Distribution on the Pareto Boundary for Integrated Sensing and Communication System

Integrated sensing and communication (ISAC) has emerged as a promising technology for realizing beyond fifth-generation (B5G) and sixth-generation (6G) wireless networks due to its ability of significantly improving both communication and sensing performances. In this paper, we study the distribution on the performance Pareto boundary for a general ISAC scenario, a dual-functional BS simultaneously estimates the target response matrix while communicating with a user. First, we investigate the effect of randomness of random signals on sensing performance and use the lower bound of minimum mean square error (MMSE) to measure sensing performance. Then, taking the transmit signal's distribution as the optimization variable, we establish the optimization problem to realize the Pareto performance boundary. Subsequently, we show that the optimal distribution is the discrete distribution with finite mass points in single-input single-output (SISO) ISAC and discrete in amplitude and uniform in phase (DAUP) in multiple-input multiple-output (MIMO) ISAC. Finally, we give simulation results and provide insights into deterministic-randomness tradeoff (DRT) through analyzing changes of the distribution on the performance Pareto boundary.