A Rate-Distortion Bound for Integrated Sensing and Communication

Abstract

We develop a general rate--distortion bound (RDB) for the fundamental sensing--communication tradeoff in integrated sensing and communication (ISAC) systems. The RDB lower-bounds the Bayesian sensing risk for arbitrary parameter alphabets, sensing-channel laws, and distortion measures without requiring regularity conditions on the parameter distribution. A key feature is that the distortion--rate function is applied to the sensing information induced by each transmitted signal before averaging. This preserves signal-dependent sensing information and yields a bound that is no weaker, and potentially strictly tighter, than one based only on average sensing information. The RDB is exact in the high-sensing-noise limit and, under scalar squared-error loss, its entropy-power specialization is no looser than the Bayesian Cramér--Rao bound (BCRB). Applications to binary occupancy detection and multiple-input multiple-output (MIMO) Nakagami target-response estimation demonstrate its scope, including discrete sensing and severe fading regimes in which the conventional BCRB yields only the trivial zero lower bound. Covariance-based outer bounds and Gaussian and semi-unitary achievable schemes further reveal how signal randomness and spatial energy allocation shape the tradeoff.