We study a distributed beamforming approach for cell-free massive multiple-input multiple-output networks, referred to as Global Statistics \& Local Instantaneous information-based minimum mean-square error (GSLI-MMSE). The scenario with multi-antenna access points (APs) is considered over three different channel models: correlated Rician fading with fixed or random line-of-sight (LoS) phase-shifts, and correlated Rayleigh fading. With the aid of matrix inversion derivations, we can construct the conventional MMSE combining from the perspective of each AP, where global instantaneous information is involved. Then, for an arbitrary AP, we apply the statistics approximation methodology to approximate instantaneous terms related to other APs by channel statistics to construct the distributed combining scheme at each AP with local instantaneous information and global statistics. With the aid of uplink-downlink duality, we derive the respective GSLI-MMSE precoding schemes. Numerical results showcase that the proposed GSLI-MMSE scheme demonstrates performance comparable to the optimal centralized MMSE scheme, under the stable LoS conditions, e.g., with static users having Rician fading with a fixed LoS path.

翻译：本文研究了一种用于无蜂窝大规模多输入多输出网络的分布式波束赋形方法，称为基于全局统计与局部瞬时信息的最小均方误差（GSLI-MMSE）。我们在三种不同信道模型下考虑配备多天线接入点（AP）的场景：具有固定或随机视距（LoS）相移的相关莱斯衰落，以及相关瑞利衰落。借助矩阵求逆推导，我们可以从每个AP的角度构建传统的MMSE合并方案，其中涉及全局瞬时信息。随后，对于任意AP，我们应用统计近似方法，将与其它AP相关的瞬时项用信道统计量进行近似，从而在每个AP处利用局部瞬时信息和全局统计量构建分布式合并方案。借助上下行链路对偶性，我们推导了相应的GSLI-MMSE预编码方案。数值结果表明，在稳定的LoS条件下（例如静态用户具有固定LoS路径的莱斯衰落场景），所提出的GSLI-MMSE方案展现出与最优集中式MMSE方案相当的性能。