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In recent years there has been a growing interest in reconfigurableintelligent surfaces (RISs) as enablers for the realization of smart radiopropagation environments which can provide performance improvements with lowenergy consumption in future wireless networks. However, to reap the potentialgains of RIS it is crucial to jointly design both the transmit precoder and thephases of the RIS elements. Within this context, in this paper we study the useof multiple RIS panels in a parallel or multi-hop configuration with the aim ofassisting a multi-stream multiple-input multiple-output (MIMO) communication.To solve the nonconvex joint optimization problem of the precoder and RISelements targeted at maximizing the achievable rate, we propose an iterativealgorithm based on the monotone accelerated proximal gradient (mAPG) methodwhich includes an extrapolation step for improving the convergence speed andmonitoring variables for ensuring sufficient descent of the algorithm. Based onthe sufficient descent property we then present a detailed convergence analysisof the algorithm which includes expressions for the step size. Simulationresults in different scenarios show that, besides being effective, the proposedapproach can often achieve higher rates than other benchmarked schemes.

Optimizing the Achievable Rate in MIMO Systems Assisted by Multiple Reconfigurable Intelligent Surfaces