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

Zhe Wang, Emil Björnson, Jiayi Zhang, Peng Zhang, Vitaly Petrov, Bo Ai

TL;DR

This paper tackles distributed beamforming for CF mMIMO with multi-antenna APs under three channel models by reducing reliance on global instantaneous CSI. It introduces GSLI-MMSE, which replaces the cross-AP instantaneous term $\sum_{m'\neq m} \mathbf{\Xi}_{m'}$ with its global statistic $\sum_{m'\neq m} \overline{\mathbf{\Xi}}_{m'}$ while retaining local instantaneous CSI at each AP, and derives corresponding uplink combining and downlink precoding via uplink–downlink duality. The approach yields closed-form GSLI-MMSE expressions and scales to multiple APs, antennas, and UEs. Numerical results show that GSLI-MMSE can match the performance of the centralized C-MMSE under stable LoS conditions and provide meaningful SE gains over L-MMSE in such regimes, with reduced fronthaul signaling and computation.

Abstract

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.

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

TL;DR

This paper tackles distributed beamforming for CF mMIMO with multi-antenna APs under three channel models by reducing reliance on global instantaneous CSI. It introduces GSLI-MMSE, which replaces the cross-AP instantaneous term with its global statistic while retaining local instantaneous CSI at each AP, and derives corresponding uplink combining and downlink precoding via uplink–downlink duality. The approach yields closed-form GSLI-MMSE expressions and scales to multiple APs, antennas, and UEs. Numerical results show that GSLI-MMSE can match the performance of the centralized C-MMSE under stable LoS conditions and provide meaningful SE gains over L-MMSE in such regimes, with reduced fronthaul signaling and computation.

Abstract

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.
Paper Structure (8 sections, 3 theorems, 22 equations, 3 figures)

This paper contains 8 sections, 3 theorems, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Fundamentals of CF mMIMO Systems
  3. Uplink Transmission
  4. Downlink Transmission
  5. Distributed GSLI-MMSE Beamforming
  6. Proposed Method
  7. Numerical Results
  8. Conclusion

Key Result

Proposition 1

The average of $\mathbf{\Xi }_{m^{\prime}} \in \mathbb{C} ^{K\times K}$ in vmk_derivation2 is called $\overline{\mathbf{\Xi }}_{m^{\prime}}\in \mathbb{C} ^{K\times K}$. For the Rician fading channel model in Rician_PS_Channel, the $(k,l)$-th element of $\overline{\mathbf{\Xi }}_{m^{\prime}}$ is give where $\overline{\mathbf{H}}_{m^{\prime} kk}=\overline{\mathbf{h}}_{m^{\prime} k}\overline{\mathbf{

Figures (3)

  • Figure 1: Average uplink SE against $M$ over Rician fading channel models with or without phase-shifts with $K=40$ and $N=4$. "PS" and "w/o PS" denote the Rician channel models with phase-shifts and without phase-shifts, respectively. "C-MMSE" denotes the centralized processing scheme with the C-MMSE combining. "GSLI-MMSE" and "L-MMSE" denote the distributed processing schemes with optimal LSFD strategies over the GSLI-MMSE and L-MMSE combining schemes, respectively.
  • Figure 2: Sum uplink SE against $N$ for different combining schemes over different channel models with $M=80$ and $K=40$.
  • Figure 3: Average downlink SE for different precoding schemes over different channel models with $M=80$ and $K=40$.

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Remark 1
  • Corollary 1