Waveform Design Based on Probabilistic Shaping for ISAC Systems with Finite Constellations

This paper investigates an integrated sensing and communication (ISAC) system with finite constellations. Both the problems of performance loss caused by discrete inputs and the conflicting requirements on symbol distribution of sensing and communication (S&C) functionalities are considered. Towards this, a waveform design based on the probabilistic shaping (PS) scheme is proposed, where a base station sends unified signals to estimate a sensing target and communicate with a user simultaneously. The analytical closed-form expressions of the sensing estimation rate (SER) and communication ergodic rate for PS-based ISAC are derived to evaluate the performance of the S&C functionalities, which are found to be mutually influenced by both the probability mass function (PMF) and power scaling factor. Furthermore, the optimal PMF and scaling factor are obtained by the alternative optimization algorithm to maximize SER while preserving communication capability. Simulation results validate the efficiency of our proposed PSbased waveform compared with those of schemes based on other input distributions. Additionally, the performance limit of ISAC systems with finite constellations is numerically obtained, which characterizes the tradeoffs between S&C functionalities.