Multi-Objective Optimization for Joint Communication and Sensing in Multi-user MIMO Systems: Characterizing the Pareto Boundary

This paper investigates the Pareto boundary performance of a joint communication and sensing (JCAS) system that addresses both sensing and communication functions at the same time. In this scenario, a multiple-antenna base station (BS) transmits information to multiple single-antenna communication users while concurrently estimating the parameters of a single sensing object using the echo signal. We present an integrated beamforming approach for JCAS in a multi-user multiple-input and multiple-output (MIMO) system. The performance measures for communication and sensing are Fisher information (FI) and mutual information (MI). Our research considers two scenarios: multiple communication users with a single sensing object and a single communication user with a single sensing object. We formulate a multi-objective optimization problem to maximize the weighted sum of MI and FI, subject to a total transmit power budget for both cases. As a particular case, we address the equivalent isotropic radiated power (EIRP) for the single communication user scenario. We use the uplink-downlink duality for the multi-user case to simplify the problem and apply Lagrangian optimization and line search methods with a block-coordinate ascending technique. We use projected gradient descent (PGD) to solve the optimization problem in the single-user case. Our numerical results demonstrate that joint beamforming is optimal for the multi-user JCAS system, as opposed to independent beamforming for each user and the sensing object. Furthermore, we reveal the Pareto boundary for the multi-user case, with variations in the number of communication users and the number of transmitting and receiving antennas. We provide the Pareto boundary depending on EIRP limitations for the single-user case.