含导频和数据载荷的OFDM信号模糊函数分析
Ambiguity Function Analysis of OFDM Signals With Pilots and Data Payloads
- National Mobile Communications Research Laboratory, Southeast University（东南大学国家移动通信重点实验室）
- School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）
- School of Information and Electronic Engineering, Beijing University of Posts and Telecommunications（北京邮电大学信息与电子工程学院）
- Southeast University（东南大学）
- Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文分析含导频和数据载荷的OFDM信号在ISAC中的模糊函数，推导两种离散AF的期望旁瓣表达式，证明规则导频图案产生高旁瓣，并提出不规则导频放置可改善目标估计性能。
AI中文摘要：
实际的正交频分复用（OFDM）通信帧同时包含确定性的导频和随机数据载荷，这促使当整个帧被重新用于集成感知与通信（ISAC）时，需要对这两个组成部分进行联合模糊函数（AF）分析。本文针对不同的多普勒体制，刻画了两种离散模糊函数形式，即离散周期模糊函数（DP-AF）和快慢时间模糊函数（FST-AF），并推导了它们期望平方值的闭式表达式。对于FST-AF，期望旁瓣电平（ESL）在时延-多普勒平面上是均匀的，且仅取决于导频数量、星座峰度和时频资源总数，而与导频符号或导频图案无关。对于DP-AF，我们建立了可达到的ESL下界和上界，并表明没有任何导频设计能同时最小化所有旁瓣。我们进一步证明，在非零多普勒处达到下界需要周期性导频图案，而等间隔的线性调频导频（包括Zadoff-Chu（ZC）序列）能同时最大化达到下界和上界的旁瓣数量。随后研究了通信帧中常见的两种代表性ZC导频图案：连续放置产生由平方Dirichlet核描述的时延-多普勒脊，而等间隔放置则产生周期性的峰谷结构。两种规则图案都表现出显著的高旁瓣，这表明面向通信的导频图案应在ISAC背景下为时延-多普勒估计而重新设计。数值结果验证了分析，并表明不规则导频放置能抑制高旁瓣并改善目标估计性能。
英文摘要：
Practical orthogonal frequency division multiplexing (OFDM) communication frames contain both deterministic pilots and random data payloads, motivating the joint ambiguity function (AF) analysis of the two components when the entire frame is reused for integrated sensing and communication (ISAC). This paper characterizes two discrete AF formulations for different Doppler regimes, namely the discrete periodic AF (DP-AF) and fast-slow-time AF (FST-AF), and derives closed-form expressions for their expected squared values. For the FST-AF, the expected sidelobe level (ESL) is uniform over the delay-Doppler plane and depends only on the pilot count, constellation kurtosis and total number of time-frequency resources, but not on the pilot symbols or pattern. For the DP-AF, we establish attainable lower and upper ESL bounds and show that no pilot design can minimize all sidelobes simultaneously. We further prove that attaining the lower bound at non-zero Doppler requires a periodic pilot pattern, while equally spaced chirp pilots, including Zadoff-Chu (ZC) sequences, maximize the numbers of sidelobes attaining the lower and upper bounds simultaneously. Two representative ZC pilot patterns widely encountered in communication frames are then examined: contiguous placement produces delay-Doppler ridges described by squared Dirichlet kernels, whereas equally spaced placement generates periodic peak-and-notch structures. Both regular patterns exhibit pronounced high sidelobes, suggesting that communication-oriented pilot patterns should be re-designed for delay-Doppler estimation in the context of ISAC. Numerical results validate the analysis and show that irregular pilot placement can suppress high sidelobes and improve target estimation performance.
