Approximate Capacity-Distortion Region of Joint State Sensing and Communication in MIMO Real Gaussian Channels

Integrated sensing and communication (ISAC), which simultaneously achieves wireless sensing and communication, is promising for next-generation wireless networks. In this paper, we consider a joint state sensing and communication system, where a multi-antenna ISAC transceiver simultaneously senses a sensing target and conveys a message to a multi-antenna communication receiver in multiple-input-multiple-output (MIMO) real Gaussian channels. Our goal is to optimize the signal input probability distribution to obtain the approximate capacity-distortion region. The formulated optimization problem is difficult because of high optimization dimension and high storage complexity. To reduce the optimization dimension, it is theoretically proved that over each transmitting antenna, the optimal signal inputs over different symbol durations should follow an independent and identical distribution. To reduce the storage complexity, it is also theoretically proved that the signal input probability distribution optimization over MIMO channels is equivalent to that over multiple-input-single-output channels. We propose an alternating optimization based Blahut-Arimoto algorithm to solve the optimization problem. Numerical results illustrate that the proposed joint state sensing and communication system achieves the larger capacity-distortion region than both the basic time-sharing (TS) and improved TS schemes.