Discrete-Periodic Ambiguity Function of Random Communication Signals

This paper investigates the ambiguity function (AF) of communication signals carrying random data payloads, which is a fundamental metric characterizing sensing capability in ISAC systems. We first develop a unified analytical framework to evaluate the AF of communication-centric ISAC signals constructed from arbitrary orthonormal bases and independent identically distributed (i.i.d.) constellation symbols. Subsequently, we derive the discrete periodic ambiguity function (DP-AF) and provide closed-form expressions for its expected integrated sidelobe level (EISL) and average sidelobe level. Notably, we prove that the normalized EISL is invariant across all constellations and modulation bases. Finally, the theoretical findings are validated through simulations.