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

TL;DR

This work investigates joint communication and sensing (JCAS) in multi-user MIMO systems, aiming to characterize the Pareto boundary between Mutual Information ($MI$) for communication and Fisher Information ($FI$) for sensing. It develops a joint beamforming framework that maximizes a weighted sum of $MI$ and $FI$ under a total transmit power budget, solving the multi-user case via uplink–downlink duality, Lagrangian optimization, and block-coordinate ascent, and the single-user case via projected gradient descent with an $EIRP$ constraint. The analysis shows that, for the multi-user scenario, the optimal downlink covariances are rank-1 and a dedicated sensing beam is unnecessary, yielding a Pareto boundary that shifts with the numbers of transmit/receive antennas and users. Simulations demonstrate that joint beamforming outperforms independent designs, and the Pareto boundary broadens with larger antenna arrays and higher $EIRP$, providing actionable guidance for real deployments. The paper contributes a tractable optimization framework for balancing $MI$ and $FI$ in MIMO JCAS and lays the groundwork for future extensions to more complex sensing environments.

Abstract

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.

Figures (9)

• Figure 1: Joint communication and sensing model of MIMO BC.
• Figure 2: Comparison between optimal and sub-optimal beamforming for various numbers of users in terms of the trade-off between sum rate and Fisher Information
• Figure 3: Comparison between optimal and sub-optimal beamforming for various numbers of transmitting and receiving antennas in terms of the trade-off between sum-rate and Fisher Information
• Figure 4: Variation of trade-off with number of communication users
• Figure 5: Variation of trade-off with transmit power budget