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 the communication users. The scenarios in this paper are considered from two perspectives: one is from the perspective of the number of communication users, and the other is from the perspective of the type of echo interference caused by other interfering scatterers. For the case of a single communication user, in order to reduce the complexity of the algorithm, we consider three types of echo interference, no interference, a point interference, and an extended interference. For the case of multiple communication users, the interference is also an extended one, and furthermore, each user's communication rate requirement needs to be satisfied. To find the optimal beamforming design in these problems, we provide a closed-form solution with low complexity, 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 Cramér-Rao bound (CRB) metric, the beampattern metric and the MSE metric, the proposed mutual information metric can bring better beampattern and root mean square error (RMSE) of angle estimation. Furthermore, our proposed schemes designed based on the mutual information metric can suppress the echo interference from interfering scatterers in the environment effectively.