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In this paper, we consider passive RIS-assisted multi-user communicationbetween wireless nodes to improve the blocked line-of-sight (LOS) linkperformance. The wireless nodes are assumed to be equipped with MassiveMultiple-Input Multiple-Output antennas, hybrid precoder, combiner, andlow-resolution analog-to-digital converters (ADCs). We first derive theexpression for the Cramer-Rao lower bound (CRLB) of the Mean Squared Error(MSE) of the received and combined signal at the intended receiver underinterference. By appropriate design of the hybrid precoder, combiner, and RISphase settings, it can be shown that the MSE achieves the CRLB. We further showthat minimizing the MSE w.r.t. the phase settings of the RIS is equivalent tomaximizing the throughput and energy efficiency of the system. We then proposea novel Information-Directed Branch-and-Prune (IDBP) algorithm to derive thephase settings of the RIS. We, for the first time in the literature, use aninformation-theoretic measure to decide on the pruning rules in a tree-searchalgorithm to arrive at the RIS phase-setting solution, which is vastlydifferent compared to the traditional branch-and-bound algorithm that usesbounds of the cost function to define the pruning rules. In addition, weprovide the theoretical guarantees of the near-optimality of the RISphase-setting solution thus obtained using the Asymptotic Equipartitionproperty. This also ensures near-optimal throughput and MSE performance.

An information-theoretic branch-and-prune algorithm for discrete phase optimization of RIS in massive MIMO