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This work studies the net sum-rate performance of a distributedreconfigurable intelligent surfaces (RISs)-assisted multi-usermultiple-input-single-output (MISO) downlink communication system underimperfect instantaneous-channel state information (I-CSI) to implementprecoding at the base station (BS) and statistical-CSI (S-CSI) to design theRISs phase-shifts. Two channel estimation (CE) protocols are considered forI-CSI acquisition: (i) a full CE protocol that estimates all direct andRISs-assisted channels over multiple training sub-phases, and (ii) alow-overhead direct estimation (DE) protocol that estimates the end-to-endchannel in a single sub-phase. We derive the deterministic equivalents ofsignal-to-interference-plus-noise ratio (SINR) and ergodic net sum-rate underRayleigh and Rician fading and both CE protocols, for given RISs phase-shifts,which are then optimized based on S-CSI. Simulation results reveal that thelow-complexity DE protocol yields better net sum-rate than the full CE protocolwhen used to obtain CSI for precoding. A benchmark full I-CSI based RISs designis also outlined and shown to yield higher SINR but lower net sum-rate than theS-CSI based RISs design due to the large overhead associated with full I-CSIacquisition. Therefore the proposed DE-S-CSI based design for precoding andreflect beamforming achieves high net sum-rate with low complexity, overheadand power consumption.

Distributed Reconfigurable Intelligent Surfaces Assisted Wireless Communication: Asymptotic Analysis under Imperfect CSI