嵌入导频的随机OFDM信号的模糊函数分析
Ambiguity Function Analysis of Pilot-Embedded Random OFDM Signals
AI总结：
研究用于ISAC的含导频符号和随机数据载荷的OFDM波形的统计模糊函数，推导其DP-AF和FST-AF的解析表达式，揭示相关依赖关系，数值模拟匹配理论，不同导频模式对应不同DP-AF特性，为导频设计提供参考。
AI中文摘要：
本文研究了用于集成感知与通信（ISAC）的、包含确定性单位模导频符号和随机数据载荷的正交频分复用（OFDM）波形的统计模糊函数（AFs）。我们推导了此类嵌入导频的OFDM信号的均方离散周期模糊函数（DP-AF）和快-慢时模糊函数（FST-AF）的解析表达式。分析表明，在固定信号长度和星座方案下，均方DP-AF联合依赖于导频模式、导频符号和导频数，而均方FST-AF仅依赖于导频数。数值模拟与理论表达式紧密匹配。此外，数值结果表明不同导频模式对应具有不同特性的DP-AF，为以通信为中心的ISAC系统中的导频设计提供了相关考虑。
英文摘要：
This paper investigates the statistical ambiguity functions (AFs) of orthogonal frequency division multiplexing (OFDM) waveforms that incorporate deterministic unit-modulus pilot symbols and random data payloads for integrated sensing and communication (ISAC). We derive analytical expressions for the mean squared discrete periodic ambiguity function (DP-AF) and fast-slow-time ambiguity function (FST-AF) of such pilot-embedded OFDM signals. Our analysis demonstrates that, under a fixed signal length and constellation scheme, the mean squared DP-AF depends jointly on the pilot patterns, pilot symbols and number of pilots, while the mean squared FST-AF relies only on the number of pilots. Numerical simulations closely match the theoretical expressions. Furthermore, in numerical results, we show that different pilot patterns correspond to DP-AF with distinct characteristics, offering relevant considerations for pilot design in communication-centric ISAC systems.
