Energy-Efficient RIS-Aided Cell-Free Massive MIMO ISAC Systems: Joint AP Operation Mode Selection and Beamforming Design

In this paper, we investigate a reconfigurable intelligent surface (RIS)-assisted cell-free massive multiple-input multiple-output (CF-mMIMO) integrated sensing and communication (ISAC) system. This study formulates the problem of maximizing the energy efficiency (EE) under the constraints of Boolean variables, communication quality of service (QoS), sensing signal-to-noise ratio (SNR), and single access point (AP) power consumption, through the joint design of AP operation mode selection (OMS), AP transmit beamforming, and the RIS phase shift matrix. To address this mixed-integer non-convex problem, we propose an iterative two-stage algorithm to split the original problem in an alternating manner. In the first stage, a heuristic strategy for AP OMS is developed based on semidefinite relaxation (SDR). In the second stage, the beamforming design problem is decomposed into two subproblems consisting of the AP transmit beamforming and the RIS phase shift optimization. To tackle the RIS phase shift optimization subproblem, a successive convex approximation (SCA) and penalty-based approach is proposed to satisfy constant-modulus phase constraints. Simulation results demonstrate that the proposed scheme boosts EE, particularly under high QoS and sensing SNR requirements, underscoring the critical roles of both the RIS and AP OMS.