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Pilot-Aided Distributed Multi-Group Multicast Precoding Design for Cell-Free Massive MIMO

Bikshapathi Gouda, Italo Atzeni, Antti Tölli

TL;DR

This work addresses multicast transmission in cell-free massive MIMO by formulating a sum-group MSE objective and relaxing it to a weighted sum MSE to enable distributed precoding without backhaul CSI exchange. It introduces a group-specific OTA uplink training resource and develops two distributed schemes—best-response and gradient-based—for joint precoding at BSs and combiners at UEs, with convergence analyses under perfect CSI. The gradient-based distributed precoding with group-specific pilots achieves performance close to centralized solutions and substantially outperforms localCSI baselines, while incurring reduced training overhead. The proposed framework enables scalable, backhaul-free coordination for multi-group multicasting in large cell-free networks, with practical implications for Unequalized fairness and spectral efficiency in future wireless systems.

Abstract

We propose fully distributed multi-group multicast precoding designs for cell-free massive multiple-input multiple-output (MIMO) systems with modest training overhead. We target the minimization of the sum of the maximum mean squared errors (MSEs) over the multicast groups, which is then approximated with a weighted sum MSE minimization to simplify the computation and signaling. To design the joint network-wide multi-group multicast precoders at the base stations (BSs) and the combiners at the user equipments (UEs) in a fully distributed fashion, we adopt an iterative bi-directional training scheme with UE-specific or group-specific precoded uplink pilots and group-specific precoded downlink pilots. To this end, we introduce a new group-specific uplink training resource that entirely eliminates the need for backhaul signaling for the channel state information (CSI) exchange. The precoders are optimized locally at each BS by means of either best-response or gradient-based updates, and the convergence of the two approaches is analyzed with respect to the centralized implementation with perfect CSI. Finally, numerical results show that the proposed distributed methods greatly outperform conventional cell-free massive MIMO precoding designs that rely solely on local CSI.

Pilot-Aided Distributed Multi-Group Multicast Precoding Design for Cell-Free Massive MIMO

TL;DR

This work addresses multicast transmission in cell-free massive MIMO by formulating a sum-group MSE objective and relaxing it to a weighted sum MSE to enable distributed precoding without backhaul CSI exchange. It introduces a group-specific OTA uplink training resource and develops two distributed schemes—best-response and gradient-based—for joint precoding at BSs and combiners at UEs, with convergence analyses under perfect CSI. The gradient-based distributed precoding with group-specific pilots achieves performance close to centralized solutions and substantially outperforms localCSI baselines, while incurring reduced training overhead. The proposed framework enables scalable, backhaul-free coordination for multi-group multicasting in large cell-free networks, with practical implications for Unequalized fairness and spectral efficiency in future wireless systems.

Abstract

We propose fully distributed multi-group multicast precoding designs for cell-free massive multiple-input multiple-output (MIMO) systems with modest training overhead. We target the minimization of the sum of the maximum mean squared errors (MSEs) over the multicast groups, which is then approximated with a weighted sum MSE minimization to simplify the computation and signaling. To design the joint network-wide multi-group multicast precoders at the base stations (BSs) and the combiners at the user equipments (UEs) in a fully distributed fashion, we adopt an iterative bi-directional training scheme with UE-specific or group-specific precoded uplink pilots and group-specific precoded downlink pilots. To this end, we introduce a new group-specific uplink training resource that entirely eliminates the need for backhaul signaling for the channel state information (CSI) exchange. The precoders are optimized locally at each BS by means of either best-response or gradient-based updates, and the convergence of the two approaches is analyzed with respect to the centralized implementation with perfect CSI. Finally, numerical results show that the proposed distributed methods greatly outperform conventional cell-free massive MIMO precoding designs that rely solely on local CSI.
Paper Structure (24 sections, 4 theorems, 65 equations, 9 figures, 2 tables, 4 algorithms)

This paper contains 24 sections, 4 theorems, 65 equations, 9 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Contribution
  3. Outline
  4. Notation
  5. System Model
  6. Pilot-Aided Channel Estimation and Iterative Bi-Directional Training
  7. Problem Formulation
  8. Sum-Group MSE Minimization
  9. Weighted Sum MSE Minimization
  10. Centralized Precoding Design with Pilot-Aided Channel Estimation
  11. Distributed Precoding Design with Perfect CSI
  12. Best-Response Distributed Precoding Design
  13. Gradient-Based Distributed Precoding Design
  14. Distributed Precoding Design with Pilot-Aided Channel Estimation
  15. Best-Response Distributed Precoding Design with UE- and Group-Specific Pilots
  16. ...and 9 more sections

Key Result

Proposition 1

As $\rho_{\textnormal{\tiny{BS}}} \to \infty$, i.e., at high SNR, the UE-specific rates obtained with the sum MSE minimization in eq:EqvprobForHi asymptotically approximate the ones resulting from the sum-group MSE minimization in eq:probForHi.

Figures (9)

  • Figure 1: Schematic representation of iterative bi-directional training in a single-UE, single-BS setting. To transmit the precoded uplink pilots, UE $k$ uses $\mathbf{v}_{k}$ as precoder.
  • Figure 2: Average sum-group rate resulting from the sum-group MSE minimization and the sum MSE minimization versus number of alternating optimization iterations for different values of $\rho_{\textnormal{\tiny{BS}}}$.
  • Figure 3: Average sum-group rate versus number of bi-directional training iterations.
  • Figure 4: Average effective sum-group rate versus number of bi-directional training iterations, with $r_{\mathrm{t}} = 1000$.
  • Figure 5: Average effective sum-group rate versus resource block size.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Proposition 1
  • Theorem 1
  • Remark 1
  • Remark 2
  • Theorem 2
  • Remark 3
  • Theorem 3
  • Remark 4
  • Remark 5