Joint beamforming algorithm for multi-stream MIMO systems assisted by multiple reconfigurable intelligent surfaces

In recent years there has been a growing interest in reconfigurable intelligent surfaces (RISs) as enablers for the realization of smart radio propagation environments which can provide performance improvements with low energy consumption in future wireless networks. However, to reap the potential gains of RIS it is crucial to jointly design both the transmit precoder and the phases of the RIS elements. Within this context, in this paper we study the use of multiple RIS panels in a parallel or multi-hop configuration with the aim of assisting a multi-stream multiple-input multiple-output (MIMO) communication. To solve the nonconvex joint optimization problem of the precoder and RIS elements targeted at maximizing the achievable rate, we propose a novel iterative algorithm based on the monotone accelerated proximal gradient (mAPG) method which includes an extrapolation step for improving the convergence speed and monitoring variables for ensuring sufficient descent of the algorithm. Based on the sufficient descent property we then present a detailed convergence analysis of the algorithm which includes expressions for the step size. Simulation results in different scenarios show that the use of multiple RIS panels combined with the proposed algorithm can be an effective solution for improving the achievable rates.