Statistics Approximation-Enabled Distributed Beamforming for Cell-Free Massive MIMO

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.

💡 Research Summary

This paper addresses the high computational and fronthaul overhead associated with centralized minimum‑mean‑square‑error (MMSE) processing in cell‑free massive multiple‑input multiple‑output (CF‑mMIMO) systems, and proposes a novel distributed beamforming scheme called Global Statistics & Local Instantaneous information‑based MMSE (GSLI‑MMSE). The authors consider a network with M access points (APs), each equipped with N antennas, serving K single‑antenna users. Three channel models are examined: (i) correlated Rician fading with a fixed line‑of‑sight (LoS) phase, (ii) correlated Rician fading with random, time‑varying LoS phase, and (iii) correlated Rayleigh fading (no LoS component).

The starting point is the optimal centralized MMSE combiner, which requires the global instantaneous channel matrix bH and a matrix inversion of dimension M N × M N for every coherence block. To reduce this burden, the authors apply a statistics‑approximation methodology: terms that involve instantaneous channel estimates from other APs are replaced by their statistical expectations (covariance matrices R and C). By exploiting the block‑diagonal structure of the interference‑plus‑noise matrix W, the centralized combiner can be rewritten using the matrix inversion lemma, yielding an expression that separates local and global components.

For each AP m, the distributed combiner vector v_mk for user k is expressed as

v_mk = p_k W_m⁻¹ b_Hm