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arXiv · 2607.17663

Ambiguity Function Analysis of Pilot-Embedded Random OFDM Signals

Jialin Wu·Fan Liu·Ying Zhang·Yifeng Xiong·Jie Yang·Shi Jin
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Abstract

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.

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Jialin Wu, Fan Liu, Ying Zhang, Yifeng Xiong, Jie Yang, Shi Jin. 2026-07-20. Ambiguity Function Analysis of Pilot-Embedded Random OFDM Signals. https://arxiv.org/abs/2607.17663

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