A Framework for Mutual Information-based MIMO Integrated Sensing and Communication Beamforming Design

Integrated sensing and communication (ISAC) unifies sensing and communication, and improves the efficiency of the spectrum, energy, and hardware. In this work, we investigate the ISAC beamforming design to maximize the mutual information between the target response matrix of a point radar target and the echo signals, while ensuring the data rate requirements of communication users. In order to study the impact of the echo interference caused by communication users on sensing performance, we consider three types of echo interference problems caused by a single communication user, including no interference, a point interference, and an extended interference, as well as the problem of an extended interference caused by multiple communication users. To address these problems, we provide a closed-form solution with low complexiy, a semidefinite relaxation (SDR) method, a low-complexity algorithm based on the Majorization-Minimization (MM) method and the successive convex approximation (SCA) method, and an algorithm based on MM method and SCA method, respectively. Numerical results demonstrate that, compared to the ISAC beamforming schemes based on the Cram\'er-Rao bound (CRB) metric and the beampattern metric, the proposed maximizing mutual information metric can bring better beampattern and root mean square error (RMSE) of angle estimation. Apart from this, our proposed schemes based on the mutual information can suppress the echo interference from the communication users effectively.