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arxiveess.SP2026-07-20

Ambiguity Function Analysis of Pilot-Embedded Random OFDM Signals

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

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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