Communication Aided Sensing for RIS Assisted MU-MIMO System: CRB Optimization with Guaranteed Ergodic Rate

Integrated-sensing-and-communication (ISAC) is an essential characteristic of the 6G communication system. One critical point to realize ISAC lies in exploiting communication functional to enhance sensing. To this end, this paper investigates utilizing communication data to improve channel state information (CSI) recovery in uplink multi-user (MU) multi-input-multi-output (MIMO) network aided by active reconfigurable intelligent surface (RIS). Specifically, we develop an efficient expectation-maximization (EM) based estimator that iteratively refines CSI analytically and derive the associated Cramér-Rao bound (CRB). This new CRB applies to settings much more generic than ever considered in the existing literature and subsumes the MU-MIMO network without RIS as a special case. Besides, we conduct beamforming design to minimize the CRB while ensuring ergodic communication rate in awareness of CSI uncertainty. Specifically, we establish two new tight lower-bounds for ergodic MIMO spectral efficiency. These new results generalize the seminal use-and-then-forget (UatF) bound to MIMO scenario and enable its robust beamforming through efficient second-order-cone-programming techniques, instead of the classical semidefinite programming methods with high complexity. Extensive numerical results verify the benefit of exploiting communication data in sensing enhancement, the validity of CRB and ergodic rate lower-bounds, and the remarkable CRB improvement yielded by our proposed beamforming design algorithms.