Transmit Beamforming Design for MIMO-ISAC Systems: A Sensing Mutual Information Optimization Perspective

Abstract

In this paper, we investigate the transmit beamforming design for a general multiple-input multiple-output integrated sensing and communication (MIMO-ISAC) system, where a dual-functional base station (BS) simultaneously communicates with multiple multi-antenna communication users (CUs) and detects the multiple targets in the presence of multiple signal-dependent clutters. In multi-target sensing scenarios, it is essential to ensure a baseline sensing performance for all targets, since the missed detection of even a single target may degrade the reliability of the overall system. To this end, we adopt the max–min fairness (MMF) criterion and formulate a minimum sensing mutual information (SMI) maximization problem under communication quality-of-service (QoS) requirements and a total transmit power constraint. Unlike conventional CVX-based methods, we develop a novel low-complexity algorithm that integrates epigraph reformulation, matrix fractional programming (FP), and the projected extragradient (PEG) method to efficiently handle the formulated non-convex and non-smooth optimization problem. In addition, two benchmark algorithms are introduced to verify the effectiveness of the proposed MMF-oriented design. Furthermore, the proposed algorithm is extended to scenarios in which the BS has imperfect channel state information (CSI) for both the communication and sensing channels. Finally, numerical simulation results demonstrate the superiority of the proposed design under both perfect and imperfect CSI conditions. In particular, the proposed schemes achieve performance comparable to that of conventional CVX-based approaches while reducing the computational time by approximately 70%.