Power Allocation and Precoding Design for Active RIS-Aided Cell-Free Massive MIMO Systems

Thanks to the customization of channel propagation, reconfigurable intelligent surface (RIS)-aided cell-free (CF) massive multiple-input-multiple-output (MIMO) is recognized as a competitive candidate technique for the future communication system. However, only the limited performance gain can be afforded by passive RIS due to the double-fading effect in RIS-aided links. In this article, we consider the CF massive MIMO system with the assistance of the active RIS, which is capable of reflecting and amplifying the incident signal, to enable the Internet of Things network. We analyze the tradeoff between the number of active RIS reflecting elements (REs) and the amplification coefficient. Considering the power constraint at the active RIS, we formulate a sum-rate maximization problem to jointly optimize the user transmission power, the receive beamforming, and the RIS reflecting precoding. Since the original problem is nonconvex, we decouple it into three subproblems and then design an alternating optimization algorithm to solve them iteratively. Using the Lagrangian dual reformulation and generalized Rayleigh quotient theory, we derive the closed-form solutions for both the user transmission power and the uplink receive beamforming. We also develop a low-complexity method to acquire the RIS reflecting precoding based on the primal-dual subgradient theory. Compared to the passive RIS, the active RIS can significantly improve the system performance with fewer REs. Moreover, the proposed optimization scheme effectively mitigates the drawbacks of the active RIS under the high-transmission power regime and enhance its benefits. Finally, the proposed alternating optimization algorithm is validated by numerical results.