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

翻译：本工作研究了在非完美瞬时信道状态信息（I-CSI）下，分布式可重构智能表面（RISs）辅助的多用户多输入单输出（MISO）下行通信系统的净和速率性能，其中I-CSI用于基站（BS）预编码，统计信道状态信息（S-CSI）用于设计RIS相移。针对I-CSI获取，考虑两种信道估计（CE）协议：（i）全CE协议，在多个训练子阶段估计所有直连和RIS辅助信道；（ii）低开销直接估计（DE）协议，在单个子阶段估计端到端信道。我们在瑞利和莱斯衰落以及两种CE协议下，针对给定RIS相移，推导了信干噪比（SINR）和遍历净和速率的确定性等价表达式，并基于S-CSI优化了这些相移。仿真结果表明：当用于预编码的CSI获取时，低复杂度DE协议比全CE协议实现了更优的净和速率。本文还概述了基于全I-CSI的基准RIS设计方案，并显示其相比基于S-CSI的RIS设计获得更高SINR但更低净和速率，原因在于全I-CSI获取的高开销。因此，所提出的基于DE-S-CSI的预编码与反射波束成形设计能够以低复杂度、低开销和低功耗实现高净和速率。