \xi_ {n, m} \geq \xi_ {\text {t h}}, \tag {7e}
$$
$$
\mathrm {C} _ {6}: \Phi_ {n, m} \geq \Phi_ {\mathrm {t h}}, \tag {7f}
$$
where $\mathrm { C _ { 1 } }$ , $\mathrm { C _ { 2 } }$ , and $\mathrm { C _ { 3 } }$ are channel assignment constraints, $\mathrm { C _ { 4 } }$ specifies the permitted range of the average number of semantic symbols per word with $K$ representing the maximum value, $\mathrm { C } _ { 5 }$ reflects the minimum required semantic similarity $\xi _ { \mathrm { t h } }$ , and $\mathrm { C _ { 6 } }$ restricts the minimum S-SE of users by $\Phi _ { \mathrm { t h } }$ .
# C. The Optimal Solution
To solve $\mathbf { \Pi } ( \mathbf { P 0 } )$ , two challenges should be addressed. One is how to deal with the term $I / L$ in the objective function, and the other is how to cope with $\xi _ { n , m }$ , which is closely related to $\Phi$ , $\mathrm { C } _ { 5 }$ , and $\mathrm { C _ { 6 } }$ .
First, we note that the term $I / L$ depends on the type of source. According to the analysis in Section III-A, this term is a constant for a particular type of source, which will not affect the resource optimization. Consequently, we can omit this term when solving $( \mathbf { P 0 } )$ . Thus the optimization problem $( \mathbf { P 0 } )$ can be rewritten as
$$
\begin{array}{l} (\mathbf {P 1}) \max _ {\boldsymbol {\alpha} _ {n}, k _ {n}} \widetilde {\Phi} = \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \alpha_ {n, m} \frac {\xi_ {n , m}}{k _ {n}} \\ s. t. \quad C _ {1}, C _ {2}, C _ {3}, C _ {4}, C _ {5}, C _ {6}, \tag {8} \\ \end{array}
$$
Then, since $\xi _ { n , m }$ is dependent of the specific semantic communication system and physical channel conditions, we run the DeepSC model over AWGN channel to obtain the mapping between $\xi _ { n , m }$ and $\left( k _ { n } , \gamma _ { n , m } \right)$ , as shown in Fig. 2.
kAfter addressing the two challenges, $( \mathbf { P 0 } )$ can be solved. Specifically, due to the orthogonality of different cellular links, (P1) can be decoupled into the following two equivalent independent optimization problems:
$$
\begin{array}{l} (\mathbf {P 2}) \max _ {k _ {n}} \widetilde {\Phi} _ {n, m} \\ \text {s . t .} \quad \mathrm {C} _ {4}, \mathrm {C} _ {5}, \mathrm {C} _ {6}, \tag {9} \\ \end{array}
$$
and
$$
\begin{array}{l} \left(\mathbf {P 3}\right) \max _ {\boldsymbol {\alpha} _ {n}} \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \alpha_ {n, m} \widetilde {\Phi} _ {n, m} ^ {\max } \\ s. t. \quad C _ {1}, C _ {2}, C _ {3}, \tag {10} \\ \end{array}
$$
where $\widetilde { \Phi } _ { n , m } = \xi _ { n , m } / k _ { n }$ and $\widetilde { \Phi } _ { n , m } ^ { \mathrm { m a x } }$ represents the maximum $\widetilde { \Phi } _ { n , m }$ kwith respect to $k _ { n }$ . (P2) targets on obtaining $\widetilde { \Phi } _ { n , m }$
for all users over all candidate channels. Since $\xi _ { n , m }$ in $\mathrm { C } _ { 5 }$ and $\mathrm { C _ { 6 } }$ can only be obtained by the look-up table method, the exhausted searching method is adopted to solve $( \mathbf { P } 2 )$ . Moreover, (P3) can be regarded as a maximum match problem of a bipartite graph. It can be solved by the Hungarian algorithm [16], where two vertex sets are $\mathcal { N }$ and $\mathcal { M }$ respectively, and $\widetilde { \Phi } _ { n , m } ^ { \mathrm { m a x } }$ is regarded as the weight between the $n$ -th user and $m$
# IV. SIMULATION RESULTS AND COMPARISON
In order to evaluate the performance of the proposed semantic-aware resource allocation scheme comprehensively, we conduct the following verifications in the simulation:
1) Comparing the proposed resource allocation model against the conventional one to verify the proposed model in semantic-aware networks.
2) Comparing the S-SE of semantic and conventional communication systems to show the superiority of semantic communications.
Since the conventional systems are usually assessed in the bit domain, we first develop a transform method to convert the typical SE to the S-SE by taking the effect of source coding into consideration, making fair comparisons possible. On this basis, simulation results are presented and analysed.
# A. The Transform Method for Fair Comparisons
In conventional communications, each letter in a word is mapped into bits through source encoder. From the semantic perspective, each bit can be loosely regarded as a semantic symbol although it may carry less semantic information than the semantic symbol of DeepSC. Similar to the definition in Section III-A, the equivalent S-R can be expressed as
$$
\Gamma_ {n, m} ^ {\prime} = C _ {n, m} \frac {I}{\mu L} \xi_ {n, m}, \tag {11}
$$
where $C _ { n , m }$ is the transmission rate of the $n$ -th user over the $m$ C-th channel, measured in bits/s, and $\mu$ is defined as the transforming factor revealing the ability of the source coding scheme in compressing data, representing the average number of bits per word, measured in bits/word. Specifically, if a word includes five letters on average and ASCII code is adopted to encode each letter, we will have $\mu = 4 0$ bits/word. Moreover, when we assume no bit error in conventional communications, $\xi _ { n , m }$ is equal to 1. By denoting $R _ { n , m } = C _ { n , m } / W$ as the SE, Rthe equivalent S-SE can be given by
$$
\Phi_ {n, m} ^ {\prime} = R _ {n, m} \frac {I}{\mu L}. \tag {12}
$$
Hence, the source coding process and bit transmission process are both considered to derive the S-SE of the conventional systems so that fair comparisons between different communication systems can be performed.
# B. Benchmarks
Considering the proposed resource allocation scheme is for a specific semantic system, i.e., DeepSC, we compare it with the following three benchmarks, including an ideal system and two practical ones that have been widely deployed:
Ideal system: Shannon limit can be achieved with no bit errors, i.e., $R _ { n , m } = \log _ { 2 } ( 1 + \gamma _ { n , m } )$ .
R 4G system: According to the measured SNR, the BS obtains the channel quality indicator (CQI) [17], based on which the achievable SE $R _ { n , m }$ can be obtained according Rto Table 7.2.3-1 in 3GPP TS 36.213.
![](https://r2.118229.xyz/2026/04/17/resource-allocation-for-text-semantic-communicat/3204db8177d30d70838729ef95d84db1c8e7c75a18367c0cd6c13425c016690f-59b349ccbb55.jpg)
Fig. 3. The S-SE of the semantic-aware network with different models.
TABLE I SIMULATION PARAMETERS
<table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Number of users, N</td><td>5</td></tr><tr><td>Number of channels, M</td><td>5</td></tr><tr><td>Channel bandwidth, W</td><td>180 KHz</td></tr><tr><td>Noise power spectral density, N0</td><td>-174 dBm/Hz</td></tr><tr><td>Pathloss model</td><td>128.1+37.6lg[d(km)] dB</td></tr><tr><td>Shadow effect factor</td><td>6 dB</td></tr><tr><td>Transmit power, pn</td><td>10 dBm</td></tr><tr><td>Maximum number of symbols per word, K</td><td>20 symbols/word</td></tr><tr><td>Semantic similarity threshold, ξth</td><td>0.9</td></tr><tr><td>S-SE threshold, Φth</td><td>0.025(I/L) sut/s/Hz</td></tr><tr><td>Transforming factor, μ</td><td>40 bits/word</td></tr></table>
5G system: Similar to 4G, the BS gets CQI based on the measured SNR [18], and then obtains the achievable SE $R _ { n , m }$ according to Table 5.2.2.1-2 in 3GPP TS 38.214.
RNote that no scheme could achieve a higher bit transmission rate than the ideal system, but we focus on the S-SE to evaluate the performance in this letter. By adopting the developed transform method, the S-SE optimization problem of the above three benchmarks can be formulated as
$$
(\mathbf {P 4}) \max _ {\boldsymbol {\alpha} _ {n}} \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \alpha_ {n, m} \Phi_ {n, m} ^ {\prime \Delta} \tag {13}
$$
s.t. $\mathrm { C _ { 1 } , C _ { 2 } , C _ { 3 } }$
$$
\mathrm {C} _ {7}: \Phi_ {n, m} ^ {\prime \Delta} \geq \Phi_ {\mathrm {t h}}, \tag {13a}
$$
where Φ-Δ $\Phi _ { n , m } ^ { \prime \Delta }$ is the S-SE of the $n$ -th user over the $m$ -th channel in system $\Delta$ , $\Delta \in \{ \mathrm { I d e a l } , 4 \mathrm { G } , 5 \mathrm { G } \}$ . (P4) can be solved by the method introduced in Section III-C.
# C. Simulation Results
In our simulation, a circular network with radius $r = 5 0 0 \mathrm { m }$ is considered where $N$ users are distributed uniformly. Unless specifically stated, the relevant parameters are listed in Table I.
We first examine the conventional resource allocation model in semantic-aware networks. In this simulation, the optimal channel assignment results of the conventional model in the ideal system is applied in the network, along with different values of $k _ { n }$ . Then the obtained S-SE is compared with that kof the proposed model. As shown in Fig. 3, the S-SE of the conventional model is smaller than that of the proposed model regardless of the value of $k _ { n }$ , which implies that the convenktional model is not suitable in semantic-aware networks. In addition, the S-SE of the conventional model with $k _ { n } ~ = ~ 3$ kis equal to 0 because the semantic similarity is less than the threshold in this case.
![](https://r2.118229.xyz/2026/04/17/resource-allocation-for-text-semantic-communicat/41c75c9a006cf5b6783405d99e1ae502a1dc6fe575f2cb897a4cf0e2aa02e733-aaad2ea28564.jpg)
(a) The S-SE versus the number of channels.
![](https://r2.118229.xyz/2026/04/17/resource-allocation-for-text-semantic-communicat/f1b5b1f978f2709f0479997e60f7010cca642327488a4d2eff6db3d5f68c4297-9e4953f5ac0d.jpg)
(b) The S-SE versus the transmit power.
![](https://r2.118229.xyz/2026/04/17/resource-allocation-for-text-semantic-communicat/419aa724b6768f034af9072caa4d8784e5d68a50c7aa83472f6c702d34d92df9-c3f8db5a983d.jpg)
(c) The S-SE versus the transforming factor.
In the following, we compare the different communication systems with the corresponding resource allocation model. Fig. 4(a) shows the S-SE of different systems versus the number of channels. When M is increased from 1 to 5, the S-SE of all systems increases rapidly because more users are served. Then when M keeps on increasing from 5 to 10, the S-SE grows slowly instead of remaining stable because more channels are available and users can choose the channel with higher SNR. Moreover, the semantic communication system outperforms all conventional communication systems.
Fig. 4(b) illustrates the S-SE versus the transmit power. As $p _ { n }$ increases, the S-SE of the ideal system increases rapidly pwhile that of the semantic communication system, 4G system, and 5G system increase first and then tend to be a constant, implying that all practical systems have an upper bound with increasing SNR. Moreover, the semantic communication system shows a larger upper bound than 4G and 5G due to its stronger ability in compressing data.
Fig. 4(c) shows the S-SE versus the transforming factor. The performance of the semantic communication system remains stable since the transforming factor is irrelevant to it. For the conventional systems, the S-SE decreases with increasing $\mu$ because the S-SE is the ratio of the SE to $\mu$ , and the maximum SE is a fixed value with different $\mu$ . Additionally, the semantic communication system yields better performance than both 4G and 5G when $\mu$ is larger than 19 bits/word. Nevertheless, when $\mu$ is smaller than approximately 27 bits/word, i.e., a word can be encoded to less than 27 bits, the semantic communication system performs worse than the ideal system. This figure demonstrates that whether semantic communication systems outperforms conventional ones to a great extent depends on the source coding scheme adopted in conventional systems.
# V. CONCLUSION
In this letter, we have studied the SE issue in the semantic domain and explored the resource allocation for semantic communications. Specifically, S-R and S-SE have been defined first to make it possible to measure the communication efficiency of the semantic communication system based on the DeepSC model. Aiming at maximizing the overall S-SE of all users, the semantic-aware resource allocation has been formulated as an optimization problem and the optimal solution has been obtained. Extensive simulation has been conducted to evaluate the performance of the proposed scheme. An insightful conclusion is that, for text transmission, semantic communication systems achieve a higher S-SE than both 4G and 5G systems when a word is mapped to more than 19 bits on average through conventional source coding techniques. Further, if
the required bits for encoding a word is increased to more than 27 bits with 10 dBm transmit power, semantic communication systems even outperforms the ideal system. In the future, how to design resource allocation method to satisfy the requirements of multiple intelligence tasks including single modal and multimodal tasks should be further investigated.
# REFERENCES
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[3] H. Xie, Z. Qin, G. Y. Li, and B.-H. Juang, “Deep learning enabled semantic communication systems,” IEEE Trans. Signal Process., vol. 69, no. 1, pp. 2663–2675, Apr. 2021.
[4] M. Sana and E. C. Strinati, “Learning semantics: An opportunity for effective 6G communications,” in Proc. IEEE 19th Annu. Consum. Commun. Netw. Conf. (CCNC), Las Vegas, NV, USA, Jan. 2022, pp. 631–636.
[5] C.-H. Lee, J.-W. Lin, P.-H. Chen, and Y.-C. Chang, “Deep learningconstructed joint transmission-recognition for Internet of Things,” IEEE Access, vol. 7, pp. 76547–76561, 2019.
[6] E. Bourtsoulatze, D. B. Kurka, and D. Gündüz, “Deep joint sourcechannel coding for wireless image transmission,” IEEE Trans. Cogn. Commun. Netw., vol. 5, no. 3, pp. 567–579, Sep. 2019.
[7] Z. Weng and Z. Qin, “Semantic communication systems for speech transmission,” IEEE J. Sel. Areas Commun., vol. 39, no. 8, pp. 2434–2444, Aug. 2021.
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[9] M. Kountouris and N. Pappas, “Semantics-empowered communication for networked intelligent systems,” IEEE Commun. Mag., vol. 59, no. 6, pp. 96–102, Jun. 2021.
[10] R. Carnap and Y. Bar-Hillel, “An outline of a theory of semantic information,” Res. Lab. Electron., Massachusetts Inst. Technol., Cambridge, MA, USA, RLE Rep. 247, Oct. 1952.
[11] J. Bao et al., “Towards a theory of semantic communication,” in Proc. IEEE Netw. Sci. Workshop, West Point, NY, USA, Jun. 2011, pp. 110– 117.
[12] F. M. J. Willems and T. Kalker, “Semantic compaction, transmission, and compression codes,” in Proc. Int. Symp. Inf. Theory (ISIT), Adelaide, SA, Australia, Sep. 2005, pp. 214–218.
[13] H. Xie, Z. Qin, and G. Y. Li, “Task-oriented multi-user semantic communications for VQA,” IEEE Wireless Commun. Lett., vol. 11, no. 3, pp. 553–557, Mar. 2022.
[14] N. Reimers and I. Gurevych, “Sentence-BERT: Sentence embeddings using siamese bert-networks,” in Proc. Empr. Methods Nat. Lang. Process. (EMNLP), Nov. 2019, pp. 3982–3992.
[15] K. Papineni, S. Roukos, T. Ward, and W.-J. Zhu, “BLEU: A method for automatic evaluation of machine translation,” in Proc. Annu. Meeting Assoc. Comput. Linguist. (ACL), Philadelphia, PA, USA, Jul. 2002, pp. 311–318.
[16] H. W. Kuhn, “The Hungarian method for the assignment problem,” Naval Res. Logist. Quart., vol. 2, pp. 83–97, Mar. 1955.
[17] A. Ghosh and R. Ratasuk, Essentials of LTE and LTE-A. Cambridge, U.K.: Cambridge Univ. Press, 2011.
[18] E. Chu, J. Yoon, and B. C. Jung, “A novel link-to-system mapping technique based on machine learning for 5G/IoT wireless networks,” Sensors, vol. 19, no. 5, p. 1196, Mar. 2019.

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# Semantic Communication-Based Dynamic Resource Allocation in D2D Vehicular Networks
Jiawei Su, Zhixin Liu , Senior Member, IEEE, Yuan-ai Xie , Kai Ma , Member, IEEE, Hongyang Du , Student Member, IEEE, Jiawen Kang , Member, IEEE, and Dusit Niyato , Fellow, IEEE
Abstract—The semantic communication mechanism enables wireless devices in vehicular networks to communicate more effectively with the semantic meaning. However, in high-dynamic vehicular networks, the transmission of semantic information faces challenges in terms of reliability and stability. To address these challenges, a long-term robust resource allocation scheme is proposed under the Device-to-Device (D2D) vehicular (D2D-V) networks, where multiple performance indicators (user satisfaction, queue stability, and communication delay) are considered. Due to the sophisticated probabilistic form with consideration of channel fluctuations, the Bernstein approximation is introduced to acquire the deterministic constraint more efficiently. The robust resource allocation problem is proposed and separated into two independent subproblems by the Lyapunov optimization method, which includes semantic access control in the application layer and power control in the physical layer. After that, the successive convex approximation method and Karush-Kuhn-Tucher conditions are adopted to solve the subproblems, thereby proposing a robust resource allocation algorithm. The simulations reveal the trade-off relationship between user satisfaction, queue stability, and communication delay, which is on the premise of meeting the user SINR requirement. Moreover, the simulations also prove the necessity of considering channel uncertainty in high-speed mobile vehicular communication scenarios.
Index Terms—D2D technology, Lyapunov optimization, resource allocation, semantic communication, vehicular networks.
Manuscript received 6 May 2022; revised 29 July 2022 and 19 December 2022; accepted 10 March 2023. Date of publication 16 March 2023; date of current version 15 August 2023. This work was supported in part by the National Natural Science Foundation of China under Grants 62273298 and 61873223, in part by the Graduate Innovation Foundation Projects of Hebei Province under Grant CXZZBS2023055, in part by the National Research Foundation Singapore and Infocomm Media Development Authority through the Future Communications Research Development Programme (FCP) under Grant FCP-NTU-RG-2022-010, and in part by DSO National Laboratories through the AI Singapore Programme AISG under Grant AISG2-RP-2020-019 through Energy Research Test-Bed and Industry Partnership Funding Initiative part of the Energy Grid (EG) 2.0 Programme. The review of this article was coordinated by Dr. Haijun Zhang. (Corresponding author: Zhixin Liu.)
Jiawei Su, Zhixin Liu, and Kai Ma are with the School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China (e-mail: Sjw@stumail.ysu.edu.cn; lzxauto@ysu.edu.cn; kma@ysu.edu.cn).
Yuan-ai Xie is with the School of computer and science, South-Central Minzu University, Wuhan 430079, China (e-mail: xieyuan_ai@163.com).
Hongyang Du is with the School of Computer Science and Engineering, Energy Research Institute at NTU, Interdisciplinary Graduate Program, Nanyang Technological University, Singapore 639798 (e-mail: hongyang001@e.ntu.edu.sg).
Jiawen Kang is with the School of Automation, Guangdong University of Technology, Guangzhou 510006, China (e-mail: kavinkang@gdut.edu.cn).
Dusit Niyato is with the School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798 (e-mail: dniyato@ntu.edu.sg).
Digital Object Identifier 10.1109/TVT.2023.3257770
# I. INTRODUCTION
T O IMPROVE traffic efficiency and driving experience forvehicle users, autonomous driving technology has been vehicle users, autonomous driving technology has been widely studied [1]. In autonomous driving systems, efficient decisions of vehicles mainly depend on the data collected from their surroundings (mainly by taking traffic pictures by cameras) and the information interaction with adjacent vehicles/roadside infrastructures (wireless communications). Compared with the perception of surroundings, information interaction based on the internet of vehicle (IoV) is particularly critical [2]. However, efficient and reliable vehicular communications face two major technical challenges [3].
On the one hand, due to the large amount of data collected by vehicles, the transmission of original data will require large bandwidth and cause severe communication overhead, which is not realistic for current IoV with scarce spectrum resources. A novel communication mode, semantic communication mechanism, has been widely studied [4]. With the improvement of intelligence and informatization, vehicles have the ability to terminal information calculation. The improvement of terminal ability provides support for semantic communication which extracts the core semantic data and only transmits the meanings [5]. On the other hand, to facilitate the direct information interaction between adjacent vehicles, device-to-device (D2D) technology is widely used in vehicular networks and facilitates a D2D vehicular (D2D-V) system [6]. However, due to the frequent topology changes caused by the high mobility of vehicles, the vehicle-to-everything link is easy to be interrupted. Therefore, the guarantee of Signal to Interference plus Noise Ratio (SINR) is the key point in a dynamic environment [7]. Recent studies demonstrated that the semantic communication mechanism is more robust in a low SINR environment [8], which increases the communication qualities of wireless devices. Based on the extracted semantic data, D2D communications aim to maximize the transmission efficiency and minimize the semantic errors by transmitting the meaning of data, rather than traditional bit errors.
Nevertheless, since the semantic data cannot be transmitted by D2D users instantaneously, it has to be temporarily cached in the buffer of the application layer. Therefore, cross-layer resource allocation which joints the application layer and physical layer is widely used to control queue stability and improve system robustness, especially in dynamic communication environments. Thus, a cross-layer robust resource allocation framework based
on the D2D-V networks is a promising solution for efficient and reliable vehicular communications.
# II. RELATED WORKS
According to Shannon’s theorem, there is a limit value of transmission rate in theory, which represents the maximum communication capacity of the channel. As Shannon argued, converting a continuous source data requires a channel with infinite capacity, and the solution is to discretize the signal within a certain tolerance of information loss [10]. In other words, traditional communication model based on Shannon’s theory has limited efficiency. Semantic communication, as a novel communication mode, has been widely studied in recent years, which extracts the semantic data and only transmits the core meanings. Instead of discretizing the continuous source signal with a certain loss tolerance, semantic communication allows transmitting the meaning of the signal, which has the potential to significantly improve transmission efficiency (lower channel resource and lossless signal delivery) [11]. Furthermore, the semantic error can be greatly reduced by transmitting the core meaning of data, which is under the help of a semantic knowledge library to encode and decode respectively [12]. However, the existing semantic communication research does not well consider the process of end-to-end data exchange, and the ultra-reliable and low-latency semantic transmission that meets various user qualities of service (QoS) has not been paid enough attention [13].
Therefore, this paper considers a joint scenario of semantic communications and D2D technology and studies the communication quality of signal links on the basis of extracted semantic data. The combination of semantic communications and D2D technology is full of advantages, i.e., reducing communication load, realizing end-to-end direct transmission, reducing transmission errors, and so on. To improve the network stability, the traditional solutions mainly focus on the power control in the physical layer [14]. However, the semantic data cannot be transmitted by D2D users instantaneously, it has to be temporarily cached in the buffer of the application layer, ignoring the access rate of semantic data in the application layer will lead to an imbalance data queue, thereby producing uncontrollable network delays. Therefore, a long-term dynamic cross-layer resource allocation framework is highlighted and constructed to guarantee the requirements of QoS and the queue stability in [9]. Lyapunov optimization method is adopted in this paper, which firstly transforms the long-term constraints into queue stability conditions and then transforms the long-term objective functions and the queue stability conditions into solvable shortterm subproblems [15].
Although the Lyapunov optimization method has greater advantages in long-term performance indexes, it cannot well depress the problems of co-channel interference. As is stated in [16], the coexistence of D2D underlay communications and cellular communication causes serious co-channel interference, and an effective interference management is crucial. What makes the problem more complex, more and more articles confirm that the channel uncertainty cannot be ignored, especially in
the high-speed mobile vehicular communication scenarios [17], [18]. In this paper, the Gauss-Markov process is proposed to statistically simulate the imperfect channel state information (CSI) [19], where the mobile characteristic of vehicles is highly considered. Furthermore, the chance constraint is used to describe the interference constraint in [20], which is in a probability form with uncertain parameters. To get the closed expression of the interference constraint, the authors proposed the Bernstein approximation method [21].
Motivated by combining the strengths of semantic communications and D2D technology, this paper proposes a long-term robust resource allocation scheme, which joints access control of the application layer and robust power control of the physical layer. This work is committed to realizing more efficient semantic information transmission.
# A. Contributions
The main contributions of this work are shown as follows:
- The combination of semantic communication and a novel long-term resource allocation scheme is proposed in this paper to realize effective link transmission, which greatly improves transmission efficiency and resource utilization. The proposed scheme achieves the compromise of user satisfaction, queue stability, and communication delay on the premise of meeting user SINR requirements.
- Lyapunov optimization method is leveraged to transform dynamic cross-layer resource allocation problem into a semantic access control subproblem and a power control subproblem. Karush-Kuhn-Tucher (KKT) conditions and Lagrangian function method are used to deal with the subproblems, respectively. Particularly, the Bernstein approximation method is adopted to convert the non-convex power control subproblem into a solvable convex one.
- The mobility characteristics of vehicles are considered, and an accurate uncertain channel state description is constructed by introducing the first-order Markov process. A robust resource allocation algorithm is proposed to realize efficient and reliable semantic signal transmission.
The rest of this paper is organized as follows: In Section III, the system model and a robust resource allocation framework are established. In Section IV, the resource allocation problem transformation based on the Lyapunov optimization method is proposed. We propose a robust resource allocation algorithm in Section V. Numerical simulation results and conclusion are shown in Section VI and VII, respectively.
Notation: In this paper, vectors are typed by bold letters. Some notations shown in Table I.
# III. PROBLEM FORMULATION
# A. System Models
Based on Open System Interconnection (OSI) model, the cross-layer optimization diagram is shown in Fig. 1, where power control of the physical layer and access control of semantic data of the application layer are performed to realize queue stability. Taking the image information as an example, we apply
TABLE I NOTATIONS
<table><tr><td>K</td><td>Index set of reused channels K = {1, . . ., K}</td></tr><tr><td>M</td><td>User index set in a reused channel M={0, 1, . . ., M}</td></tr><tr><td>T</td><td>Index set of time slots T = {0, 1, . . ., T}</td></tr><tr><td>Pr{·}</td><td>Probability function</td></tr><tr><td>E{·}</td><td>Exponential distribution</td></tr><tr><td>E{·}</td><td>Mathematical expectation</td></tr><tr><td>RM</td><td>Euclidean space</td></tr><tr><td>RM</td><td>Set of M-dimensional real vectors</td></tr><tr><td>Qm(t)</td><td>Data queue of CUE and VUEs</td></tr><tr><td>Zm(t)</td><td>Virtual queue of CUE and VUEs</td></tr><tr><td>G</td><td>Channel gain vector</td></tr><tr><td>D</td><td>Source data vector</td></tr><tr><td>H</td><td>Encoded semantic data vector</td></tr><tr><td>F</td><td>Received semantic data vector</td></tr><tr><td>ˆD</td><td>Decoded semantic data vector</td></tr></table>
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/a33416aa25ad2de30e8e638b741f6591add2473da822ae2b5902d6014829eb14-723d3541af8c.jpg)
Fig. 1. Semantic communication-based cross-layer optimization model.
the end-to-end scene graph generation model with encoderdecoder architecture to process the source image data [22]. In the semantic communication mechanism, the collected source data is represented as $\mathbf { D } = [ d _ { 1 } , d _ { 2 } , \ldots ]$ , they are further encoded by = [ ]semantic encoder and channel encoder. The extracted semantic data is represented by $\mathbf H = e n c _ { c } ( e n c _ { s } ( \mathbf D ) )$ , where $e n c _ { c } ( \cdot )$ and $e n c _ { s } ( \cdot )$ = ( ( )) ( )are the channel encoder and the semantic encoder, re-( )spectively. At the end of receiving devices, the received signal is represented as $\mathbf { F } = \mathbf { G } \mathbf { H } + \sigma ^ { 2 }$ , where $\sigma ^ { 2 }$ is the background noise = +and G is the channel gain vector. Furthermore, The decoded semantic data is obtained by $\hat { \bf D } = d e c _ { s } ( d e c _ { c } ( { \bf F } ) )$ , where $d e c _ { c } ( \cdot )$ is the channel decoder, and $d e c _ { s } ( \cdot )$ ( ( ))is the semantic decoder.
( )The extraction process of traffic semantic data is shown in Fig. 2. The D2D-V transmitter uses a semantic encoder to extract the semantic features from the real-time traffic images taken by vehicular cameras. These extracted key features are stored in a form of text and are cached in the buffer of the application layer. Based on these key features, vehicles can make rapid and efficient decisions. Meanwhile, the continuously generated semantic information can also be used to monitor real-time dynamic traffic environments and achieve safe and efficient autonomous driving. Furthermore, the semantic transmission process based on D2D communication technology is studied.
The stability of the data queue is ensured by controlling the access rate and transmission rate. Thus, the multiple performance indexes are optimized.
Fig. 3 is the D2D-V communication model in the physical layer. Based on effective encoding and decoding technology, this paper focuses on the link transmission process. As shown in Fig. 3, a macrocell and numerous D2D-V pairs are included in the D2D-V networks, a vehicle transmitter (VT) and a vehicle receiver (VR) constitute a D2D-V pair. Each VT and VR is equipped with a semantic encoder and a semantic decoder, respectively. Multiple D2D-V pairs communicate directly by reusing the uplink allocated to CUE without passing through the base station (BS). When the distance between two neighbor vehicles exceeds the applicable distance of D2D communications, the D2D pairs are spontaneously formed. Cowan’s M3 model can well describe the traffic pattern [23]. Cowan’s M3 model stated that the distances between adjacent D2D pairs follow a truncated exponential distribution.
To improve the spectrum efficiency of semantic data transmission, a reusing mechanism is adopted where the CUE and VUEs are the spectrum owner and sharers, respectively. Fig. 3 also shows five kinds of links in a specific reused channel: CUE-I link between CUE and the BS, D2D-V link, V2I link between VT and the BS, CUE-V link between CUE and VR, V2V interference link between VT and VR. Particularly, the interference link and signal link are distinguished in this figure. The signal links include the CUE-I link and D2D-V link. V2I link, CUE-V link, and V2V interference link are the interference links. As a tricky feature of the vehicular communication scenarios, these links are regarded as Non-Line of Sight (NLoS) transmissions. It is believed that there are always many uncertain environmental factors in the semantic communication process, such as the obstruction of obstacles, the high-speed relative movement of communication terminals, channel estimation error, and so on [24]. In the process of resource allocation, $M + 1$ transmission users are considered (i.e., one CUE and $M$ +VTs), which are connected to the BS and $M$ VRs, respectively. At the tth time slot, $A _ { m } ( t )$ bits of semantic data is required to transformed by user $m$ ( ), where $m \in \mathcal { M }$ , $\mathcal { M } = \{ 0 , 1 , \ldots , M \}$ . The arrival data is first stored in =a buffer of the mth transmission user before being sent out. Let $R _ { m } ( p _ { m } ( t ) )$ denotes the transmission rate at time slot $t$ of the ( ( ))physical layer, the queue $m$ formed and is expressed as $Q _ { m } ( t )$ . In other words, $A _ { m } ( t )$ and $R _ { m } ( p _ { m } ( t ) )$ ( )specify the amount of semantic data that should arrive from the application layer and be sent out in the physical layer, respectively.
# B. Channel Models
The channel gain between the mth transmitter and the nth receiver is formulated as
$$
g _ {m, n} ^ {k} = S _ {m, n} ^ {k} \left(\eta_ {m, n} ^ {k}\right) ^ {2}, \quad m \in \mathcal {M}, n \in \mathcal {M} \tag {1}
$$
where $S _ { m , n } ^ { k }$ and $( \eta _ { m , n } ^ { k } ) ^ { 2 }$ denote the large-scale fading and ( )small-scal fading effects in the channel $k$ , respectively [25], $k \in$ K, ${ \mathcal { K } } = \{ 0 , 1 , \ldots , K \}$ . The large-scale slow fading includes =shadow fading and path loss,
$$
S _ {m, n} ^ {k} = L _ {m, n} ^ {k} \left(d _ {m, n} ^ {k}\right) ^ {- \alpha_ {m}}, \quad m \in \mathcal {M}, n \in \mathcal {M} \tag {2}
$$
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/3af5c46a3e2cb7887ac0bb6f852b020ae4a882eba746721166a003bdd6b89d14-0241be3bed44.jpg)
Fig. 2. Extracted image semantic data.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/ab34b6bc4fdc4acd0060f075ca32b19476118112fd6b0f53d07cea2da688f05c-55e2b5f2e9bb.jpg)
Fig. 3. Physical communication model.
where $L _ { m , n }$ denotes the shadow fading and $d _ { m , n } ^ { - \alpha _ { m } }$ denotes the path loss, $\alpha _ { m }$ is the path-loss exponent and $d _ { m , n }$ is the communication distance.
The IoV is always in a dynamic communication scenario, vehicle movement will lead to the Doppler effect, thereby affecting the channel state. A well-function resource allocation strategy is inseparable from the capture of imperfect CSI. Therefore, the first-order Markov process is adopted to accurately simulate the small-scale fading component $\eta _ { m , n }$ , which is shown as follows [26]:
$$
\eta = \vartheta \hat {\eta} + \epsilon , \tag {3}
$$
where $\eta$ and $\hat { \eta }$ are the channel responses of the current and ˆprevious time slots, respectively. The coefficient $\vartheta$ $\left( 0 < \vartheta < 1 \right)$ ) ( )quantifies the channel correlation between the two consecutive time slots. In the probabilistic statistical model [26], $\epsilon$ is formulated by $\vartheta = J _ { 0 } ( 2 \pi f _ { d } T _ { f } )$ , where $J _ { 0 } ( \cdot )$ is the zero-order Bessel function. $T _ { f }$ ( ) ( )is the feedback time interval of the channel state information. $f _ { d } = v f _ { c } / c$ is the maximum Doppler frequency, where $v$ =is the relative speed between users, $f _ { c }$ denotes the carrier frequency, and $c = 3 \times 1 0 ^ { 8 } ~ \mathrm { m / s }$ .  is the channel discrepancy =term, which is independent to $\hat { \eta }$ and with the distribution of $\mathcal { C N } ( 0 , 1 - \vartheta ^ { 2 } )$ .
( )The small-scale fading in the dynamic channel model is represented as follows,
$$
\left(\eta_ {m, n} ^ {k}\right) ^ {2} = \left(\vartheta_ {m, n} ^ {k} \hat {\eta} _ {m, n} ^ {k}\right) ^ {2} + \left(\epsilon_ {m, n} ^ {k}\right) ^ {2}, \quad m \in \mathcal {M}, n \in \mathcal {M}. \tag {4}
$$
The dynamic channel model is represented as follows,
$$
g _ {m, n} ^ {k} = S _ {i, j} ^ {k} \left(\left(\vartheta_ {m, n} ^ {k} \hat {\eta} _ {m, n} ^ {k}\right) ^ {2} + \left(\epsilon_ {m, n} ^ {k}\right) ^ {2}\right), \quad m \in \mathcal {M}, n \in \mathcal {M}. \tag {5}
$$
Given that $\hat { g } _ { m , n } ^ { k } = S _ { m , n } ^ { k } ( \vartheta _ { m , n } ^ { k } \hat { \eta } _ { m , n } ^ { k } ) ^ { 2 }$ and $\tilde { g } _ { m , n } ^ { k } =$ $S _ { m , n } ^ { k } ( \epsilon _ { m , n } ^ { k } ) ^ { 2 }$ ˆ = (, (5) can be changed to
$$
g _ {m, n} ^ {k} = \hat {g} _ {m, n} ^ {k} + \tilde {g} _ {m, n} ^ {k}, \quad m \in \mathcal {M}, n \in \mathcal {M}, \tag {6}
$$
where gkm,n $\hat { g } _ { m , n } ^ { k }$ denotes the sampling channel gain of the previous slots, $\tilde { g } _ { m , n } ^ { k }$ denotes the error channel gain. $\hat { g } _ { m , n } ^ { k }$ is a constant ˜ that can be measured, and $\begin{array} { r } { \tilde { g } _ { m , n } ^ { k } \sim E \biggl ( \frac { 1 } { S _ { m , n } ^ { k } ( 1 - ( \vartheta _ { m , n } ^ { k } ) ^ { 2 } ) } \biggr ) } \end{array}$ [25].
When $m = n = 0$ , $g _ { m , n } ^ { k }$ denotes the CUE-I link’s channel gain in the $k$ =th channel; When $m = n \neq 0$ , $g _ { m , n } ^ { k }$ denotes the = D2D-V links’ channel gain; When $m \neq n$ , $g _ { m , n } ^ { k }$ denotes the interference links’ channel gain, $g _ { m , 0 } ^ { k } , g _ { 0 , n } ^ { k } , g _ { m , n } ^ { k }$ are the channel gains of V2I link, CUE-V link, V2V interference link in the $k$ th uplink channel, respectively.
# C. Cross-Layer Resource Allocation Problem Formulation
In this subsection, the cross-layer problem includes access control in the application layer and power allocation in the physical layer. Since the semantic data cannot be transmitted to VR instantaneously, the data has to be temporarily stored in the queue of the VT. In the time slot t, $t \in \mathcal T$ , the queue backlogs of the mth VT are represented as
$$
Q _ {m} (t + 1) = \max \left\{Q _ {m} (t) - R _ {m} \left(p _ {m} (t)\right), 0 \right\} + A _ {m} (t), \tag {7}
$$
It is shown that the dynamic data queue is composed of the transmission rate $R _ { m } ( p _ { m } ( t ) )$ and the access extracted semantic rate $A _ { m } ( t )$ ( ( )). The data transmission process is controlled by the ( )power control strategy. The data access process is controlled by the semantic access rate control strategy. There is no data overflow if the transmission rate $R _ { m } ( p _ { m } ( t ) )$ is larger than or equal to the access rate $A _ { m } ( t )$ ( ( ))in the data queue $Q _ { m } ( t )$ .
( ) ( )Definition 1: According to the definition of network stability, the data queue $Q _ { m } ( t )$ is mean rate stable [27] when
$$
\lim _ {T \rightarrow \infty} \frac {\mathbb {E} \left\{\left| Q _ {m} (T) \right|\right\}}{T} = 0. \tag {8}
$$
Channel reusing mechanism is assumed to improve spectrum efficiency in the physical layer. However, the coexistence communications in the same frequency band will cause serious co-channel interference, the interference of the mth signal link
is expressed as
$$
I _ {m} (t) = \sum_ {n = 0, n \neq m} ^ {M} p _ {n} (t) g _ {n, m}, \quad m \in \mathcal {M}, n \in \mathcal {M}, \tag {9}
$$
where $p _ { 0 }$ is the CUE’s transmission power and $I _ { 0 }$ is the interference of CUE-I link. When $n \geq 1 , p _ { n }$ denotes the nth VT’s power. Furthermore, the signal links’ real-time SINR is formulated as
$$
\gamma_ {m} \left(p _ {m} (t)\right) = \frac {p _ {m} (t) g _ {m , m}}{I _ {m} (t) + \sigma^ {2}}, \quad m \in \mathcal {M}, \tag {10}
$$
The deterministic maximum equivalent transmission rate of VUEs calculated by Shannon’s theorem is
$$
R _ {m} = \omega \log_ {2} (1 + \bar {\gamma} _ {m} (p _ {m} (t))), \quad m \in \mathcal {M}. \tag {11}
$$
where γm $\begin{array} { r } { \bar { \gamma } _ { m } = \frac { \mathbb { E } \{ p _ { m } g _ { m , m } \} } { \mathbb { E } \{ \sum _ { n = 0 , n \neq m } ^ { M } p _ { n } g _ { n , m } \} + \sigma ^ { 2 } } = \frac { p _ { m } \bar { g } _ { m , m } } { \sum _ { n = 0 , n \neq m } ^ { M } p _ { n } \bar { g } _ { n , m } + \sigma ^ { 2 } } } \end{array}$ - Mn=0,n=m png¯n,m+σ2
The application-layer satisfaction $U _ { m }$ is positively related to the arrival rate. On the premise of maintaining the stability of the network, the throughput of the network can be expressed by the access rate of semantic date $A _ { m }$ . Therefore, user satisfaction $U _ { m }$ is positively related to the access rate in the application layer, and we defined $U _ { m }$ as a concave function, which is represented as
$$
U _ {m} \left[ A _ {m} (t) \right] = \Omega_ {m} \log_ {2} \left[ A _ {m} (t) \right], \tag {12}
$$
where $\Omega _ { m }$ is a predefined weight parameter of the mth user.
ΩThe transmission delay of the data queue at the mth user is defined as $D _ { m }$ . According to Little Law, the average delay is represented as the quotient between the amount of access data and the transmission rate, which is shown as follows
$$
\bar {D} _ {m} (t) = \frac {\underset {T \rightarrow \infty} {\lim } \frac {1}{T} \sum_ {t = 0} ^ {T - 1} \mathbb {E} \left\{\left| Q _ {m} (t) \right|\right\}}{\underset {T \rightarrow \infty} {\lim } \frac {1}{T} \sum_ {t = 0} ^ {T - 1} \mathbb {E} \left\{\left| R _ {m} \left(p _ {m} (t)\right)\right|\right\}}. \tag {13}
$$
The objective function is to optimize the long-term timeaverage satisfaction of CUE and VUEs. The cross-layer robust resource allocation problem is constructed as
$\mathbf { P 1 } \underset { A _ { m } ( t ) , p _ { m } ( t ) } { \operatorname* { m a x } } \operatorname* { l i m } _ { T \to \infty } \frac { 1 } { T } \sum _ { t = 0 } ^ { T - 1 } \mathbb { E } \left\{ \sum _ { m = 0 } ^ { M } U _ { m } [ A _ { m } ( t ) ] \right\}$ lim
s. $\begin{array} { l } { \displaystyle \operatorname* { P } 1 \operatorname* { m a x } _ { A _ { m } ( t ) , p _ { m } ( t ) } \operatorname* { l i m } _ { T \to \infty } \frac { 1 } { T } \sum _ { t = 0 } ^ { T - 1 } \mathbb { E } \left\{ \sum _ { m = 0 } ^ { M } U _ { m } [ A _ { m } ( t ) ] \right\} } \\ { \displaystyle C 1 : 0 \le p _ { m } ( t ) \le p _ { m , \operatorname* { m a x } } , \quad \forall m , t } \\ { \displaystyle C 2 : 0 \le A _ { m } ( t ) \le A _ { m , \operatorname* { m a x } } , \quad \forall m , t } \\ { \displaystyle C 3 : Q _ { m } ( t ) \mathrm { i s ~ m e a n ~ r a t e ~ s t a b l e } , \quad \forall m , t } \\ { \displaystyle C 4 : \operatorname* { P r } \left\{ \gamma _ { m } ( p _ { m } ( t ) ) \ge \gamma _ { m , \operatorname* { m i n } } \right\} \ge 1 - \varepsilon , \quad \forall m , t } \\ { \displaystyle C 5 : \bar { D } _ { m } ( t ) \le D _ { m , \operatorname* { m a x } } , \quad \forall m , t } \end{array}$ (14)
where $C 1$ is the power constraint, $p _ { m , \mathrm { m a x } }$ is the maximal power. $C 2$ is the constraint of access rate, and $A _ { m , \mathrm { m a x } }$ is the maximum access rate of extracted semantic data. $C 3$ represents the queue stability constraint defined in (8). $C 4$ is the SINR constraint in the physical layer, $\gamma _ { m , \mathrm { { m i n } } }$ is the SINR threshold, $\varepsilon$ denotes the outage probability threshold of SINR constraint, where $\varepsilon \in$ $( 0 , 1 )$ . $C 5$ represents the long-term constraint of the delay, and $D _ { m , \mathrm { m a x } }$ is the delay threshold.
In the traditional static communication networks, we do not advocate expressing probability constraints of the user SINR in a short time slot by adopting a statistical model. However, in high-speed dynamic vehicular networks, the mobility characteristics may cause large distance changes, so it is necessary to constantly update the collected topology changes in the time slots. Since the adopted channel model includes path loss, while the communication distance is updated periodically, the statistical channel model parameters of the corresponding time slot should also be updated. Therefore, it is reasonable and necessary to use the short-term probability constraint $C 4$ to describe the accurate service demands in mobile scenarios.
# IV. PROBLEM TRANSFORMATION BASED ON LYAPUNOV OPTIMIZATION
# A. Problem Transformation
By exploiting the virtual queue concept [28], the long-term delay constraint in problem P1 is converted to queue stability conditions. The virtual queue of the mth transmission user associated with delay constraint $C 5$ is shown as follows
$$
Z _ {m} (t + 1) = \max \left\{Z _ {m} (t) - R _ {m} \left(p _ {m} (t)\right) D _ {m, \max }, 0 \right\} + Q _ {m} (t), \tag {15}
$$
where the queue $Z _ { m } ( t )$ is not a real data queue, and (15) is just ( )an equivalent queue that satisfies the constraint $C 5$ .
Theorem 1: If $Z _ { m } ( t )$ is mean rate stable, $C 5$ holds.
( )Proof: Since the space is limited, the process of the proof is omitted. The meticulous proof is shown in [29].
According to Theorem 1, problem P1 is rewritten as
$$
\mathbf {P 2}: \max _ {A _ {m} (t), p _ {m} (t)} \lim _ {T \rightarrow \infty} \frac {1}{T} \sum_ {t = 0} ^ {T - 1} \mathbb {E} \left\{\sum_ {m = 0} ^ {M} U _ {m} [ A _ {m} (t) ] \right\}
$$
s.t $\cdot \left\{ { \cal C } 1 , { \cal C } 2 , { \cal C } 4 , \right.$ $\left\backslash C 6 : Q _ { m } ( t ) , Z _ { m } ( t ) \right.$ (16)
# B. Lyapunov Optimization
Lyapunov optimization is a powerful method theory to deal with the long-term resource optimization schemes, which need less prior information and owns lower computational complexity [15]. Let $\mathbf { M } ( t ) = [ \mathbf { Q } ( t ) , \mathbf { Z } ( t ) ]$ be the concatenated vector ( ) = [ ( ) ( )]of the data queue and the virtual queue. Then, the Lyapunov function is defined as
$$
L (\mathbf {M} (t)) = \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{Q _ {m} ^ {2} (t) + Z _ {m} ^ {2} (t) \right\}. \tag {17}
$$
The Lyapunov drift function is expressed as
$$
\triangle (\mathbf {M} (t)) = \mathbb {E} \left\{L (\mathbf {M} (t + 1)) - L (\mathbf {M} (t)) | \mathbf {M} (t) \right\}, \tag {18}
$$
According to [30], a smaller drift value would have more conducive to queue stability. We can adjust the final queue length of the Lyapunov function to optimize the optimal value of Lyapunov drift, thereby realizing system stability. To minimize the network delay and maximize user satisfaction, the
drift-minus-reward term is expressed as
$$
\triangle (\mathbf {M} (t)) - V \mathbb {E} \left\{\sum_ {m = 0} ^ {M} U _ {m} [ A _ {m} (t) ] \right\}, \tag {19}
$$
where $V$ is a non-negative control parameter that affects the tradeoff between queue stability and user satisfaction.
Theorem 2: Define $\Delta _ { \mathrm { m a x } }$ as the upper bound of the driftminus-reward, for all $\mathbf { Q } ( t )$ and $V \geq 0$ , the maximum value of ( )the drift-minus-reward term can be obtained by
$$
\begin{array}{l} \Delta_ {\max } = \sum_ {m = 0} ^ {M} \left(\mathbb {E} \left\{Q _ {m} (t) A _ {m} (t) - V U _ {m} [ A _ {m} (t) ] | \mathbf {M} (t) \right\} \right. \\ + Z _ {m} (t) \mathbb {E} \left\{Q _ {m} (t) - R _ {m} (p _ {m} (t)) D _ {m, \max} ^ {Q} | \mathbf {M} (t) \right\} \\ \left. - Q _ {m} (t) \mathbb {E} \left\{R _ {m} \left(p _ {m} (t)\right) | \mathbf {M} (t) \right\} + \Theta\right), \tag {20} \\ \end{array}
$$
where $\Theta$ is a positive constant that satisfies the constraint
$$
\begin{array}{l} \Theta \geq \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{R _ {m} ^ {2} \left(p _ {m} (t)\right) + A _ {m} ^ {2} (t) | \mathbf {M} (t) \right\} \\ + \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{\left(R _ {m} \left(p _ {m} (t)\right) D _ {m, \max } ^ {Q}\right) ^ {2} + Q _ {m} ^ {2} (t) | \mathbf {M} (t) \right\}. \tag {21} \\ \end{array}
$$
Proof: The detailed proof is shown in Appendix A.
# C. Joint Access Control and Power Control Optimization
Based on Lyapunov optimization theory, the rewritten objective function is regarded as the tradeoff between “network stability,” “network delay,” and “user satisfaction,” and the optimization scheme should satisfy the constraints $C 1$ , $C 2$ , and $C 4$ . Therefore, the rewritten problem is
$$
\mathbf {P 3}: \min \Delta_ {\max }
$$
$$
\text {s . t .} \quad C 1, C 2, C 4. \tag {22}
$$
Problem P3 is divided into two independent subproblems, which are the access control subproblem and the power control subproblem.
1) Access Control Subproblem: The access rate control subproblem is expressed as
$$
\mathbf {P 4}: \min _ {A _ {m} (t)} \sum_ {m = 0} ^ {M} Q _ {m} (t) A _ {m} (t) - V U _ {m} [ A _ {m} (t) ]
$$
$$
s. t. \quad C 2: 0 \leq A _ {m} (t) \leq A _ {m, \max }, \forall m, t. \tag {23}
$$
2) Power Control Subproblem: The remaining items in the objective function are
$$
\begin{array}{l} \sum_ {m = 0} ^ {M} Z _ {m} (t) \left(Q _ {m} (t) - R _ {m} (p _ {m} (t))\right) D _ {m, \mathrm {m a x}} ^ {Q} \\ - \sum_ {m = 0} ^ {M} Q _ {m} (t) R _ {m} \left(p _ {m} (t)\right) + \Theta . \tag {24} \\ \end{array}
$$
Since the terms $Z _ { m } ( t ) Q _ { m } ( t )$ and $\Theta$ involve no variables, the ( ) ( ) Θoptimization objective function in the power control subproblem is formulated as
$$
\sum_ {m = 0} ^ {M} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) R _ {m} \left(p _ {m} (t)\right). \tag {25}
$$
Furthermore, the power control subproblem is given as
$$
\begin{array}{l} \mathbf {P} 5: \max _ {p _ {m} (t)} \sum_ {m = 0} ^ {M} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) R _ {m} \left(p _ {m} (t)\right) \\ \text {s . t .} \left\{ \begin{array}{l} C 1: 0 \leq p _ {m} (t) \leq p _ {m, \max }, \quad \forall m, t \\ C 4: \Pr \left\{\gamma_ {m} \left(p _ {m} (t)\right) \geq \gamma_ {m, \min } \right\} \geq 1 - \varepsilon , \quad \forall m, t \end{array} \right. \tag {26} \\ \end{array}
$$
# V. SOLUTIONS TO CROSS-LAYER RESOURCE OPTIMIZATION PROBLEM
# A. Solution to Access Control Subproblem
KKT conditions is adopted to solve the optimization problem P4. The Lagrangian function of problem P4 is,
$$
L _ {m} \left(A _ {m} (t)\right) = Q _ {m} (t) A _ {m} (t) - V U _ {m} \left[ A _ {m} (t) \right] \tag {27}
$$
where $\nu$ is the Lagrangian multiplier and $\nu \geq 0$ .
The first-order derivative of (27) in terms of $A _ { m } ( t )$ is formulated as:
$$
\frac {\partial L _ {m} \left(A _ {m} (t)\right)}{\partial A _ {m} (t)} = Q _ {m} (t) - \frac {V \Omega_ {m}}{A _ {m} (t) \ln 2} = 0. \tag {28}
$$
The optimal arrival rate of semantic data is obtained
$$
A _ {m} ^ {*} (t) = \min \left\{\frac {V \Omega_ {m}}{Q _ {m} (t) \ln 2}, A _ {m, \max } \right\}. \tag {29}
$$
# B. Transformation of Power Control Subproblem
1) Successive Convex Approximation of the Objective Function: In the power control subproblem, the function is
$$
\sum_ {m = 0} ^ {M} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \omega \log_ {2} \left(1 + \bar {\gamma} _ {m} (\mathbf {p} (t))\right). \tag {30}
$$
The method of successive convex approximation is adopted to approximate the objective function by the theory of
$$
\log_ {2} (1 + x) \geq \frac {1}{\ln 2} [ X \ln (x) + Y ], \tag {31}
$$
where $x > 0$ , $X$ and $Y$ are two coefficients that should be definitely settled.
Supposed that the equal form of lower bound approximation is acquired when $x = \bar { \gamma } _ { m } ( { \mathbf { p } } ( t ) )$ ,
$$
\log_ {2} (1 + \bar {\gamma} _ {m} (\mathbf {p} (t))) = \frac {1}{\ln 2} [ X _ {m} \ln (\bar {\gamma} _ {m} (\mathbf {p} (t))) + Y _ {m} ]. \tag {32}
$$
According to the equality condition, (32) can be converted to,
$$
\left(\frac {x}{\bar {\gamma} _ {m} (\mathbf {p} (t))}\right) ^ {X _ {m}} \geq \frac {1 + x}{1 + \bar {\gamma} _ {m} (\mathbf {p} (t))}. \tag {33}
$$
For any $X _ { m }$ which meets (33), to obtain the lower-limit approximation, $X _ { m }$ is a valid coefficient for and less than 1.
If Xm ≥ 1, xγ¯ (p(t)) $X _ { m } \geq 1$ $\big ( \frac { x } { \bar { \gamma } _ { m , } ( { \bf p } ( t ) ) } \big ) ^ { X _ { m } }$ is a concave function, there exists $x > 0$ ( ), which will cause that (33) is not valid. It can be learned that the function y 1+¯γ (p(t)) $\begin{array} { r } { y = \frac { 1 + x } { 1 + \bar { \gamma } _ { m } ( \mathbf { p } ( t ) ) } } \end{array}$ 1+x is a tangent line for $y =$ $\Big ( \frac { x } { \bar { \gamma } _ { m } ( { \bf p } ( t ) ) } \Big ) ^ { \frac { \bar { \gamma } m ( { \bf p } ( t ) ) } { 1 + \bar { \gamma } _ { m } ( { \bf p } ( t ) ) } }$ at $x = \bar { \gamma } _ { m } ( { \mathbf { p } } ( t ) )$ . Therefore, it is concluded that Xm $\begin{array} { r } { X _ { m } = \frac { \bar { \gamma } _ { m } ( \mathbf { p } ( t ) ) } { 1 + \bar { \gamma } _ { m } ( \mathbf { p } ( t ) ) } } \end{array}$ is the maximum value which satisfies (33), and $Y _ { m } = \ln ( 1 + { \bar { \gamma } } _ { m } ( \mathbf { p } ( t ) ) ) - X _ { m } \ln ( { \bar { \gamma } } _ { m } ( \mathbf { p } ( t ) ) )$ .
= ln( + ¯ ( ( ))) ln(¯ ( ( )))To acquire a standard convex objective function, the transformation $\tilde { p } _ { m } ( t ) = \ln p _ { m } ( t )$ is introduced, and the standard convex optimization structure is obtained with respect to $\widetilde { p } _ { m } ( t )$ , and the prove process is shown in [31]. The lower bound of the objective function in problem P5 is obtained
$$
\begin{array}{l} \max _ {p _ {m} (t)} \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \\ \cdot \left[ X _ {m} \ln \left(\bar {\gamma} _ {m} \left(e ^ {\tilde {p} _ {m} (t)}\right)\right) + Y _ {m} \right]. \tag {34} \\ \end{array}
$$
2) Approximation of Probability Constraint: To depress the uncertain probability constraint (10), the Bernstein approximation which is a convex approximation method is proposed [25]. The probability constraint is reformulated as
$$
\Pr \left\{\phi_ {0} (\mathbf {p}) + \sum_ {m = 0} ^ {M} \xi_ {m} \phi_ {m} (\mathbf {p}) \leq 0 \right\} \geq 1 - \varepsilon , \tag {35}
$$
where $\mathbf { p }$ is a deterministic variable vector, $\left\{ \xi _ { m } \right\}$ is a random variable with marginal distribution $\{ \psi _ { m } \}$ . With the following conditions, inequality (35) is potentially satisfied for a given family of $\left\{ \xi _ { m } \right\}$ distributions,
1) $\{ \phi _ { m } ( \mathbf { p } ) \}$ are affine in p;
2) $\left\{ \xi _ { m } \right\}$ ( )are independent of each other;
3) $\{ \psi _ { m } \}$ is with the bounded support of $[ - 1 , 1 ] .$ , which is expressed as $- 1 \leq \psi _ { m } \leq 1 , \forall m = 0 , 1 , \cdot \cdot \cdot , M$ .
=Theorem 3: By Bernstein approximation, the uncertain probability constraint $\operatorname* { P r } \{ \gamma _ { m } ( p _ { m } ( t ) ) \geq \gamma _ { m , \mathrm { m i n } } \} \geq 1 - \varepsilon$ can be transformed into the $l _ { \infty }$ ( ( ))-approximate constraint.
$$
\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} e ^ {\tilde {p} _ {n} (t)} + \sqrt {2 \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m} \leq 0. \tag {36}
$$
$$
\delta_ {n, m} \beta_ {n, m} e ^ {\tilde {\rho} _ {n} (t)} \leq \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m}. \tag {37}
$$
Proof: The detailed proof is shown in Appendix B.
Based on Theorem 3 and the approximated objective function (34), the subproblem P5 can be transformed as,
$$
\begin{array}{l} \mathbf {P 6}: \max _ {\tilde {p} _ {m} (t)} \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \\ \cdot \left[ X _ {m} \mathrm {l n} (\bar {\gamma} _ {m} (e ^ {\tilde {p} _ {m} (t)})) + Y _ {m} \right] \\ \text {s . t .} \left\{ \begin{array}{l} \sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} e ^ {\tilde {p} _ {n} (t)} + \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m} \leq 0 \\ \delta_ {n, m} \beta_ {n, m} e ^ {\tilde {p} _ {n} (t)} \leq \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m} \\ - \infty \leq \tilde {p} _ {n} (t) \leq \ln p _ {m, \max }, \quad \forall m, t \end{array} \right. \tag {38} \\ \end{array}
$$
where P6 is the $l _ { \infty }$ -approximate power control subproblem.
C. Solution to the $l _ { \infty }$ -Approximate Power Control Subproblem
Since the problem P6 is a standard convex problem, the Lagrangian function method is adopted to solve it.
Theorem 4: By solving the Lagrangian function of problem P6, the iteration for the power control is formulated as
$$
\begin{array}{l} p _ {m} ^ {t _ {\infty}} (t + 1) = \left[ \ln \left(\frac {\omega X _ {m} (t)}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right)\right) \right. \\ - \ln \left(\frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \sum_ {n \neq m} ^ {M} X _ {n} (t) \frac {\bar {\gamma} _ {n} \left(\mathrm {e} ^ {\tilde {\mathbf {p}}}\right) \bar {g} _ {m , n}}{\mathrm {e} ^ {\tilde {p} _ {n}} \bar {g} _ {n , n}} \right. \\ \left. \left. + \sum_ {n = 0} ^ {M} \zeta_ {m} (t) \chi_ {n, m} + \lambda_ {n, m} (t) \sqrt {M} \delta_ {n, m} \beta_ {n, m}\right) \right] _ {- \infty} ^ {\ln p _ {m, \max }} \tag {39} \\ \end{array}
$$
where $[ x ] _ { i } ^ { j } = \mathrm { m i n } \{ \mathrm { m a x } \{ x , i \} , j \}$ . $\zeta _ { m }$ and $\lambda _ { n , m }$ denote La-[ ] = mingrangian multipliers, $\mu _ { m } \geq 0$ and $\lambda _ { n , m } \geq 0$ , which are shown
$$
\lambda_ {n, m} (t + 1) = \left[ \lambda_ {n, m} (t) + K _ {\lambda} (t) \left(\sqrt {M} \delta_ {n, m} \beta_ {n, m} \mathrm {e} ^ {\tilde {p} _ {n}} + \varrho\right) \right] ^ {+}, \tag {40}
$$
$$
\zeta_ {m} (t + 1) = (2 \ln (\varepsilon)) ^ {- \frac {1}{2}} \sum_ {n ^ {\prime} = 0} ^ {M} \mu_ {n ^ {\prime}, m} (t + 1), \tag {41}
$$
where Kλ denotes the step-size,  -Mm=0 $K _ { \lambda }$ $\begin{array} { r } { \varrho = \frac { \sum _ { m = 0 } ^ { M } \chi _ { n , m } \mathrm { e } ^ { \tilde { p } n } - I _ { t h } } { \sqrt { - 2 \ln ( \varepsilon ) } } } \end{array}$ χn,me √ p˜n −Ith .
Proof: See Appendix C.
# D. Robust Resource Allocation Algorithm
We constructed a long-term cross-layer resource allocation problem (14) and proposed a robust resource allocation algorithm to solve it. Firstly, a series of values are set, including the maximum number of time slots $T$ , the initial length of data queue $Q _ { m } ( 0 )$ , the initial power $\tilde { p } _ { m } ( 0 )$ , and the step size $K$ . ( ) ˜ ( )According to (29), we can obtain the optimal arrival rate of the application layer. Then, update the Lagrange multipliers $\lambda _ { n , m } ( t + 1 )$ of the $l _ { \infty } -$ approximation. Furthermore, the power ( + )iteration expressions $p _ { m } ( t + 1 )$ are shown in (39). At last, the ( + )algorithm based on the Lyapunov optimization framework is shown as follows.
# VI. SIMULATION AND PERFORMANCE EVALUATION
Numerical simulations are shown here to verify the effectiveness of the robust resource allocation algorithm. First of all, the extraction process of traffic semantic data is finished and shown in Fig. 2 of Section III. In this process, the end-to-end scene graph generation model Relation Transformer for Scene Graph Generation (RelTR) is adopted, and we regard scene graph generation as a set prediction problem. The encoder reasons about the visual feature context and infers a set of fixed-size triples. In the D2D-V networks, a simplified communication
# Algorithm 1: Robust resource allocation algorithm.
1: Initialize
• Set $T = 1 0 0$ , $t \gets 1$ .
• Set $Q _ { m } ( 0 ) = 2 0$ , $\tilde { p } _ { m } ( 0 ) = - 8$ .
• Set $K _ { \mu } = 0 . 1$ , $K _ { \lambda } = 0 . 1$
=2: Initialize $\lambda _ { n , m } > 0$ for the $l _ { \infty }$ -approximation.
3: while ( $A _ { m }$ and $p _ { m }$ are not converged) and $\mathit { t } < T$ ) do
4: for $\forall t \in \mathcal T$ do
5: Calculate the optimal arrival rate $A _ { m } ( t )$ by (29).
6: Update $\lambda _ { n , m } ( t + 1 )$ and $\zeta _ { m } ( t + 1 )$ ( )by (40) and (41).
7: ( + ) ( Calculate the optimal power $p _ { m } ( t + 1 )$ by (39).
8: end for
9: Set $t = t + 1$ .
=10: end while
TABLE II SYSTEM PARAMETERS
<table><tr><td>Parameters</td><td>Values</td></tr><tr><td>SINR threshold (γm,min)</td><td>0.9</td></tr><tr><td>Delay threshold (Dm,max)</td><td>0.1s</td></tr><tr><td>Bandwidth (ω)</td><td>10 MHz</td></tr><tr><td>Outage probability threshold (ε)</td><td>0.1</td></tr><tr><td>Background noise (δ2)</td><td>-30 dBm</td></tr><tr><td>Control parameter (V)</td><td>75</td></tr><tr><td>Weight parameter related to the service (Ωm)</td><td>1</td></tr><tr><td>Maximum power (pm,max)</td><td>0.02 W</td></tr><tr><td>Carrier frequency (fc)</td><td>2 GHz</td></tr><tr><td>Feedback time interval (Tf)</td><td>2 ms</td></tr><tr><td>Speed of CUE</td><td>0 m/s</td></tr><tr><td>Speed of four D2D-V pairs</td><td>34, 30, 32, 30 m/s</td></tr><tr><td>Shadow fading Lm,n</td><td>0.5</td></tr><tr><td>Path-loss exponent αm</td><td>2</td></tr></table>
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/52212a47eb38b309a2aaa3310d8c40d8eb11ffc9e80d253f9528313e2d96716b-252bb788c33e.jpg)
Fig. 4. Dynamic convergence of semantic access rates.
model involving one CUE and four D2D-V pairs is formulated, which is under the communication range of the BS. Some parameters are shown in Table II.
Since the accessed semantic image data is still huge, access control and power control are combined to control the queue length and optimize the performance indicators in cross-layer optimization. As depicted in Figs. 4 and 5, the access rates of semantic data and powers of CUE and VUEs all achieve dynamic convergence within several steps. Figs. 6, 7, and 8 show the dynamic convergence performance of the data queue, the virtual queue, and the time delay, respectively. The backlogs of the data queue and the virtual queue also achieve the dynamic convergence within several steps, and the time delays of all users reach the ideal values which are less than the delay threshold
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/99a812b2e2eaf390a275d01b1bca6989602d904d4c17be39176087da0cd6d6d3-de55d7082ad4.jpg)
Fig. 5. Dynamic convergence of powers.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/9a90d2e5d6a7a01431b7021893e0d58f9a06c8becf43c4b7a06590174df4f11d-b1141160da6d.jpg)
Fig. 6. Dynamic convergence of the data queue.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/df1e33ef2a823e7825818dbf53533c0c633d806595d11d71556e6c8e3babb40f-d197f5881b05.jpg)
Fig. 7. Dynamic convergence of the virtual queue.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/db0f3506bf92679acd60c62a9c7970cd6274afc6492bfcaf99335b9442c720bd-d7d899372357.jpg)
Fig. 8. Dynamic convergence of the time delay.
$D _ { m , \mathrm { m a x } }$ . Therefore, the results in these figures demonstrate that the proposed robust resource allocation algorithm of the $l _ { \infty }$ -approximation is effective and shows rapid convergence speed. It is noted that the long-term optimization scheme is different from traditional short-time ones, dynamic adjustment
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/fbc92242d136a686756b124108f6f8793a615ecbcbea382cd8ddffa4bfdbb15c-122a3d075efe.jpg)
Fig. 9. Long-term sum transmission rate versus outage probability threshold ε.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/9bfe3357bfb469851f98a3b101124010a52d52beaf8f1eaf962ee8ab4738f528-b4281d6041c1.jpg)
Fig. 10. Long-term average time delay versus outage probability threshold $\varepsilon$
of power strategies is necessary to cope with uncertain channel changes, so the dynamic strategies contribute more robustness to the long-term scenario.
Figs. 9 and 10 illustrate the influence of the outage probability threshold $\varepsilon$ on the long-term average sum transmission rate and time delay. According to Fig. 9, the sum transmission rate is higher when the outage probability threshold $\varepsilon$ increases. A bigger value of $\varepsilon$ means that the range of the variable $p _ { m }$ will be expanded, so the optimal power will be searched in a larger region and committed to improving the objective function. In this regard, the objective function is positively correlated with the access rate. When the system is stable, the input and output also reach a dynamic balance, so the increase of $\varepsilon$ increases the access rate, and further increases the sum transmission rate. As shown in Fig. 10, the average time delay of CUE and four VUEs increases with the increase of $\varepsilon$ . This is because the increase of $\varepsilon$ brings a greater queue backlog, even if the transmission rate elevates, the average time delay will still increase. A comprehensive analysis of these two indicators in Figs. 9 and 10 can draw a conclusion that the transmission rate and delay restrict each other in the D2D-V communication system. The increase in transmission rate will lead to the loss of delay performance, which further reflects the importance of system performance compromising.
In this paper, the first-order Gauss-Markov process is used to describe the channel environment with imperfect CSI, and the $l _ { \infty }$ -approximation robust resource allocation algorithm is proposed. To show the importance of considering channel uncertainty, we make a comparison with the benchmark [15],
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/7295a615ab43f1fd77349c14dffef954cd7fc7250d2ffe6f33e0c0815984e193-52f1cd9811f5.jpg)
Fig. 11. Comparison of user real outage probability in different cases.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/6590774c0c090c5e5d9559df00fbc55b97875cf0852677728be998c384050a9c-ca40a5392733.jpg)
Fig. 12. Comparison of user powers in different cases.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/03b24478c4d4994ab28d65f0a3158389295e7d25ecd63f18e30a4ccdd3de262f-f49fd024179d.jpg)
Fig. 13. Comparison of user transmission rates in different cases.
where perfect CSI is assumed. Besides, $l _ { 1 }$ -approximation, another method to transform the $l _ { 2 }$ -norm structure by $\| \mathbf { z } \| _ { 2 } \leq \| \mathbf { z } \| _ { 1 }$ $( \mathbf { z } \in \mathbb { R } ^ { M \setminus }$ ) [25], is also simulated to compared with this work. Under the same target probability $\varepsilon = 0 . 1$ , the comparison of the =real outage probability is formulated. As shown in Fig. 11, the real outage probability of $l _ { \infty }$ -approximation algorithm is lower than the $l _ { 1 }$ -approximation algorithm, and much lower than the benchmark [15]. According to $C 4$ in the P1, it is believed that the lower real outage probability means a better guarantee of the SINR constraint and the stronger system robustness. Therefore, this paper can achieve a more stable signal transmission than the benchmark [15] and the $l _ { 1 }$ -approximation method [25].
The other performance indicators are also compared, and they are shown in Figs. 12, 13, and 14. It can be seen by comparing the $l _ { \infty }$ -approximation and the $l _ { 1 }$ -approximation that the $l _ { \infty }$ -approximation algorithm is outstanding in the performance of transmission rate and delay.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/eba3e19c2f44fb99e982fd776e204f9c5f350c5f0d9fd811d45439933dc0deef-d7378bfab53c.jpg)
Fig. 14. Comparison of user delays in different cases.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/393ab5cb3505e92b66f7bdc1a0fb97e7b546331f191bf57f717ac62dc7c4a9c8-f810b80cbf4d.jpg)
Fig. 15. Sum transmission rate versus vehicle speed in different cases.
Moreover, by comparing with the $l _ { \infty }$ -approximation algorithm, the three figures show that the benchmark [15] consumes much more transmission powers, but it does not get an obvious performance improvement. This is because the perfect CSI is impractical, and users are willing to increase the transmission rate by excessively increasing its powers. However, higher powers also bring more different-levels interference, and then the transmission rate and delay performances of different users will be affected to varying degrees. Therefore, the perfect CSI assumption always shows unstable and dissatisfied performances in the actual communication environment. To sum up, based on the comprehensive analysis as shown in Figs. 11, 12, 13, and 14, the $l _ { \infty }$ -approximation algorithm is more well-function than the benchmark [15], especially for the system robustness and power consumption.
To verify the impact of vehicle mobility on sum transmission rate, different levels of vehicle speeds are simulated in D2D-V communication scenarios. In this numerical simulation, network topologies are assumed to be the same and the velocities of all VUEs are identical. Since the moving speed of CUE is slow, the CUE is assumed to be stationary. The unified vehicle velocities are set to 0, 10, 20, and $3 0 ~ \mathrm { m / s }$ , respectively. As depicted in Fig. 15, when the vehicle speed increases, the sum transmission rate decreases in both the $l _ { \infty }$ -approximation method of this paper and the $l _ { 1 }$ -approximation method of [25]. It is because that higher speed causes a more serious Doppler effect, which deteriorates the channel environment and makes the communication links suffer more co-channel interference. Therefore, taking the vehicle mobility characteristic into account is necessary for the accurate description of channel state and performance improvement.
# VII. CONCLUSION
In this paper, the extraction process of traffic semantic data is shown, and then the extracted semantic data is transmitted by D2D communications. Based on the Lyapunov optimization theory, this paper designs a long-term dynamic cross-layer resource allocation framework, which includes a semantic access control scheme and a power control scheme. A robust online resource allocation algorithm is proposed to achieve real-time optimization strategy. Simulation results demonstrated the converged performances of the proposed algorithms under the uncertain channel environment. The simulations also validate that the data queue is stabile, low delay and high-reliability semantic communications are finished, the user QoS requirements are guaranteed, especially the system robustness and power consumption outperform the benchmark. To sum up, the proposed algorithm is well-function in the communication environment with multi-user interference and channel uncertainty.The Lyapunov control parameter can be adjusted to realize the tradeoff between user satisfaction maximization, queue stability, and delay minimization.
# APPENDIX A
Proof: Assumed that A, B, and $C$ are non-negative real numbers, it is clearly established that
$$
\left(\max \{A - B, 0 \} + C\right) ^ {2} \leq A ^ {2} + B ^ {2} + C ^ {2} + 2 A (C - B). \tag {42}
$$
According to (42), we can obtain
$$
\begin{array}{l} \triangle (\mathbf {M} (t)) = \mathbb {E} \left\{L (\mathbf {M} (t + 1)) - L (\mathbf {M} (t)) | \mathbf {M} (t) \right\} \\ \leq \sum_ {m = 0} ^ {M} \mathbb {E} \left\{Q _ {m} (t) A _ {m} (t) | \mathbf {M} (t) \right\} \\ + \sum_ {m = 0} ^ {M} Z _ {m} (t) \mathbb {E} \left\{Q _ {m} (t) - R _ {m} \left(p _ {m} (t)\right) D _ {m, \max } ^ {Q} | \mathbf {M} (t) \right\} \\ - \sum_ {m = 0} ^ {M} Q _ {m} (t) \mathbb {E} \left\{R _ {m} \left(p _ {m} (t)\right) | \mathbf {M} (t) \right\} + \Theta \tag {43} \\ \end{array}
$$
where $\Theta$ is a positive constant that satisfies:
$$
\begin{array}{l} \Theta \geq \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{R _ {m} ^ {2} \left(p _ {m} (t)\right) + A _ {m} ^ {2} (t) | \mathbf {M} (t) \right\} \\ + \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{\left(R _ {m} \left(p _ {m} (t)\right) D _ {m, \max } ^ {Q}\right) ^ {2} + Q _ {m} ^ {2} (t) | \mathbf {M} (t) \right\}. \tag {44} \\ \end{array}
$$
Adding $\begin{array} { r } { V \mathbb { E } \{ \sum _ { m = 0 } ^ { M } U _ { m } [ A _ { m } ( t ) ] \} } \end{array}$ to both sides of (43), we [can obtain the formula (20).
# APPENDIX B
Proof: The conservative approximation for (35) is,
$$
\inf _ {\rho > 0} \left[ \phi_ {0} (\mathbf {p}) + \rho \sum_ {n = 0} ^ {N} \iota_ {m} \left(\rho^ {- 1} \phi_ {n} (\mathbf {p})\right) + \rho \ln \left(\frac {1}{\varepsilon}\right) \right] \leq 0, \tag {45}
$$
where $\begin{array} { r } { \iota _ { m } ( y ) = \operatorname* { m a x } _ { \psi _ { m } } \ln ( \int \exp ( x y ) d \psi _ { m } ( x ) ) } \end{array}$ , $\rho$ is the conser-( ) = max ln( exvative approximate parameter. $\mathbf { p } = [ p _ { 1 } , p _ { 2 } , \dots , p _ { m } ]$ , which is the vector of transmission powers.
The transformation process can further perform by using the upper bound of $\iota _ { m } ( y )$ ,
$$
\iota_ {m} (y) \leq \max \left\{o _ {m} ^ {-} y, o _ {m} ^ {+} y \right\} + \frac {\delta_ {m} ^ {2}}{2} y ^ {2}, m = 0, 1, \dots , M, \tag {46}
$$
where $o _ { m } ^ { - } , o _ { m } ^ { + }$ and $\delta _ { m }$ are both constants and determined by the given families $- 1 \leq o _ { m } ^ { - } \leq o _ { m } ^ { + } \leq 1$ , $\delta _ { m } \geq 0$ .
When $\iota _ { m } ( \cdot )$ in (46) is substituted with the upper bound, the ( )convex conservative surrogate of (45) is reformulated as,
$$
\begin{array}{l} \phi_ {0} (\mathbf {p} (t)) + \sum_ {m = 0} ^ {M} \max \left\{o _ {m} ^ {-} \phi_ {m} (\mathbf {p} (t)), o _ {m} ^ {+} \phi_ {m} (\mathbf {p} (t)) \right\} \\ + \sqrt {2} \ln \left(\frac {1}{\varepsilon}\right) \left(\sum_ {m = 0} ^ {M} \left(\delta_ {m} \phi_ {m} (\mathbf {p} (t))\right) ^ {2}\right) ^ {\frac {1}{2}} \leq 0. \tag {47} \\ \end{array}
$$
The outage probability constraint of the mth signal link in the optimization problem can be rewritten as a matrix,
$$
\Pr \left\{\left(\mathbf {G} _ {m}\right) ^ {T} \mathbf {p} + \sigma^ {2} \leq 0 \right\} \geq 1 - \varepsilon , \tag {48}
$$
where $\begin{array} { r } { \mathbf { G } _ { m } = [ g _ { 0 , m } , g _ { 1 , m } , \ldots , - \frac { g _ { m , m } } { \gamma _ { m , \mathrm { m i n } } } , \ldots , g _ { M , m } ] . } \end{array}$ Here, $\tilde { g } _ { n , m }$ is assumed to be bounded by $[ a _ { n , m } , b _ { n , m } ]$ , $\beta _ { m , n } = { \textstyle \frac { 1 } { 2 } } ( b _ { m , n } -$ $a _ { m , n } ) \neq 0$ and $\varpi _ { n , m } = \frac { 1 } { 2 } ( b _ { n , m } + a _ { n , m } )$ are constructed to ) =normalize the support $\psi _ { n , m }$ ( +, which is
$$
\psi_ {n, m} = \frac {\tilde {g} _ {n , m} - \varpi_ {n , m}}{\beta_ {n , m}} \in [ - 1, 1 ]. \tag {49}
$$
Let $\begin{array} { r } { \phi _ { 0 } ( \mathbf { p } ( t ) ) = \sigma ^ { 2 } + \sum _ { i = 0 } ^ { N } ( \hat { g } _ { m , n } + \varpi _ { m , n } ) p _ { m } ( t ) , \phi _ { m } ( \mathbf { p } ( t ) } \end{array}$ $\phi _ { m } ( { \mathbf { p } } ( t ) )$ $= \beta _ { m , n } p _ { m } ( t )$ )) = + (ˆ + ) ( ), (47) is an equivalent constraint with $C 4$ ( in $\mathbf { P 5 }$ = ( )Hence, substituting $f _ { 0 } ( \mathbf { p } )$ and $f _ { m } ( \mathbf { p } )$ into (47),
$$
\begin{array}{l} \sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} p _ {n} (t) + \sqrt {2 \ln \left(\frac {1}{\varepsilon}\right)} \\ \left(\sum_ {n = 0} ^ {M} \left(\delta_ {n, m} \beta_ {n, m} p _ {n} (t)\right) ^ {2}\right) ^ {\frac {1}{2}} \leq 0, \tag {50} \\ \end{array}
$$
where $\chi _ { n , m } = \hat { g } _ { n , m } + \varpi _ { n , m } + v _ { m } ^ { + } \beta _ { n , m }$ . In (50), the coupling = ˆ + +power variables bring a high computational difficulty to the problem solving process. To reduce the computational complexity,√ according to $\| \mathbf { z } \| _ { 2 } \leq \ \sqrt { N } \| \mathbf { z } \| _ { \infty } ~ ( \mathbf { z } \in \mathbb { R } ^ { \bar { M } } )$ $( \mathbf { z } \in \mathbb { R } ^ { M } )$ , the $l _ { 2 }$ -norm structure of (50) is further transformed into the $l _ { \infty }$ -approximation problem,
$$
\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} p _ {n} (t) + \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \max _ {n \in \mathcal {M}} \delta_ {n, m} \beta_ {n, m} p _ {n} (t) \leq 0 \tag {51}
$$
By setting auxiliary variables $\pmb { v } = [ v _ { 0 , m } , v _ { 1 , m } , \dots , v _ { M , m } ]$ , the $l _ { \infty }$ = [ ]-approximation constraint (51) can be further reformulated as the separable constraints (52) and (53).
$$
\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} p _ {n} (t) + \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m} \leq 0 \tag {52}
$$
$$
\delta_ {n, m} \beta_ {n, m} p _ {n} (t) \leq \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m} \tag {53}
$$
Letting $\tilde { p } _ { n } ( t ) = \ln p _ { n } ( t )$ , (36) and (37) can be obtained.
# APPENDIX C
Proof: Since P6 is a convex problem, the Lagrangian function of P6 is shown as follows,
$$
\begin{array}{l} L (\tilde {p} _ {m} (t): \lambda_ {n, m}, \zeta_ {m}) = \\ \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \left[ X _ {m} \ln \left(\bar {\gamma} _ {m} \left(e ^ {\tilde {p} _ {m} (t)}\right)\right) + Y _ {m} \right] \\ - \sum_ {m = 0} ^ {M} \zeta_ {m} \left(\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} e ^ {\tilde {p} _ {m} (t)} \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m}\right) \\ - \sum_ {m = 0} ^ {M} \sum_ {N = 0} ^ {M} \lambda_ {n, m} \left(\delta_ {n, m} \beta_ {n, m} e ^ {\tilde {p} _ {m} (t)} - \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m}\right), \tag {54} \\ \end{array}
$$
where $\lambda _ { n , m } \geq 0$ and $\zeta _ { m } \geq 0$ , respectively. Then, the corresponding dual function is formulated as,
$$
\begin{array}{l} D \left(\lambda_ {n, m}, \zeta_ {m}\right) = \max _ {- \infty \leq \tilde {p} _ {i} \leq \ln p _ {i, m a x}} L \left(\tilde {p} _ {m} (t): \lambda_ {n, m}, \zeta_ {m}\right) \\ = \max _ {- \infty \leq \tilde {p} _ {i} \leq \ln p _ {i, m a x}} \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} (Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)) \\ \cdot \left[ X _ {m} \ln (\bar {\gamma} _ {m} (e ^ {\tilde {p} _ {m} (t)})) + Y _ {m} \right] - \sum_ {m = 0} ^ {M} \zeta_ {m} \sigma^ {2} \\ - \sum_ {m = 0} ^ {M} \sum_ {n = 0} ^ {M} \left(\zeta_ {m} \chi_ {n, m} + \lambda_ {n, m} \sqrt {M} \delta_ {n, m} \beta_ {n, m}\right) \mathrm {e} ^ {\tilde {p} _ {n}} \\ + \sum_ {m = 0} ^ {M} \sum_ {n = 0} ^ {M} \left(\sum_ {n ^ {\prime} = 0} ^ {M} \lambda_ {n ^ {\prime}, m} - \zeta_ {m} \sqrt {2 \ln \left(\frac {1}{\varepsilon}\right)}\right) v _ {n, m}. \tag {55} \\ \end{array}
$$
Furthermore, the dual problem of (25) is as follows,
$$
\min _ {\lambda_ {n, m} > 0, \zeta_ {m} > 0} D \left(\lambda_ {n, m}, \zeta_ {m}\right). \tag {56}
$$
The power vector $\tilde { \mathbf { p } }$ ’s iteration function can be obtained by
$$
\begin{array}{l} \frac {\partial L (\tilde {p} _ {m} (t) : \lambda_ {n , m} , \zeta_ {m})}{\partial \tilde {p} _ {m}} = \frac {\omega X _ {m}}{\ln 2} (Z _ {m} (t) D _ {m, \mathrm {m a x}} ^ {Q} + Q _ {m} (t)) \\ - \left(\frac {\omega}{\ln 2} (Z _ {m} (t) D _ {m, \mathrm {m a x}} ^ {Q} + Q _ {m} (t)) \sum_ {n \neq m} ^ {M} X _ {n} \frac {\bar {\gamma} _ {n} (\mathrm {e} ^ {\tilde {\mathbf {p}} (t)}) \overline {{g}} _ {m , n}}{\mathrm {e} ^ {\tilde {p} _ {n} (t)} \overline {{g}} _ {n , n}} \right. \\ + \sum_ {n = 0} ^ {M} \zeta_ {m} ^ {(t)} \chi_ {m, n} + \sum_ {n = 0} ^ {M} \mu_ {m, n} ^ {(t)} (\sqrt {M} \sigma_ {m, n} \alpha_ {m, n}) \mathrm {e} ^ {\tilde {\rho} _ {m}} = 0, \tag {57} \\ \end{array}
$$
where $\overline { { g } } _ { m , n }$ and $\overline { { g } } _ { n , n }$ are the expectation values of $g _ { m , n }$ and $g _ { n , n }$ , respectively; $\overline { { g } } _ { m , n } = \mathbb { E } \{ g _ { m , n } \}$ and $\overline { { g } } _ { n , n } = \mathbb { E } \{ g _ { n , n } \} , m \in \mathcal { M }$ $m \in \mathcal { M }$ and $n \in \mathcal { M }$ . Besides, $\bar { \gamma } _ { n } ( \mathrm { e } ^ { \tilde { \mathbf { p } } ( t ) } )$ =is the average SINR as
$$
\bar {\gamma} _ {n} \left(\mathrm {e} ^ {\tilde {\mathbf {p}} (t)}\right) = \frac {\mathrm {e} ^ {\tilde {p} _ {n} (t)} \bar {g} _ {n , n}}{\sum_ {m \neq n} ^ {M} \mathrm {e} ^ {\tilde {p} _ {m} (t)} \bar {g} _ {m , n} + \delta^ {2}}. \tag {58}
$$
Let ∂L(˜pm(t):λn,m,ζm) 0, the iterations of the powers and $\begin{array} { r } { \frac { \partial L ( \tilde { p } _ { m } ( t ) : \lambda _ { n , m } , \zeta _ { m } ) } { \partial \tilde { p } _ { m } } = 0 } \end{array}$ =the Lagrangian multipliers are given as (39), (40), (41). ∂p˜m
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![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/4baa31a1a55818c630239c728ab0af8fbb7d9d93bdcbbbdc133864be753f91d6-ef2520fcccf3.jpg)
Jiawei Su received the B.S. degree in automation from Yanshan University, Qinhuangdao, China, in 2019. He is currently working toward the Ph.D. degree in control science and engineering in Yanshan University, Qinhuangdao, China. His research interests include Internet of Vehicles and D2D communication.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/d48519240f02c0d89b59d8eecaf60dfb885a8b6e3960c82b7cc8b9b15701e2f8-e7de8e455fe0.jpg)
Zhixin Liu (Senior Member, IEEE) received the B.S., M.S., and Ph.D. degrees in control theory and engineering from Yanshan University, Qinhuangdao, China, in 2000, 2003, and 2006, respectively. He is currently a Professor with the School of Electrical Engineering, Yanshan University, China. From 2009 to 2010, he visited the University of Alberta, Edmonton, AB, Canada. His research interests include performance optimization and resource allocation in wireless networks.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/d6dd35957c2b74b58fc45e9755bc36d58036100e2d3b677fdb66e21933c8fa2d-2fc942c22b0d.jpg)
Yuan-ai Xie received the Ph.D. degree in control science and engineering from Yanshan University, Qinhuangdao, China, in 2022. From 2021 to 2022, he was a visiting Ph.D. Student with Nanyang Technological University, Singapore. In 2023, he joined the School of Computer and Science, South-Central Minzu University, Wuhan, China. His research interests include wireless resource optimization in vehicular networks and physical layer security.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/651b82d44819515263120cdc35cb1f230feb7889f36a5e8de0c446ffcbb961e1-0b0eaf714a8e.jpg)
Kai Ma (Member, IEEE) received the B.S. degree in automation and the Ph.D. degree in control science and engineering from Yanshan University, China, in 2005 and 2011, respectively. From 2013 to 2014, he was a Post-Doctoral Research Fellow with Nanyang Technological University, Singapore. He is currently a Professor with the School of Electrical Engineering, Yanshan University. His research interests include demand response in smart grid and resource allocation in communication networks.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/237176dd4243704eb40174c9a67b735b18d88591121d9f91aec143bfce4b59d7-f7ef582615b4.jpg)
Jiawen Kang (Member, IEEE) received the Ph.D. degree from the Guangdong University of Technology, Guangzhou, China, in 2018. From 2018 to 2021, he was a Postdoc with Nanyang Technological University, Singapore. He currently is a Professor with the Guangdong University of Technology. His research interests mainly focus on blockchain, security, and privacy protection in wireless communications and networking.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/413971f0b3c9c9f1af7db7ccefe760ed4d62f8635f35a0db205e0f2c05d6e090-eed7a6736a0b.jpg)
Hongyang Du (Student Member, IEEE) received the B.Sc. degree from Beijing Jiaotong University, Beijing, China, in 2021. He is currently working toward the Ph.D. degree with the School of Computer Science and Engineering, Nanyang Technological University, Singapore, under the Interdisciplinary Graduate Program. His research interests include semantic communications, reconfigurable intelligent surface, and communication theory. He was the recipient of the IEEE Daniel E. Noble Fellowship Award in 2022.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/2819faeb6ca12e1735ea9c50d52d57baa847bafaabd5cc8880e916020250021e-389f8cf2a6e1.jpg)
Dusit Niyato (Fellow, IEEE) received the B.Eng. degree from the King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand, in 1999, and the Ph.D. degree in electrical and computer engineering from the University of Manitoba, Winnipeg, MB, Canada, in 2008. He is currently a Professor with the School of Computer Science and Engineering, Nanyang Technological University, Singapore. His research interests include the Internet of Things (IoT), machine learning, and incentive mechanism design.

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# 基于语义通信的 D2D 车联网动态资源分配
Jiawei Su, Zhixin Liu, Senior Member, IEEE, Yuan-ai Xie, Kai Ma, Member, IEEE, Hongyang Du, Student Member, IEEE, Jiawen Kang, Member, IEEE, and Dusit Niyato, Fellow, IEEE
摘要: 语义通信机制使车联网中的无线设备能够围绕语义含义进行更高效的信息交互。然而，在高度动态的车联网环境中，语义信息的传输在可靠性和稳定性方面仍面临挑战。为解决这些问题，本文在设备到设备（D2D）车联网（D2D-V）场景下提出一种长期鲁棒资源分配方案，综合考虑用户满意度、队列稳定性和通信时延等多项性能指标。由于信道波动下的概率约束形式较为复杂，本文引入 Bernstein 近似以更高效地获得确定性约束。随后，利用 Lyapunov 优化方法将鲁棒资源分配问题拆分为两个相互独立的子问题，分别对应应用层的语义接入控制和物理层的功率控制。进一步地，采用连续凸近似方法以及 Karush-Kuhn-Tucker 条件求解这些子问题，从而提出一套鲁棒资源分配算法。仿真结果表明，在满足用户 SINR 要求的前提下，用户满意度、队列稳定性与通信时延之间存在明显的折中关系。同时，仿真也证明了在高速移动的车联网通信场景中考虑信道不确定性的必要性。
关键词: D2D 技术, Lyapunov 优化, 资源分配, 语义通信, 车联网
稿件于 2022 年 5 月 6 日收到; 于 2022 年 7 月 29 日和 2022 年 12 月 19 日修回; 于 2023 年 3 月 10 日接受。发表日期为 2023 年 3 月 16 日，当前版本日期为 2023 年 8 月 15 日。本工作部分受国家自然科学基金 62273298 和 61873223 资助，部分受河北省研究生创新基金项目 CXZZBS2023055 资助，部分受新加坡国家研究基金会和新加坡资讯通信媒体发展局未来通信研发计划（FCP）项目 FCP-NTU-RG-2022-010 资助，部分受 DSO National Laboratories 通过 AI Singapore 项目 AISG2-RP-2020-019 以及 Energy Grid 2.0 项目中的 Energy Research Test-Bed 与 Industry Partnership Funding Initiative 资助。本文审稿由 Haijun Zhang 博士协调完成。通讯作者: Zhixin Liu。
Jiawei Su、Zhixin Liu 和 Kai Ma 就职于中国河北秦皇岛 066004，燕山大学电气工程学院（e-mail: Sjw@stumail.ysu.edu.cn; lzxauto@ysu.edu.cn; kma@ysu.edu.cn）。
Yuan-ai Xie 就职于中国湖北武汉 430079，中南民族大学计算机科学学院（e-mail: xieyuan_ai@163.com）。
Hongyang Du 就职于新加坡 639798，南洋理工大学计算机科学与工程学院、能源研究所及跨学科研究生项目（e-mail: hongyang001@e.ntu.edu.sg）。
Jiawen Kang 就职于中国广东广州 510006，广东工业大学自动化学院（e-mail: kavinkang@gdut.edu.cn）。
Dusit Niyato 就职于新加坡 639798，南洋理工大学计算机科学与工程学院（e-mail: dniyato@ntu.edu.sg）。
数字对象标识符: 10.1109/TVT.2023.3257770
# I. 引言
为了提升交通效率和车辆用户的驾驶体验，自动驾驶技术已被广泛研究 [1]。在自动驾驶系统中，车辆能否做出高效决策，主要取决于其从周围环境中采集的数据（尤其是摄像头拍摄的交通图像）以及与相邻车辆/路侧基础设施之间的信息交互（无线通信）。相比环境感知，基于车联网（IoV）的信息交互尤为关键 [2]。然而，高效且可靠的车联网通信仍面临两个主要技术挑战 [3]。
一方面，由于车辆采集的数据量巨大，直接传输原始数据会占用大量带宽并带来严重通信开销，这在当前频谱资源紧张的车联网中并不现实。近年来，一种新的通信模式，即语义通信机制，受到了广泛关注 [4]。随着智能化和信息化水平的提升，车辆终端具备了一定的信息计算能力，这为语义通信提供了支持，即提取核心语义数据，仅传输“含义”本身 [5]。另一方面，为了实现相邻车辆之间的直接信息交互，设备到设备（D2D）技术被广泛用于车联网，形成 D2D 车联网（D2D-V）系统 [6]。然而，由于车辆高速移动带来的拓扑频繁变化，车联网中的各类链路很容易中断。因此，在动态环境下保证信号干扰加噪声比（SINR）成为关键问题 [7]。近期研究表明，语义通信机制在低 SINR 环境中具有更强鲁棒性 [8]，能够提升无线设备的通信质量。基于提取后的语义数据，D2D 通信通过传输数据含义而不是传统比特，从而追求更高的传输效率和更低的语义误差。
然而，由于语义数据无法被 D2D 用户瞬时发送，必须暂时缓存在应用层缓冲区中。因此，联合应用层与物理层的跨层资源分配被广泛用于控制队列稳定性并增强系统鲁棒性，尤其是在动态通信环境中。由此可见，基于 D2D-V 网络的跨层鲁棒资源分配框架，是实现高效可靠车联网通信的一种有前景的方案。
# II. 相关工作
根据 Shannon 定理，信道传输速率在理论上存在上限，该上限代表信道的最大通信容量。Shannon 指出，若要无失真地转换连续源数据，需要无限容量的信道，因此常见做法是在允许一定信息损失的前提下对信号进行离散化 [10]。换言之，基于 Shannon 理论的传统通信模型在效率上存在天然限制。作为一种新型通信模式，语义通信近年来得到了广泛研究，它通过提取语义数据，仅传输核心含义。与在一定损失容忍度下离散化连续源信号不同，语义通信直接传输信号的“意义”，因而有潜力显著提升传输效率，表现为更少的信道资源消耗以及更低的信息失真 [11]。此外，在语义知识库的辅助编码和解码下，语义通信能够显著降低语义误差 [12]。不过，现有语义通信研究对端到端数据交换过程考虑不足，对于同时满足多种服务质量（QoS）要求的超可靠、低时延语义传输关注仍不充分 [13]。
因此，本文考虑语义通信与 D2D 技术相结合的场景，在已提取语义数据的基础上研究信号链路通信质量。语义通信和 D2D 技术的结合具有明显优势，例如降低通信负载、实现端到端直连传输、减少传输误差等。为了提升网络稳定性，传统方案大多集中在物理层功率控制 [14]。然而，语义数据无法被 D2D 用户即时传输，而需要暂存于应用层缓冲区；若忽略应用层语义数据的接入速率，就会造成数据队列失衡，进而导致不可控的网络时延。因此，需要构建长期动态跨层资源分配框架，以同时保证 QoS 要求和队列稳定性 [9]。本文采用 Lyapunov 优化方法，先将长期约束转化为队列稳定条件，再将长期目标函数与队列稳定条件进一步转化为可求解的短时子问题 [15]。
尽管 Lyapunov 优化在长期性能指标处理上具有明显优势，但它并不能很好地抑制同信道干扰问题。文献 [16] 指出，D2D 下行复用通信与蜂窝通信共存会造成严重的同频干扰，因此有效的干扰管理非常关键。更复杂的是，越来越多研究表明，尤其在高速移动的车联网通信场景中，信道不确定性不容忽视 [17], [18]。本文采用 Gauss-Markov 过程对不完美信道状态信息（CSI）进行统计建模 [19]，以充分反映车辆移动特性。同时，文献 [20] 使用机会约束来描述干扰约束，其形式是带有不确定参数的概率约束。为了获得该干扰约束的闭式表达，文献 [21] 提出了 Bernstein 近似方法。
受到语义通信与 D2D 技术各自优势的启发，本文提出一种长期鲁棒资源分配方案，联合应用层的接入控制与物理层的鲁棒功率控制，目标是实现更高效、更可靠的语义信息传输。
# A. 贡献
本文的主要贡献如下:
- 提出了一种结合语义通信与长期资源分配的新方案，用于实现高效链路传输，显著提升传输效率与资源利用率。在满足用户 SINR 要求的前提下，该方案实现了用户满意度、队列稳定性和通信时延之间的折中。
- 利用 Lyapunov 优化方法，将动态跨层资源分配问题分解为语义接入控制子问题和功率控制子问题，并分别借助 KKT 条件和拉格朗日函数方法求解。尤其是，采用 Bernstein 近似将非凸功率控制子问题转化为可解的凸问题。
- 结合车辆移动特性，引入一阶 Markov 过程构造精确的不确定信道状态描述，并据此提出鲁棒资源分配算法，实现高效可靠的语义信号传输。
本文其余部分安排如下: 第 III 节建立系统模型和鲁棒资源分配框架; 第 IV 节给出基于 Lyapunov 优化的资源分配问题变换; 第 V 节提出鲁棒资源分配算法; 第 VI 节和第 VII 节分别给出数值仿真结果与结论。
记号说明: 本文中，向量采用黑体表示。部分记号见表 I。
# III. 问题建模
# A. 系统模型
基于开放系统互连（OSI）模型，跨层优化示意图如图 1 所示，其中通过物理层功率控制和应用层语义数据接入控制来实现队列稳定。以图像信息为例，本文采用编码器-解码器架构的端到端场景图生成模型来处理源图像数据 [22]。
表 I 记号说明
<table><tr><td>符号</td><td>含义</td></tr><tr><td>K</td><td>复用信道索引集合 K = {1, . . ., K}</td></tr><tr><td>M</td><td>复用信道中的用户索引集合 M = {0, 1, . . ., M}</td></tr><tr><td>T</td><td>时隙索引集合 T = {0, 1, . . ., T}</td></tr><tr><td>Pr{·}</td><td>概率函数</td></tr><tr><td>E{·}</td><td>指数分布</td></tr><tr><td>E{·}</td><td>数学期望</td></tr><tr><td>R<sup>M</sup></td><td>欧氏空间</td></tr><tr><td>R<sup>M</sup></td><td>M 维实向量集合</td></tr><tr><td>Qm(t)</td><td>CUE 和 VUE 的数据队列</td></tr><tr><td>Zm(t)</td><td>CUE 和 VUE 的虚拟队列</td></tr><tr><td>G</td><td>信道增益向量</td></tr><tr><td>D</td><td>源数据向量</td></tr><tr><td>H</td><td>编码后的语义数据向量</td></tr><tr><td>F</td><td>接收语义数据向量</td></tr><tr><td>D̂</td><td>解码后的语义数据向量</td></tr></table>
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/a33416aa25ad2de30e8e638b741f6591add2473da822ae2b5902d6014829eb14-723d3541af8c.jpg)
图 1. 基于语义通信的跨层优化模型。
在语义通信机制中，采集到的源数据表示为 $\mathbf { D } = [ d _ { 1 } , d _ { 2 } , \ldots ]$，随后由语义编码器和信道编码器进一步编码。提取后的语义数据表示为 $\mathbf H = e n c _ { c } ( e n c _ { s } ( \mathbf D ) )$，其中 $e n c _ { c } ( \cdot )$ 和 $e n c _ { s } ( \cdot )$ 分别表示信道编码器和语义编码器。在接收端，接收信号表示为 $\mathbf { F } = \mathbf { G } \mathbf { H } + \sigma ^ { 2 }$，其中 $\sigma ^ { 2 }$ 为背景噪声，$\mathbf G$ 为信道增益向量。进一步地，解码后的语义数据可表示为 $\hat { \bf D } = d e c _ { s } ( d e c _ { c } ( { \bf F } ) )$，其中 $d e c _ { c } ( \cdot )$ 为信道解码器，$d e c _ { s } ( \cdot )$ 为语义解码器。
图 2 展示了交通语义数据的提取过程。D2D-V 发射端利用语义编码器从车辆摄像头实时拍摄的交通图像中提取语义特征。这些关键特征以文本形式存储，并缓存在应用层缓冲区中。基于这些关键特征，车辆能够做出快速且高效的决策。同时，连续生成的语义信息还可用于监测实时动态交通环境，以实现安全高效的自动驾驶。进一步地，本文研究了基于 D2D 通信技术的语义传输过程。
通过联合控制接入速率和传输速率，可以保证数据队列稳定，从而优化多项性能指标。
图 3 为物理层中的 D2D-V 通信模型。基于有效的编码与解码技术，本文重点研究链路传输过程。如图 3 所示，D2D-V 网络包含一个宏蜂窝和多个 D2D-V 用户对，其中一个车辆发射端（VT）和一个车辆接收端（VR）组成一个 D2D-V 对。每个 VT 和 VR 分别配备语义编码器和语义解码器。多个 D2D-V 对通过复用分配给 CUE 的上行链路进行直接通信，而不经过基站（BS）。当相邻两辆车之间的距离超过 D2D 通信的适用范围时，D2D 对会自发形成。Cowan 的 M3 模型能够较好地描述交通模式 [23]，该模型指出，相邻 D2D 对之间的距离服从截断指数分布。
为提高语义数据传输的频谱效率，本文采用频谱复用机制，其中 CUE 为频谱拥有者，VUE 为频谱共享者。图 3 还展示了特定复用信道中的五种链路: CUE 与 BS 之间的 CUE-I 链路、D2D-V 链路、VT 与 BS 之间的 V2I 链路、CUE 与 VR 之间的 CUE-V 链路，以及 VT 与 VR 之间的 V2V 干扰链路。特别地，图中区分了信号链路与干扰链路。信号链路包括 CUE-I 链路和 D2D-V 链路，而 V2I 链路、CUE-V 链路和 V2V 干扰链路均为干扰链路。作为车联网场景的典型特征，这些链路通常被视为非视距（NLoS）传输。语义通信过程中通常存在诸多不确定环境因素，例如障碍物遮挡、通信终端的高速相对运动以及信道估计误差等 [24]。在资源分配过程中，考虑 $M + 1$ 个传输用户（即 1 个 CUE 和 $M$ 个 VT），它们分别连接至 BS 和 $M$ 个 VR。在第 $t$ 个时隙，用户 $m$ 需要传输 $A _ { m } ( t )$ 比特语义数据，其中 $m \in \mathcal { M }$，$\mathcal { M } = \{ 0 , 1 , \ldots , M \}$。到达的数据首先存储在第 $m$ 个传输用户的缓冲区中，然后再发送出去。令 $R _ { m } ( p _ { m } ( t ) )$ 表示物理层在时隙 $t$ 的传输速率，则形成队列 $Q _ { m } ( t )$。换言之，$A _ { m } ( t )$ 和 $R _ { m } ( p _ { m } ( t ) )$ 分别表示应用层到达的数据量和物理层发出的数据量。
# B. 信道模型
第 $m$ 个发射端与第 $n$ 个接收端之间的信道增益表示为
$$
g _ {m, n} ^ {k} = S _ {m, n} ^ {k} \left(\eta_ {m, n} ^ {k}\right) ^ {2}, \quad m \in \mathcal {M}, n \in \mathcal {M} \tag {1}
$$
其中，$S _ { m , n } ^ { k }$ 和 $( \eta _ { m , n } ^ { k } ) ^ { 2 }$ 分别表示信道 $k$ 中的大尺度衰落和小尺度衰落效应 [25]，$k \in {\mathcal { K } } = \{ 0 , 1 , \ldots , K \}$。大尺度慢衰落包括阴影衰落与路径损耗:
$$
S _ {m, n} ^ {k} = L _ {m, n} ^ {k} \left(d _ {m, n} ^ {k}\right) ^ {- \alpha_ {m}}, \quad m \in \mathcal {M}, n \in \mathcal {M} \tag {2}
$$
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/3af5c46a3e2cb7887ac0bb6f852b020ae4a882eba746721166a003bdd6b89d14-0241be3bed44.jpg)
图 2. 提取后的图像语义数据。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/ab34b6bc4fdc4acd0060f075ca32b19476118112fd6b0f53d07cea2da688f05c-55e2b5f2e9bb.jpg)
图 3. 物理通信模型。
其中，$L _ { m , n }$ 表示阴影衰落，$d _ { m , n } ^ { - \alpha _ { m } }$ 表示路径损耗，$\alpha _ { m }$ 为路径损耗指数，$d _ { m , n }$ 为通信距离。
车联网始终处于动态通信场景中，车辆移动会带来多普勒效应，从而影响信道状态。有效的资源分配策略离不开对不完美 CSI 的刻画。因此，本文采用一阶 Markov 过程对小尺度衰落分量 $\eta _ { m , n }$ 进行精确模拟，如下所示 [26]:
$$
\eta = \vartheta \hat {\eta} + \epsilon , \tag {3}
$$
其中，$\eta$ 和 $\hat { \eta }$ 分别表示当前时隙和前一时隙的信道响应。系数 $\vartheta$（$0 < \vartheta < 1$）量化了相邻两个时隙之间的信道相关性。在概率统计模型 [26] 中，$\vartheta = J _ { 0 } ( 2 \pi f _ { d } T _ { f } )$，其中 $J _ { 0 } ( \cdot )$ 是零阶 Bessel 函数，$T _ { f }$ 是信道状态信息的反馈时间间隔，$f _ { d } = v f _ { c } / c$ 为最大多普勒频率，其中 $v$ 是用户间相对速度，$f _ { c }$ 是载波频率，$c = 3 \times 1 0 ^ { 8 } ~ \mathrm { m / s }$。$\epsilon$ 为与 $\hat { \eta }$ 独立的信道偏差项，服从 $\mathcal { C N } ( 0 , 1 - \vartheta ^ { 2 } )$ 分布。
动态信道模型中的小尺度衰落可表示为:
$$
\left(\eta_ {m, n} ^ {k}\right) ^ {2} = \left(\vartheta_ {m, n} ^ {k} \hat {\eta} _ {m, n} ^ {k}\right) ^ {2} + \left(\epsilon_ {m, n} ^ {k}\right) ^ {2}, \quad m \in \mathcal {M}, n \in \mathcal {M}. \tag {4}
$$
于是，动态信道模型表示为:
$$
g _ {m, n} ^ {k} = S _ {i, j} ^ {k} \left(\left(\vartheta_ {m, n} ^ {k} \hat {\eta} _ {m, n} ^ {k}\right) ^ {2} + \left(\epsilon_ {m, n} ^ {k}\right) ^ {2}\right), \quad m \in \mathcal {M}, n \in \mathcal {M}. \tag {5}
$$
令 $\hat { g } _ { m , n } ^ { k } = S _ { m , n } ^ { k } ( \vartheta _ { m , n } ^ { k } \hat { \eta } _ { m , n } ^ { k } ) ^ { 2 }$，$\tilde { g } _ { m , n } ^ { k } = S _ { m , n } ^ { k } ( \epsilon _ { m , n } ^ { k } ) ^ { 2 }$，则式 (5) 可改写为
$$
g _ {m, n} ^ {k} = \hat {g} _ {m, n} ^ {k} + \tilde {g} _ {m, n} ^ {k}, \quad m \in \mathcal {M}, n \in \mathcal {M}, \tag {6}
$$
其中，$\hat { g } _ { m , n } ^ { k }$ 表示前一时隙采样得到的信道增益，$\tilde { g } _ { m , n } ^ { k }$ 表示误差信道增益。$\hat { g } _ { m , n } ^ { k }$ 是可测的常量，而 $\tilde { g } _ { m , n } ^ { k } \sim E \biggl ( \frac { 1 } { S _ { m , n } ^ { k } ( 1 - ( \vartheta _ { m , n } ^ { k } ) ^ { 2 } ) } \biggr )$ [25]。
当 $m = n = 0$ 时，$g _ { m , n } ^ { k }$ 表示第 $k$ 个信道上的 CUE-I 链路信道增益; 当 $m = n \neq 0$ 时，$g _ { m , n } ^ { k }$ 表示 D2D-V 链路的信道增益; 当 $m \neq n$ 时，$g _ { m , n } ^ { k }$ 表示干扰链路的信道增益。$g _ { m , 0 } ^ { k }$、$g _ { 0 , n } ^ { k }$ 和 $g _ { m , n } ^ { k }$ 分别对应第 $k$ 个上行信道中的 V2I 链路、CUE-V 链路和 V2V 干扰链路的信道增益。
# C. 跨层资源分配问题建模
本小节中的跨层问题包括应用层接入控制和物理层功率分配。由于语义数据无法瞬时传输给 VR，因此需要暂时存储在 VT 的队列中。在时隙 $t$，$t \in \mathcal T$，第 $m$ 个 VT 的队列积压表示为
$$
Q _ {m} (t + 1) = \max \left\{Q _ {m} (t) - R _ {m} \left(p _ {m} (t)\right), 0 \right\} + A _ {m} (t), \tag {7}
$$
可见，动态数据队列由传输速率 $R _ { m } ( p _ { m } ( t ) )$ 和接入的语义数据速率 $A _ { m } ( t )$ 共同决定。数据传输过程由功率控制策略控制，数据接入过程由语义接入速率控制策略控制。当队列 $Q _ { m } ( t )$ 中的传输速率 $R _ { m } ( p _ { m } ( t ) )$ 大于或等于接入速率 $A _ { m } ( t )$ 时，不会发生数据溢出。
定义 1: 根据网络稳定性的定义，当满足下式时，数据队列 $Q _ { m } ( t )$ 被称为均值速率稳定 [27]:
$$
\lim _ {T \rightarrow \infty} \frac {\mathbb {E} \left\{\left| Q _ {m} (T) \right|\right\}}{T} = 0. \tag {8}
$$
物理层假设采用信道复用机制以提高频谱效率。然而，同频段下的共存通信会造成严重的同信道干扰，第 $m$ 条信号链路的干扰表示为
$$
I _ {m} (t) = \sum_ {n = 0, n \neq m} ^ {M} p _ {n} (t) g _ {n, m}, \quad m \in \mathcal {M}, n \in \mathcal {M}, \tag {9}
$$
其中，$p _ { 0 }$ 是 CUE 的发射功率，$I _ { 0 }$ 是 CUE-I 链路所受干扰。当 $n \geq 1$ 时，$p _ { n }$ 表示第 $n$ 个 VT 的发射功率。进一步地，信号链路的实时 SINR 表示为
$$
\gamma_ {m} \left(p _ {m} (t)\right) = \frac {p _ {m} (t) g _ {m , m}}{I _ {m} (t) + \sigma^ {2}}, \quad m \in \mathcal {M}, \tag {10}
$$
依据 Shannon 定理，VUE 的确定性最大等效传输速率为
$$
R _ {m} = \omega \log_ {2} (1 + \bar {\gamma} _ {m} (p _ {m} (t))), \quad m \in \mathcal {M}. \tag {11}
$$
其中，
$$
\bar { \gamma } _ { m } = \frac { \mathbb { E } \{ p _ { m } g _ { m , m } \} } { \mathbb { E } \{ \sum _ { n = 0 , n \neq m } ^ { M } p _ { n } g _ { n , m } \} + \sigma ^ { 2 } } = \frac { p _ { m } \bar { g } _ { m , m } } { \sum _ { n = 0 , n \neq m } ^ { M } p _ { n } \bar { g } _ { n , m } + \sigma ^ { 2 } } .
$$
应用层满意度 $U _ { m }$ 与到达速率正相关。在保持网络稳定的前提下，网络吞吐量可由语义数据接入速率 $A _ { m }$ 表示。因此，用户满意度 $U _ { m }$ 与应用层接入速率正相关，本文将其定义为一个凹函数:
$$
U _ {m} \left[ A _ {m} (t) \right] = \Omega_ {m} \log_ {2} \left[ A _ {m} (t) \right], \tag {12}
$$
其中，$\Omega _ { m }$ 为第 $m$ 个用户的预设权重参数。
第 $m$ 个用户的数据队列传输时延定义为 $D _ { m }$。根据 Little 定律，平均时延表示为接入数据量与传输速率之比:
$$
\bar {D} _ {m} (t) = \frac {\underset {T \rightarrow \infty} {\lim } \frac {1}{T} \sum_ {t = 0} ^ {T - 1} \mathbb {E} \left\{\left| Q _ {m} (t) \right|\right\}}{\underset {T \rightarrow \infty} {\lim } \frac {1}{T} \sum_ {t = 0} ^ {T - 1} \mathbb {E} \left\{\left| R _ {m} \left(p _ {m} (t)\right)\right|\right\}}. \tag {13}
$$
本文的目标函数是最大化 CUE 和 VUE 的长期时间平均满意度。据此构建跨层鲁棒资源分配问题:
$\mathbf { P 1 } \underset { A _ { m } ( t ) , p _ { m } ( t ) } { \operatorname* { m a x } } \operatorname* { l i m } _ { T \to \infty } \frac { 1 } { T } \sum _ { t = 0 } ^ { T - 1 } \mathbb { E } \left\{ \sum _ { m = 0 } ^ { M } U _ { m } [ A _ { m } ( t ) ] \right\}$
s.t.
$\begin{array} { l } { \displaystyle C 1 : 0 \le p _ { m } ( t ) \le p _ { m , \operatorname* { m a x } } , \quad \forall m , t } \\ { \displaystyle C 2 : 0 \le A _ { m } ( t ) \le A _ { m , \operatorname* { m a x } } , \quad \forall m , t } \\ { \displaystyle C 3 : Q _ { m } ( t ) \mathrm { ~均值速率稳定 } , \quad \forall m , t } \\ { \displaystyle C 4 : \operatorname* { P r } \left\{ \gamma _ { m } ( p _ { m } ( t ) ) \ge \gamma _ { m , \operatorname* { m i n } } \right\} \ge 1 - \varepsilon , \quad \forall m , t } \\ { \displaystyle C 5 : \bar { D } _ { m } ( t ) \le D _ { m , \operatorname* { m a x } } , \quad \forall m , t } \end{array}$ (14)
其中，$C 1$ 为功率约束，$p _ { m , \mathrm { m a x } }$ 是最大功率; $C 2$ 为接入速率约束，$A _ { m , \mathrm { m a x } }$ 是提取语义数据的最大接入速率; $C 3$ 表示由式 (8) 定义的队列稳定性约束; $C 4$ 为物理层 SINR 约束，$\gamma _ { m , \mathrm { m i n } }$ 为 SINR 门限，$\varepsilon$ 为 SINR 约束的中断概率门限，且 $\varepsilon \in ( 0 , 1 )$; $C 5$ 为长期时延约束，$D _ { m , \mathrm { m a x } }$ 为时延门限。
在传统静态通信网络中，我们通常不会在短时隙内使用统计模型来表达用户 SINR 的概率约束。然而，在高速动态车联网中，车辆移动特性可能导致距离发生较大变化，因此必须不断更新各时隙中采集到的拓扑变化。由于所采用的信道模型包含路径损耗，而通信距离又会周期性更新，因此对应时隙的统计信道模型参数也应同步更新。因此，使用短期概率约束 $C 4$ 来描述移动场景中的精确服务需求是合理且必要的。
# IV. 基于 Lyapunov 优化的问题变换
# A. 问题变换
利用虚拟队列概念 [28]，可将问题 P1 中的长期时延约束转化为队列稳定条件。与时延约束 $C 5$ 对应的第 $m$ 个传输用户的虚拟队列如下:
$$
Z _ {m} (t + 1) = \max \left\{Z _ {m} (t) - R _ {m} \left(p _ {m} (t)\right) D _ {m, \max }, 0 \right\} + Q _ {m} (t), \tag {15}
$$
其中，队列 $Z _ { m } ( t )$ 不是实际数据队列，式 (15) 只是一个满足约束 $C 5$ 的等效队列。
定理 1: 若 $Z _ { m } ( t )$ 均值速率稳定，则约束 $C 5$ 成立。
证明: 由于篇幅限制，证明过程略去，详见文献 [29]。
根据定理 1，问题 P1 可重写为
$$
\mathbf {P 2}: \max _ {A _ {m} (t), p _ {m} (t)} \lim _ {T \rightarrow \infty} \frac {1}{T} \sum_ {t = 0} ^ {T - 1} \mathbb {E} \left\{\sum_ {m = 0} ^ {M} U _ {m} [ A _ {m} (t) ] \right\}
$$
s.t. $\{ C1, C2, C4, C6: Q _ { m } ( t ) , Z _ { m } ( t ) \text{ 均值速率稳定} \}$ (16)
# B. Lyapunov 优化
Lyapunov 优化是处理长期资源优化方案的一种强大方法，其所需先验信息较少、计算复杂度较低 [15]。令 $\mathbf { M } ( t ) = [ \mathbf { Q } ( t ) , \mathbf { Z } ( t ) ]$ 为数据队列和虚拟队列的拼接向量，则 Lyapunov 函数定义为
$$
L (\mathbf {M} (t)) = \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{Q _ {m} ^ {2} (t) + Z _ {m} ^ {2} (t) \right\}. \tag {17}
$$
Lyapunov 漂移函数表示为
$$
\triangle (\mathbf {M} (t)) = \mathbb {E} \left\{L (\mathbf {M} (t + 1)) - L (\mathbf {M} (t)) | \mathbf {M} (t) \right\}, \tag {18}
$$
根据文献 [30]，较小的漂移值更有利于队列稳定。我们可以通过调节 Lyapunov 函数中的最终队列长度来优化漂移值，从而实现系统稳定。为了最小化网络时延并最大化用户满意度，定义漂移减收益项为
$$
\triangle (\mathbf {M} (t)) - V \mathbb {E} \left\{\sum_ {m = 0} ^ {M} U _ {m} [ A _ {m} (t) ] \right\}, \tag {19}
$$
其中，$V$ 为非负控制参数，用于调节队列稳定性和用户满意度之间的折中。
定理 2: 定义 $\Delta _ { \mathrm { m a x } }$ 为漂移减收益项的上界。对于任意 $\mathbf { Q } ( t )$ 和 $V \geq 0$，其最大值可表示为
$$
\begin{array}{l} \Delta_ {\max } = \sum_ {m = 0} ^ {M} \left(\mathbb {E} \left\{Q _ {m} (t) A _ {m} (t) - V U _ {m} [ A _ {m} (t) ] | \mathbf {M} (t) \right\} \right. \\ + Z _ {m} (t) \mathbb {E} \left\{Q _ {m} (t) - R _ {m} (p _ {m} (t)) D _ {m, \max} ^ {Q} | \mathbf {M} (t) \right\} \\ \left. - Q _ {m} (t) \mathbb {E} \left\{R _ {m} \left(p _ {m} (t)\right) | \mathbf {M} (t) \right\} + \Theta\right), \tag {20} \\ \end{array}
$$
其中，$\Theta$ 是满足下式约束的正常数:
$$
\begin{array}{l} \Theta \geq \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{R _ {m} ^ {2} \left(p _ {m} (t)\right) + A _ {m} ^ {2} (t) | \mathbf {M} (t) \right\} \\ + \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{\left(R _ {m} \left(p _ {m} (t)\right) D _ {m, \max } ^ {Q}\right) ^ {2} + Q _ {m} ^ {2} (t) | \mathbf {M} (t) \right\}. \tag {21} \\ \end{array}
$$
证明见附录 A。
# C. 联合接入控制与功率控制优化
基于 Lyapunov 优化理论，改写后的目标函数可看作“网络稳定性”“网络时延”和“用户满意度”之间的折中，且优化方案应满足约束 $C 1$、$C 2$ 和 $C 4$。因此，改写后的问题为
$$
\mathbf {P 3}: \min \Delta_ {\max }
$$
$$
\text {s . t .} \quad C 1, C 2, C 4. \tag {22}
$$
问题 P3 可分解为两个相互独立的子问题，即接入控制子问题和功率控制子问题。
1) 接入控制子问题: 接入速率控制子问题表示为
$$
\mathbf {P 4}: \min _ {A _ {m} (t)} \sum_ {m = 0} ^ {M} Q _ {m} (t) A _ {m} (t) - V U _ {m} [ A _ {m} (t) ]
$$
$$
s. t. \quad C 2: 0 \leq A _ {m} (t) \leq A _ {m, \max }, \forall m, t. \tag {23}
$$
2) 功率控制子问题: 目标函数中剩余项为
$$
\begin{array}{l} \sum_ {m = 0} ^ {M} Z _ {m} (t) \left(Q _ {m} (t) - R _ {m} (p _ {m} (t))\right) D _ {m, \mathrm {m a x}} ^ {Q} \\ - \sum_ {m = 0} ^ {M} Q _ {m} (t) R _ {m} \left(p _ {m} (t)\right) + \Theta . \tag {24} \\ \end{array}
$$
由于项 $Z _ { m } ( t ) Q _ { m } ( t )$ 和 $\Theta$ 不含变量，因此功率控制子问题的优化目标可表示为
$$
\sum_ {m = 0} ^ {M} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) R _ {m} \left(p _ {m} (t)\right). \tag {25}
$$
进一步地，功率控制子问题写为
$$
\begin{array}{l} \mathbf {P} 5: \max _ {p _ {m} (t)} \sum_ {m = 0} ^ {M} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) R _ {m} \left(p _ {m} (t)\right) \\ \text {s . t .} \left\{ \begin{array}{l} C 1: 0 \leq p _ {m} (t) \leq p _ {m, \max }, \quad \forall m, t \\ C 4: \Pr \left\{\gamma_ {m} \left(p _ {m} (t)\right) \geq \gamma_ {m, \min } \right\} \geq 1 - \varepsilon , \quad \forall m, t \end{array} \right. \tag {26} \\ \end{array}
$$
# V. 跨层资源优化问题的求解
# A. 接入控制子问题的求解
本文采用 KKT 条件求解优化问题 P4。问题 P4 的拉格朗日函数为
$$
L _ {m} \left(A _ {m} (t)\right) = Q _ {m} (t) A _ {m} (t) - V U _ {m} \left[ A _ {m} (t) \right] \tag {27}
$$
其中，$\nu$ 为拉格朗日乘子，且 $\nu \geq 0$。
式 (27) 关于 $A _ { m } ( t )$ 的一阶导数为
$$
\frac {\partial L _ {m} \left(A _ {m} (t)\right)}{\partial A _ {m} (t)} = Q _ {m} (t) - \frac {V \Omega_ {m}}{A _ {m} (t) \ln 2} = 0. \tag {28}
$$
由此得到语义数据的最优到达速率
$$
A _ {m} ^ {*} (t) = \min \left\{\frac {V \Omega_ {m}}{Q _ {m} (t) \ln 2}, A _ {m, \max } \right\}. \tag {29}
$$
# B. 功率控制子问题的变换
1) 目标函数的连续凸近似: 在功率控制子问题中，目标函数为
$$
\sum_ {m = 0} ^ {M} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \omega \log_ {2} \left(1 + \bar {\gamma} _ {m} (\mathbf {p} (t))\right). \tag {30}
$$
本文采用连续凸近似方法，依据如下不等式对目标函数进行近似:
$$
\log_ {2} (1 + x) \geq \frac {1}{\ln 2} [ X \ln (x) + Y ], \tag {31}
$$
其中，$x > 0$，$X$ 和 $Y$ 为待确定系数。
假设当 $x = \bar { \gamma } _ { m } ( { \mathbf { p } } ( t ) )$ 时取得下界近似的等号形式，则
$$
\log_ {2} (1 + \bar {\gamma} _ {m} (\mathbf {p} (t))) = \frac {1}{\ln 2} [ X _ {m} \ln (\bar {\gamma} _ {m} (\mathbf {p} (t))) + Y _ {m} ]. \tag {32}
$$
根据等式条件，式 (32) 可转化为
$$
\left(\frac {x}{\bar {\gamma} _ {m} (\mathbf {p} (t))}\right) ^ {X _ {m}} \geq \frac {1 + x}{1 + \bar {\gamma} _ {m} (\mathbf {p} (t))}. \tag {33}
$$
对于满足式 (33) 的任意 $X _ { m }$，要获得下界近似，$X _ { m }$ 必须是小于 1 的有效系数。综合分析可得
$$
X _ { m } = \frac { \bar { \gamma } _ { m } ( \mathbf { p } ( t ) ) } { 1 + \bar { \gamma } _ { m } ( \mathbf { p } ( t ) ) },
$$
且
$$
Y _ { m } = \ln ( 1 + { \bar { \gamma } } _ { m } ( \mathbf { p } ( t ) ) ) - X _ { m } \ln ( { \bar { \gamma } } _ { m } ( \mathbf { p } ( t ) ) ).
$$
为获得标准凸目标函数，引入变换 $\tilde { p } _ { m } ( t ) = \ln p _ { m } ( t )$，从而得到关于 $\widetilde { p } _ { m } ( t )$ 的标准凸优化结构，其证明过程见文献 [31]。于是，问题 P5 中目标函数的下界为
$$
\begin{array}{l} \max _ {p _ {m} (t)} \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \\ \cdot \left[ X _ {m} \ln \left(\bar {\gamma} _ {m} \left(e ^ {\tilde {p} _ {m} (t)}\right)\right) + Y _ {m} \right]. \tag {34} \\ \end{array}
$$
2) 概率约束的近似: 为处理含不确定性的概率约束 (10)，本文采用一种凸近似方法，即 Bernstein 近似 [25]。概率约束可改写为
$$
\Pr \left\{\phi_ {0} (\mathbf {p}) + \sum_ {m = 0} ^ {M} \xi_ {m} \phi_ {m} (\mathbf {p}) \leq 0 \right\} \geq 1 - \varepsilon , \tag {35}
$$
其中，$\mathbf { p }$ 为确定性变量向量，$\left\{ \xi _ { m } \right\}$ 为边缘分布为 $\{ \psi _ { m } \}$ 的随机变量。若满足以下条件，则对于给定的一族 $\left\{ \xi _ { m } \right\}$ 分布，不等式 (35) 可以被满足:
1. $\{ \phi _ { m } ( \mathbf { p } ) \}$ 关于 $\mathbf p$ 为仿射函数。
2. $\left\{ \xi _ { m } \right\}$ 相互独立。
3. $\{ \psi _ { m } \}$ 的支撑集有界于 $[ - 1 , 1 ]$，即 $- 1 \leq \psi _ { m } \leq 1 , \forall m = 0 , 1 , \cdots , M$。
定理 3: 通过 Bernstein 近似，不确定概率约束 $\operatorname* { P r } \{ \gamma _ { m } ( p _ { m } ( t ) ) \geq \gamma _ { m , \mathrm { m i n } } \} \geq 1 - \varepsilon$ 可被转化为 $l _ { \infty }$ 近似约束:
$$
\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} e ^ {\tilde {p} _ {n} (t)} + \sqrt {2 \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m} \leq 0. \tag {36}
$$
$$
\delta_ {n, m} \beta_ {n, m} e ^ {\tilde {\rho} _ {n} (t)} \leq \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m}. \tag {37}
$$
证明见附录 B。
结合定理 3 和近似目标函数 (34)，子问题 P5 可进一步转化为
$$
\begin{array}{l} \mathbf {P 6}: \max _ {\tilde {p} _ {m} (t)} \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \\ \cdot \left[ X _ {m} \mathrm {l n} (\bar {\gamma} _ {m} (e ^ {\tilde {p} _ {m} (t)})) + Y _ {m} \right] \\ \text {s . t .} \left\{ \begin{array}{l} \sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} e ^ {\tilde {p} _ {n} (t)} + \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m} \leq 0 \\ \delta_ {n, m} \beta_ {n, m} e ^ {\tilde {p} _ {n} (t)} \leq \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m} \\ - \infty \leq \tilde {p} _ {n} (t) \leq \ln p _ {m, \max }, \quad \forall m, t \end{array} \right. \tag {38} \\ \end{array}
$$
其中，P6 是一个基于 $l _ { \infty }$ 近似的功率控制子问题。
# C. $l _ { \infty }$ 近似功率控制子问题的求解
由于问题 P6 是标准凸问题，本文采用拉格朗日函数方法求解。
定理 4: 通过求解问题 P6 的拉格朗日函数，功率控制的迭代形式可写为
$$
\begin{array}{l} p _ {m} ^ {t _ {\infty}} (t + 1) = \left[ \ln \left(\frac {\omega X _ {m} (t)}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right)\right) \right. \\ - \ln \left(\frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \sum_ {n \neq m} ^ {M} X _ {n} (t) \frac {\bar {\gamma} _ {n} \left(\mathrm {e} ^ {\tilde {\mathbf {p}}}\right) \bar {g} _ {m , n}}{\mathrm {e} ^ {\tilde {p} _ {n}} \bar {g} _ {n , n}} \right. \\ \left. \left. + \sum_ {n = 0} ^ {M} \zeta_ {m} (t) \chi_ {n, m} + \lambda_ {n, m} (t) \sqrt {M} \delta_ {n, m} \beta_ {n, m}\right) \right] _ {- \infty} ^ {\ln p _ {m, \max }} \tag {39} \\ \end{array}
$$
其中，$[ x ] _ { i } ^ { j } = \mathrm { m i n } \{ \mathrm { m a x } \{ x , i \} , j \}$。$\zeta _ { m }$ 和 $\lambda _ { n , m }$ 为拉格朗日乘子，其更新式为
$$
\lambda_ {n, m} (t + 1) = \left[ \lambda_ {n, m} (t) + K _ {\lambda} (t) \left(\sqrt {M} \delta_ {n, m} \beta_ {n, m} \mathrm {e} ^ {\tilde {p} _ {n}} + \varrho\right) \right] ^ {+}, \tag {40}
$$
$$
\zeta_ {m} (t + 1) = (2 \ln (\varepsilon)) ^ {- \frac {1}{2}} \sum_ {n ^ {\prime} = 0} ^ {M} \mu_ {n ^ {\prime}, m} (t + 1), \tag {41}
$$
其中，$K _ { \lambda }$ 表示步长，$\varrho = \frac { \sum _ { m = 0 } ^ { M } \chi _ { n , m } \mathrm { e } ^ { \tilde { p } n } - I _ { t h } } { \sqrt { - 2 \ln ( \varepsilon ) } }$。
证明见附录 C。
# D. 鲁棒资源分配算法
本文构建了长期跨层资源分配问题 (14)，并提出一种鲁棒资源分配算法对其求解。首先设置一系列初值，包括最大时隙数 $T$、数据队列初始长度 $Q _ { m } ( 0 )$、初始功率 $\tilde { p } _ { m } ( 0 )$ 以及步长 $K$。根据式 (29)，可得到应用层的最优到达速率。然后，更新 $l _ { \infty }$ 近似下的拉格朗日乘子 $\lambda _ { n , m } ( t + 1 )$。进一步地，根据式 (39) 更新功率迭代值 $p _ { m } ( t + 1 )$。最终，基于 Lyapunov 优化框架的算法如下所示。
# VI. 仿真与性能评估
本文通过数值仿真验证所提鲁棒资源分配算法的有效性。首先，交通语义数据的提取过程已在第 III 节图 2 中展示。在该过程中，采用端到端场景图生成模型 Relation Transformer for Scene Graph Generation（RelTR），并将场景图生成视为集合预测问题。编码器对视觉特征上下文进行推理，并输出一组固定大小的三元组。在 D2D-V 网络中，本文构建了一个包含 1 个 CUE 和 4 对 D2D-V 的简化通信模型，且这些用户均位于基站通信覆盖范围内。部分系统参数如表 II 所示。
# 算法 1: 鲁棒资源分配算法
1: 初始化
• 设置 $T = 1 0 0$，$t \gets 1$。
• 设置 $Q _ { m } ( 0 ) = 2 0$，$\tilde { p } _ { m } ( 0 ) = - 8$。
• 设置 $K _ { \mu } = 0 . 1$，$K _ { \lambda } = 0 . 1$。
2: 为 $l _ { \infty }$ 近似初始化 $\lambda _ { n , m } > 0$。
3: 当 ($A _ { m }$ 和 $p _ { m }$ 尚未收敛) 且 $t < T$ 时
4: 对所有 $t \in \mathcal T$ 执行
5: 根据式 (29) 计算最优到达速率 $A _ { m } ( t )$。
6: 根据式 (40) 和式 (41) 更新 $\lambda _ { n , m } ( t + 1 )$ 与 $\zeta _ { m } ( t + 1 )$。
7: 根据式 (39) 计算最优功率 $p _ { m } ( t + 1 )$。
8: end for
9: 设置 $t = t + 1$。
10: end while
表 II 系统参数
<table><tr><td>参数</td><td>取值</td></tr><tr><td>SINR 门限 (γm,min)</td><td>0.9</td></tr><tr><td>时延门限 (Dm,max)</td><td>0.1s</td></tr><tr><td>带宽 (ω)</td><td>10 MHz</td></tr><tr><td>中断概率门限 (ε)</td><td>0.1</td></tr><tr><td>背景噪声 (δ2)</td><td>-30 dBm</td></tr><tr><td>控制参数 (V)</td><td>75</td></tr><tr><td>与业务相关的权重参数 (Ωm)</td><td>1</td></tr><tr><td>最大发射功率 (pm,max)</td><td>0.02 W</td></tr><tr><td>载波频率 (fc)</td><td>2 GHz</td></tr><tr><td>反馈时间间隔 (Tf)</td><td>2 ms</td></tr><tr><td>CUE 速度</td><td>0 m/s</td></tr><tr><td>四对 D2D-V 的速度</td><td>34, 30, 32, 30 m/s</td></tr><tr><td>阴影衰落 Lm,n</td><td>0.5</td></tr><tr><td>路径损耗指数 αm</td><td>2</td></tr></table>
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/52212a47eb38b309a2aaa3310d8c40d8eb11ffc9e80d253f9528313e2d96716b-252bb788c33e.jpg)
图 4. 语义接入速率的动态收敛。
由于接入的语义图像数据量仍然较大，因此本文联合采用接入控制与功率控制来控制队列长度，并优化跨层性能指标。如图 4 和图 5 所示，语义数据接入速率以及 CUE 和 VUE 的发射功率都能在若干步内实现动态收敛。图 6、图 7 和图 8 分别给出了数据队列、虚拟队列和时延的动态收敛性能。数据队列和虚拟队列的积压均在若干步内实现了动态收敛，且所有用户的时延都达到理想值，低于时延门限 $D _ { m , \mathrm { m a x } }$。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/99a812b2e2eaf390a275d01b1bca6989602d904d4c17be39176087da0cd6d6d3-de55d7082ad4.jpg)
图 5. 功率的动态收敛。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/9a90d2e5d6a7a01431b7021893e0d58f9a06c8becf43c4b7a06590174df4f11d-b1141160da6d.jpg)
图 6. 数据队列的动态收敛。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/df1e33ef2a823e7825818dbf53533c0c633d806595d11d71556e6c8e3babb40f-d197f5881b05.jpg)
图 7. 虚拟队列的动态收敛。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/db0f3506bf92679acd60c62a9c7970cd6274afc6492bfcaf99335b9442c720bd-d7d899372357.jpg)
图 8. 时延的动态收敛。
因此，这些图中的结果表明，所提出的基于 $l _ { \infty }$ 近似的鲁棒资源分配算法是有效的，并表现出快速收敛速度。需要指出的是，长期优化方案不同于传统短时优化方案。为了应对不确定信道变化，功率策略必须进行动态调整，因此动态策略在长期场景中提供了更强鲁棒性。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/fbc92242d136a686756b124108f6f8793a615ecbcbea382cd8ddffa4bfdbb15c-122a3d075efe.jpg)
图 9. 长期总传输速率与中断概率门限 ε 的关系。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/9bfe3357bfb469851f98a3b101124010a52d52beaf8f1eaf962ee8ab4738f528-b4281d6041c1.jpg)
图 10. 长期平均时延与中断概率门限 $\varepsilon$ 的关系。
图 9 和图 10 说明了中断概率门限 $\varepsilon$ 对长期平均总传输速率和时延的影响。由图 9 可知，当中断概率门限 $\varepsilon$ 增大时，总传输速率更高。更大的 $\varepsilon$ 意味着变量 $p _ { m }$ 的可行范围扩大，因此最优功率会在更大的区域内搜索，从而更有利于提升目标函数。就此而言，目标函数与接入速率正相关。当系统稳定时，输入和输出也达到动态平衡，因此 $\varepsilon$ 的增加会提高接入速率，进而提高总传输速率。如图 10 所示，随着 $\varepsilon$ 增加，CUE 和 4 个 VUE 的平均时延也随之上升。这是因为 $\varepsilon$ 的增大带来了更大的队列积压，即使传输速率提升，平均时延仍会增加。综合分析图 9 和图 10 可得出结论: 在 D2D-V 通信系统中，传输速率与时延相互制约，传输速率的提升会导致时延性能的损失，这进一步说明了系统性能折中的重要性。
本文利用一阶 Gauss-Markov 过程描述具有不完美 CSI 的信道环境，并提出基于 $l _ { \infty }$ 近似的鲁棒资源分配算法。为说明考虑信道不确定性的必要性，本文与假设完美 CSI 的基准方案 [15] 进行了对比。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/7295a615ab43f1fd77349c14dffef954cd7fc7250d2ffe6f33e0c0815984e193-52f1cd9811f5.jpg)
图 11. 不同方案下用户实际中断概率比较。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/6590774c0c090c5e5d9559df00fbc55b97875cf0852677728be998c384050a9c-ca40a5392733.jpg)
图 12. 不同方案下用户功率比较。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/03b24478c4d4994ab28d65f0a3158389295e7d25ecd63f18e30a4ccdd3de262f-f49fd024179d.jpg)
图 13. 不同方案下用户传输速率比较。
此外，还将另一种利用 $\| \mathbf { z } \| _ { 2 } \leq \| \mathbf { z } \| _ { 1 }$ 将 $l _ { 2 }$ 范数结构转化的 $l _ { 1 }$ 近似方法 [25] 与本文方法进行了对比。在相同目标概率 $\varepsilon = 0 . 1$ 下，对实际中断概率进行了比较。由图 11 可知，$l _ { \infty }$ 近似算法的实际中断概率低于 $l _ { 1 }$ 近似算法，且显著低于基准方案 [15]。根据问题 P1 中的约束 $C 4$，实际中断概率越低意味着对 SINR 约束的保障越好，系统鲁棒性越强。因此，本文方法比基准方案 [15] 和 $l _ { 1 }$ 近似方法 [25] 能实现更稳定的信号传输。
其他性能指标的比较结果如图 12、图 13 和图 14 所示。通过比较 $l _ { \infty }$ 近似和 $l _ { 1 }$ 近似可知，$l _ { \infty }$ 近似算法在传输速率和时延性能方面更优。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/eba3e19c2f44fb99e982fd776e204f9c5f350c5f0d9fd811d45439933dc0deef-d7378bfab53c.jpg)
图 14. 不同方案下用户时延比较。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/393ab5cb3505e92b66f7bdc1a0fb97e7b546331f191bf57f717ac62dc7c4a9c8-f810b80cbf4d.jpg)
图 15. 不同车速下的总传输速率比较。
进一步地，与 $l _ { \infty }$ 近似算法相比，三幅图表明基准方案 [15] 消耗了更多发射功率，但并未获得明显的性能提升。这是因为完美 CSI 的假设并不现实，用户往往倾向于通过过度提高功率来提升传输速率。然而，更高功率也会带来更强的多级干扰，从而对不同用户的传输速率和时延性能产生不同程度的负面影响。因此，在实际通信环境中，完美 CSI 假设往往表现出不稳定且不理想的性能。综合图 11、图 12、图 13 和图 14 的分析可知，$l _ { \infty }$ 近似算法整体优于基准方案 [15]，尤其在系统鲁棒性和功耗方面更具优势。
为验证车辆移动性对总传输速率的影响，本文在 D2D-V 通信场景中仿真了不同级别的车速。在该仿真中，假设网络拓扑相同，所有 VUE 的速度一致。由于 CUE 的移动速度较低，因此将其视为静止。统一设置车辆速度分别为 0、10、20 和 $3 0 ~ \mathrm { m / s }$。如图 15 所示，当车速增加时，无论是本文的 $l _ { \infty }$ 近似方法，还是文献 [25] 的 $l _ { 1 }$ 近似方法，总传输速率都会下降。这是因为更高速度会导致更严重的多普勒效应，恶化信道环境，使通信链路承受更强的同信道干扰。因此，在信道状态精确描述和性能提升中考虑车辆移动特性是必要的。
# VII. 结论
本文展示了交通语义数据的提取过程，并进一步通过 D2D 通信传输提取后的语义数据。基于 Lyapunov 优化理论，设计了一种长期动态跨层资源分配框架，其中包括语义接入控制方案和功率控制方案。本文提出了一种鲁棒在线资源分配算法，以实现实时优化策略。仿真结果表明，在不确定信道环境下，所提算法具有良好的收敛性能。仿真还验证了数据队列保持稳定，低时延、高可靠性的语义通信能够得以实现，并满足用户 QoS 要求，尤其在系统鲁棒性和功耗方面优于基准方案。总体而言，所提算法适用于存在多用户干扰和信道不确定性的通信环境。通过调节 Lyapunov 控制参数，可以实现用户满意度最大化、队列稳定性和时延最小化之间的折中。
# 附录 A
证明: 假设 $A$、$B$ 和 $C$ 为非负实数，则显然有
$$
\left(\max \{A - B, 0 \} + C\right) ^ {2} \leq A ^ {2} + B ^ {2} + C ^ {2} + 2 A (C - B). \tag {42}
$$
根据式 (42)，可得
$$
\begin{array}{l} \triangle (\mathbf {M} (t)) = \mathbb {E} \left\{L (\mathbf {M} (t + 1)) - L (\mathbf {M} (t)) | \mathbf {M} (t) \right\} \\ \leq \sum_ {m = 0} ^ {M} \mathbb {E} \left\{Q _ {m} (t) A _ {m} (t) | \mathbf {M} (t) \right\} \\ + \sum_ {m = 0} ^ {M} Z _ {m} (t) \mathbb {E} \left\{Q _ {m} (t) - R _ {m} \left(p _ {m} (t)\right) D _ {m, \max } ^ {Q} | \mathbf {M} (t) \right\} \\ - \sum_ {m = 0} ^ {M} Q _ {m} (t) \mathbb {E} \left\{R _ {m} \left(p _ {m} (t)\right) | \mathbf {M} (t) \right\} + \Theta \tag {43} \\ \end{array}
$$
其中，$\Theta$ 为满足下式的正常数:
$$
\begin{array}{l} \Theta \geq \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{R _ {m} ^ {2} \left(p _ {m} (t)\right) + A _ {m} ^ {2} (t) | \mathbf {M} (t) \right\} \\ + \frac {1}{2} \sum_ {m = 0} ^ {M} \left\{\left(R _ {m} \left(p _ {m} (t)\right) D _ {m, \max } ^ {Q}\right) ^ {2} + Q _ {m} ^ {2} (t) | \mathbf {M} (t) \right\}. \tag {44} \\ \end{array}
$$
将 $\begin{array} { r } { V \mathbb { E } \{ \sum _ { m = 0 } ^ { M } U _ { m } [ A _ { m } ( t ) ] \} } \end{array}$ 同时加到式 (43) 两边，即可得到式 (20)。
# 附录 B
证明: 对式 (35) 的保守近似为
$$
\inf _ {\rho > 0} \left[ \phi_ {0} (\mathbf {p}) + \rho \sum_ {n = 0} ^ {N} \iota_ {m} \left(\rho^ {- 1} \phi_ {n} (\mathbf {p})\right) + \rho \ln \left(\frac {1}{\varepsilon}\right) \right] \leq 0, \tag {45}
$$
其中，$\iota _ { m } ( y ) = \operatorname* { m a x } _ { \psi _ { m } } \ln ( \int \exp ( x y ) d \psi _ { m } ( x ) )$，$\rho$ 为保守近似参数，$\mathbf { p } = [ p _ { 1 } , p _ { 2 } , \dots , p _ { m } ]$ 为发射功率向量。
进一步地，可利用 $\iota _ { m } ( y )$ 的上界完成变换:
$$
\iota_ {m} (y) \leq \max \left\{o _ {m} ^ {-} y, o _ {m} ^ {+} y \right\} + \frac {\delta_ {m} ^ {2}}{2} y ^ {2}, m = 0, 1, \dots , M, \tag {46}
$$
其中，$o _ { m } ^ { - }$、$o _ { m } ^ { + }$ 和 $\delta _ { m }$ 均为常数，并由给定分布族确定，满足 $- 1 \leq o _ { m } ^ { - } \leq o _ { m } ^ { + } \leq 1$，$\delta _ { m } \geq 0$。
将式 (46) 中 $\iota _ { m } ( \cdot )$ 替换为其上界后，式 (45) 的凸保守代理可改写为
$$
\begin{array}{l} \phi_ {0} (\mathbf {p} (t)) + \sum_ {m = 0} ^ {M} \max \left\{o _ {m} ^ {-} \phi_ {m} (\mathbf {p} (t)), o _ {m} ^ {+} \phi_ {m} (\mathbf {p} (t)) \right\} \\ + \sqrt {2} \ln \left(\frac {1}{\varepsilon}\right) \left(\sum_ {m = 0} ^ {M} \left(\delta_ {m} \phi_ {m} (\mathbf {p} (t))\right) ^ {2}\right) ^ {\frac {1}{2}} \leq 0. \tag {47} \\ \end{array}
$$
优化问题中第 $m$ 条信号链路的中断概率约束可以重写为矩阵形式:
$$
\Pr \left\{\left(\mathbf {G} _ {m}\right) ^ {T} \mathbf {p} + \sigma^ {2} \leq 0 \right\} \geq 1 - \varepsilon , \tag {48}
$$
其中，$\mathbf { G } _ { m } = [ g _ { 0 , m } , g _ { 1 , m } , \ldots , - \frac { g _ { m , m } } { \gamma _ { m , \mathrm { m i n } } } , \ldots , g _ { M , m } ]$。这里假设 $\tilde { g } _ { n , m }$ 的取值范围为 $[ a _ { n , m } , b _ { n , m } ]$，构造 $\beta _ { m , n } = \frac { 1 } { 2 } ( b _ { m , n } - a _ { m , n } ) \neq 0$ 和 $\varpi _ { n , m } = \frac { 1 } { 2 } ( b _ { n , m } + a _ { n , m } )$，用于归一化支撑集 $\psi _ { n , m }$，即
$$
\psi_ {n, m} = \frac {\tilde {g} _ {n , m} - \varpi_ {n , m}}{\beta_ {n , m}} \in [ - 1, 1 ]. \tag {49}
$$
令 $\phi _ { 0 } ( \mathbf { p } ( t ) ) = \sigma ^ { 2 } + \sum _ { i = 0 } ^ { N } ( \hat { g } _ { m , n } + \varpi _ { m , n } ) p _ { m } ( t )$，$\phi _ { m } ( \mathbf { p } ( t ) ) = \beta _ { m , n } p _ { m } ( t )$，则式 (47) 与问题 $\mathbf { P 5 }$ 中约束 $C 4$ 等价。于是，将 $f _ { 0 } ( \mathbf { p } )$ 和 $f _ { m } ( \mathbf { p } )$ 代入式 (47) 后，可得
$$
\begin{array}{l} \sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} p _ {n} (t) + \sqrt {2 \ln \left(\frac {1}{\varepsilon}\right)} \\ \left(\sum_ {n = 0} ^ {M} \left(\delta_ {n, m} \beta_ {n, m} p _ {n} (t)\right) ^ {2}\right) ^ {\frac {1}{2}} \leq 0, \tag {50} \\ \end{array}
$$
其中，$\chi _ { n , m } = \hat { g } _ { n , m } + \varpi _ { n , m } + v _ { m } ^ { + } \beta _ { n , m }$。在式 (50) 中，功率变量之间的耦合给求解带来了较高计算复杂度。为降低复杂度，根据 $\| \mathbf { z } \| _ { 2 } \leq \sqrt { N } \| \mathbf { z } \| _ { \infty }$，可将式 (50) 中的 $l _ { 2 }$ 范数结构进一步转化为 $l _ { \infty }$ 近似问题:
$$
\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} p _ {n} (t) + \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \max _ {n \in \mathcal {M}} \delta_ {n, m} \beta_ {n, m} p _ {n} (t) \leq 0 \tag {51}
$$
通过设置辅助变量 $\pmb { v } = [ v _ { 0 , m } , v _ { 1 , m } , \dots , v _ { M , m } ]$，式 (51) 中的 $l _ { \infty }$ 近似约束可进一步改写为下列可分离约束:
$$
\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} p _ {n} (t) + \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m} \leq 0 \tag {52}
$$
$$
\delta_ {n, m} \beta_ {n, m} p _ {n} (t) \leq \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m} \tag {53}
$$
令 $\tilde { p } _ { n } ( t ) = \ln p _ { n } ( t )$，即可得到式 (36) 和式 (37)。
# 附录 C
证明: 由于 P6 是凸问题，其拉格朗日函数如下:
$$
\begin{array}{l} L (\tilde {p} _ {m} (t): \lambda_ {n, m}, \zeta_ {m}) = \\ \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} \left(Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)\right) \left[ X _ {m} \ln \left(\bar {\gamma} _ {m} \left(e ^ {\tilde {p} _ {m} (t)}\right)\right) + Y _ {m} \right] \\ - \sum_ {m = 0} ^ {M} \zeta_ {m} \left(\sigma^ {2} + \sum_ {n = 0} ^ {M} \chi_ {n, m} e ^ {\tilde {p} _ {m} (t)} \sqrt {2 M \ln \left(\frac {1}{\varepsilon}\right)} \sum_ {n = 0} ^ {M} v _ {n, m}\right) \\ - \sum_ {m = 0} ^ {M} \sum_ {N = 0} ^ {M} \lambda_ {n, m} \left(\delta_ {n, m} \beta_ {n, m} e ^ {\tilde {p} _ {m} (t)} - \sum_ {n ^ {\prime} = 0} ^ {M} v _ {n ^ {\prime}, m}\right), \tag {54} \\ \end{array}
$$
其中，$\lambda _ { n , m } \geq 0$，$\zeta _ { m } \geq 0$。对应的对偶函数为
$$
\begin{array}{l} D \left(\lambda_ {n, m}, \zeta_ {m}\right) = \max _ {- \infty \leq \tilde {p} _ {i} \leq \ln p _ {i, m a x}} L \left(\tilde {p} _ {m} (t): \lambda_ {n, m}, \zeta_ {m}\right) \\ = \max _ {- \infty \leq \tilde {p} _ {i} \leq \ln p _ {i, m a x}} \sum_ {m = 0} ^ {M} \frac {\omega}{\ln 2} (Z _ {m} (t) D _ {m, \max } ^ {Q} + Q _ {m} (t)) \\ \cdot \left[ X _ {m} \ln (\bar {\gamma} _ {m} (e ^ {\tilde {p} _ {m} (t)})) + Y _ {m} \right] - \sum_ {m = 0} ^ {M} \zeta_ {m} \sigma^ {2} \\ - \sum_ {m = 0} ^ {M} \sum_ {n = 0} ^ {M} \left(\zeta_ {m} \chi_ {n, m} + \lambda_ {n, m} \sqrt {M} \delta_ {n, m} \beta_ {n, m}\right) \mathrm {e} ^ {\tilde {p} _ {n}} \\ + \sum_ {m = 0} ^ {M} \sum_ {n = 0} ^ {M} \left(\sum_ {n ^ {\prime} = 0} ^ {M} \lambda_ {n ^ {\prime}, m} - \zeta_ {m} \sqrt {2 \ln \left(\frac {1}{\varepsilon}\right)}\right) v _ {n, m}. \tag {55} \\ \end{array}
$$
进一步地，式 (25) 的对偶问题为
$$
\min _ {\lambda_ {n, m} > 0, \zeta_ {m} > 0} D \left(\lambda_ {n, m}, \zeta_ {m}\right). \tag {56}
$$
幂向量 $\tilde { \mathbf { p } }$ 的迭代函数可通过下式得到:
$$
\begin{array}{l} \frac {\partial L (\tilde {p} _ {m} (t) : \lambda_ {n , m} , \zeta_ {m})}{\partial \tilde {p} _ {m}} = \frac {\omega X _ {m}}{\ln 2} (Z _ {m} (t) D _ {m, \mathrm {m a x}} ^ {Q} + Q _ {m} (t)) \\ - \left(\frac {\omega}{\ln 2} (Z _ {m} (t) D _ {m, \mathrm {m a x}} ^ {Q} + Q _ {m} (t)) \sum_ {n \neq m} ^ {M} X _ {n} \frac {\bar {\gamma} _ {n} (\mathrm {e} ^ {\tilde {\mathbf {p}} (t)}) \overline {{g}} _ {m , n}}{\mathrm {e} ^ {\tilde {p} _ {n} (t)} \overline {{g}} _ {n , n}} \right. \\ + \sum_ {n = 0} ^ {M} \zeta_ {m} ^ {(t)} \chi_ {m, n} + \sum_ {n = 0} ^ {M} \mu_ {m, n} ^ {(t)} (\sqrt {M} \sigma_ {m, n} \alpha_ {m, n}) \mathrm {e} ^ {\tilde {\rho} _ {m}} = 0, \tag {57} \\ \end{array}
$$
其中，$\overline { { g } } _ { m , n }$ 和 $\overline { { g } } _ { n , n }$ 分别是 $g _ { m , n }$ 和 $g _ { n , n }$ 的期望值，即 $\overline { { g } } _ { m , n } = \mathbb { E } \{ g _ { m , n } \}$，$\overline { { g } } _ { n , n } = \mathbb { E } \{ g _ { n , n } \}$。此外，平均 SINR 表示为
$$
\bar {\gamma} _ {n} \left(\mathrm {e} ^ {\tilde {\mathbf {p}} (t)}\right) = \frac {\mathrm {e} ^ {\tilde {p} _ {n} (t)} \bar {g} _ {n , n}}{\sum_ {m \neq n} ^ {M} \mathrm {e} ^ {\tilde {p} _ {m} (t)} \bar {g} _ {m , n} + \delta^ {2}}. \tag {58}
$$
令 $\frac { \partial L ( \tilde { p } _ { m } ( t ) : \lambda _ { n , m } , \zeta _ { m } ) } { \partial \tilde { p } _ { m } } = 0$，即可得到功率和拉格朗日乘子的迭代式，即式 (39)、式 (40) 和式 (41)。
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[29] Y. Mao, J. Zhang, Y. Li, and K. Letaief, “A Lyapunov optimization approach for green cellular networks with hybrid energy supplies,” IEEE J. Sel. Areas Commun., vol. 33, no. 12, pp. 2463–2477, Dec. 2015.
[30] M. Neely, Stochastic Network Optimization With Application to Communication and Queueing Systems. San Rafael, CA, USA: Morgan & Claypool, 2010.
[31] J. Papandriopoulos and J. Evans, “Low-complexity distributed algorithms for spectrum balancing in multi-user DSL networks,” in Proc. IEEE Int. Conf. Commun., 2006, pp. 3270–3275.
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/4baa31a1a55818c630239c728ab0af8fbb7d9d93bdcbbbdc133864be753f91d6-ef2520fcccf3.jpg)
Jiawei Su 于 2019 年获得中国秦皇岛燕山大学自动化学士学位，现于燕山大学攻读控制科学与工程博士学位。其研究方向包括车联网与 D2D 通信。
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Zhixin Liu（IEEE 高级会员）分别于 2000 年、2003 年和 2006 年获得中国秦皇岛燕山大学控制理论与控制工程学士、硕士和博士学位。现任燕山大学电气工程学院教授。2009 年至 2010 年曾访问加拿大阿尔伯塔大学。其研究方向包括无线网络性能优化与资源分配。
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Yuan-ai Xie 于 2022 年获得中国秦皇岛燕山大学控制科学与工程博士学位。2021 年至 2022 年期间，他曾作为访问博士生在新加坡南洋理工大学学习。2023 年加入中国武汉中南民族大学计算机科学学院。其研究方向包括车联网中的无线资源优化与物理层安全。
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Kai Ma（IEEE 会员）分别于 2005 年和 2011 年获得中国燕山大学自动化学士学位和控制科学与工程博士学位。2013 年至 2014 年曾在新加坡南洋理工大学从事博士后研究。现任燕山大学电气工程学院教授。其研究方向包括智能电网需求响应和通信网络资源分配。
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Jiawen Kang（IEEE 会员）于 2018 年获得中国广州广东工业大学博士学位。2018 年至 2021 年，他在新加坡南洋理工大学从事博士后研究。现任广东工业大学教授。其研究方向主要集中于无线通信与网络中的区块链、安全与隐私保护。
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Hongyang Du（IEEE 学生会员）于 2021 年获得中国北京北京交通大学理学学士学位。现于新加坡南洋理工大学计算机科学与工程学院跨学科研究生项目攻读博士学位。其研究方向包括语义通信、可重构智能表面和通信理论。其于 2022 年获得 IEEE Daniel E. Noble Fellowship Award。
![](https://r2.118229.xyz/2026/04/17/semantic-communication-based-dynamic-resource-al/2819faeb6ca12e1735ea9c50d52d57baa847bafaabd5cc8880e916020250021e-389f8cf2a6e1.jpg)
Dusit Niyato（IEEE Fellow）于 1999 年获得泰国曼谷 King Mongkut’s Institute of Technology Ladkrabang（KMITL）工学学士学位，并于 2008 年获得加拿大曼尼托巴大学电子与计算机工程博士学位。现任新加坡南洋理工大学计算机科学与工程学院教授。其研究方向包括物联网（IoT）、机器学习和激励机制设计。

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