In this paper, we consider cell-free communication systems with several access points (APs) serving terrestrial users (UEs) simultaneously. To enhance the uplink multi-user multiple-input multiple-output communications, we adopt a hybrid-CSI-based two-layer distributed multi-user detection scheme comprising the local minimum mean-squared error (MMSE) detection at APs and the one-shot weighted combining at the central processing unit (CPU). Furthermore, to improve the propagation environment, we introduce multiple reconfigurable intelligent surfaces (RISs) to assist the transmissions from UEs to APs. Aiming to maximize the weighted sum rate, we formulate the weighted sum-MMSE (WMMSE) problem, where the UEs' beamforming matrices, the CPU's weighted combining matrix, and the RISs' phase-shifting matrices are alternately optimized. Considering the limited fronthaul capacity constraint in cell-free networks, we resort to the operator-valued free probability theory to derive the asymptotic alternating optimization (AO) algorithm to solve the WMMSE problem, which only depends on long-term channel statistics and thus reduces the interaction overhead. Numerical results demonstrate that the asymptotic AO algorithm can achieve a high communication rate as well as reduce the interaction overhead.

翻译：本文研究了一种由多个接入点(AP)同时服务地面用户(UE)的无蜂窝通信系统。为增强上行多用户多输入多输出通信性能，我们采用基于混合信道状态信息的两层分布式多用户检测方案，该方案包含AP端的局部最小均方误差检测与中央处理单元的单次加权合并。此外，为改善传播环境，我们引入多个可重构智能表面辅助用户至接入点的传输。以最大化加权和速率为目标，我们构建了加权和最小均方误差优化问题，其中用户波束成形矩阵、中央处理单元加权合并矩阵与可重构智能表面相移矩阵通过交替优化进行求解。考虑到无蜂窝网络中前传容量受限的约束，我们借助算子值自由概率理论推导出渐近交替优化算法以求解加权和最小均方误差问题，该算法仅依赖长期信道统计特性，从而显著降低交互开销。数值仿真结果表明，所提渐近交替优化算法在实现高通信速率的同时能有效减少交互开销。