Performance Analysis and Joint Beamforming for Hybrid RIS-Aided Massive MIMO ISAC

In integrated sensing and communication (ISAC) systems, stringent sensing performance constraints can severely limit the power available for communication. Hybrid reconfigurable intelligent surfaces (HRISs) with capabilities of both passive reflection and active signal amplification can significantly improve communication performance in the power-limited regime. This motivates us to analyze and optimize the performance of an HRIS-aided multiple-input-multiple-output (mMIMO) ISAC system. We first estimate the effective uplink/downlink channels using the minimum mean square error method. We then derive closed-form expressions for the communication sum-rate and sensing Cram\'er-Rao lower bound (CRLB). It is shown that under the equal power allocation strategy, the CRLB remains independent of the HRIS coefficients. Then, we formulate a joint optimization problem of power allocation and HRIS beamforming to maximize the communication sum-rate while ensuring specified sensing CRLB constraints. To solve the formulated non-convex problem, we propose an alternating optimization algorithm based on fractional programming and successive convex approximation. Extensive simulations validate our analysis and proposed algorithm, showing significant improvements in both communication and sensing performances enabled by the HRIS. For example, an HRIS with only $4$ active elements offers $97.30\%$ improvement in the communication sum-rate, while ensuring a sensing CRLB constraint of $-30$ dB.