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Expectation Propagation for Distributed Inference in Grant-Free Cell-Free Massive MIMO

Christian Forsch, Laura Cottatellucci

TL;DR

This work tackles the challenge of pilot contamination in grant-free cell-free MaMIMO by formulating JACD as a distributed Bayesian inference problem. It develops an Expectation Propagation framework on a factor graph, introducing two algorithms: JACD-EP with Gaussian channels and JACD-EP-BG with Bernoulli-Gaussian channels, the latter supported by an exponential-family BG representation. The proposed methods enable scalable, AP-CPU distributed processing with controllable fronthaul load, and they show substantial performance gains over centralized linear detectors, particularly under severe pilot contamination. The results indicate that nonlinear Bayesian inference with BG priors effectively mitigates PC and yields accurate activity detection, channel estimation, and data decoding in large GF-CF-MaMIMO networks.

Abstract

Grant-free cell-free massive multiple-input multiple-output (GF-CF-MaMIMO) systems are anticipated to be a key enabling technology for next-generation Internet-of-Things (IoT) networks, as they support massive connectivity without explicit scheduling. However, the large amount of connected devices prevents the use of orthogonal pilot sequences, resulting in severe pilot contamination (PC) that degrades channel estimation and data detection performance. Furthermore, scalable GF-CF-MaMIMO networks inherently rely on distributed signal processing. In this work, we consider the uplink of a GF-CF-MaMIMO system and propose two novel distributed algorithms for joint activity detection, channel estimation, and data detection (JACD) based on expectation propagation (EP). The first algorithm, denoted as JACD-EP, uses Gaussian approximations for the channel variables, whereas the second, referred to as JACD-EP-BG, models them as Bernoulli-Gaussian (BG) random variables. To integrate the BG distribution into the EP framework, we derive its exponential family representation and develop the two algorithms as efficient message passing over a factor graph constructed from the a posteriori probability (APP) distribution. The proposed framework is inherently scalable with respect to both the number of access points (APs) and user equipments (UEs). Simulation results show the efficient mitigation of PC by the proposed distributed algorithms and their superior detection accuracy compared to (genie-aided) centralized linear detectors.

Expectation Propagation for Distributed Inference in Grant-Free Cell-Free Massive MIMO

TL;DR

This work tackles the challenge of pilot contamination in grant-free cell-free MaMIMO by formulating JACD as a distributed Bayesian inference problem. It develops an Expectation Propagation framework on a factor graph, introducing two algorithms: JACD-EP with Gaussian channels and JACD-EP-BG with Bernoulli-Gaussian channels, the latter supported by an exponential-family BG representation. The proposed methods enable scalable, AP-CPU distributed processing with controllable fronthaul load, and they show substantial performance gains over centralized linear detectors, particularly under severe pilot contamination. The results indicate that nonlinear Bayesian inference with BG priors effectively mitigates PC and yields accurate activity detection, channel estimation, and data decoding in large GF-CF-MaMIMO networks.

Abstract

Grant-free cell-free massive multiple-input multiple-output (GF-CF-MaMIMO) systems are anticipated to be a key enabling technology for next-generation Internet-of-Things (IoT) networks, as they support massive connectivity without explicit scheduling. However, the large amount of connected devices prevents the use of orthogonal pilot sequences, resulting in severe pilot contamination (PC) that degrades channel estimation and data detection performance. Furthermore, scalable GF-CF-MaMIMO networks inherently rely on distributed signal processing. In this work, we consider the uplink of a GF-CF-MaMIMO system and propose two novel distributed algorithms for joint activity detection, channel estimation, and data detection (JACD) based on expectation propagation (EP). The first algorithm, denoted as JACD-EP, uses Gaussian approximations for the channel variables, whereas the second, referred to as JACD-EP-BG, models them as Bernoulli-Gaussian (BG) random variables. To integrate the BG distribution into the EP framework, we derive its exponential family representation and develop the two algorithms as efficient message passing over a factor graph constructed from the a posteriori probability (APP) distribution. The proposed framework is inherently scalable with respect to both the number of access points (APs) and user equipments (UEs). Simulation results show the efficient mitigation of PC by the proposed distributed algorithms and their superior detection accuracy compared to (genie-aided) centralized linear detectors.
Paper Structure (25 sections, 2 theorems, 62 equations, 5 figures, 1 algorithm)

This paper contains 25 sections, 2 theorems, 62 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation
  4. Bernoulli-Gaussian Distribution in Exponential Family Form
  5. Exponential Family
  6. Bernoulli-Gaussian Distribution
  7. Bernoulli-Gaussian Distribution
  8. EP-based JACD Algorithms
  9. Factor Graph Representation
  10. EP Approximations and Fronthaul Load
  11. Initialization and Scheduling
  12. Message-Passing Update Rules
  13. Final Estimation
  14. Computational Complexity and Scalability
  15. Numerical Results
  16. ...and 10 more sections

Key Result

Proposition 1

The exponential family representation of the BG distribution with activity probability $\lambda$ and the proper complex Gaussian event characterized by mean $\boldsymbol{\mu}$ and covariance matrix $\mathbf{C}$ is given by with vector of natural parameters $\boldsymbol{\eta}_\mathrm{BG}=\left[\kappa,\boldsymbol{\eta}_\mathrm{G}^{\mkern-1mu\mathsf{T}}\right]^{\mkern-1mu\mathsf{T}}$, sufficient sta

Figures (5)

  • Figure 1: GF-CF-MaMIMO network with geographically distributed AP and UE exhibiting different activity states.
  • Figure 2: Example BG product with $\lambda_1=0.8$ and $\lambda_2=0.9$.
  • Figure 3: Factor graph for the EP-based JACD algorithms with $\mathcal{T}\coloneq T_p+1$. The numbered red dashed arrows show the flow of information according to the scheduling presented in Algorithm \ref{['alg:JACD-EP-BG']}. Each number corresponds to one message update in Algorithm \ref{['alg:JACD-EP-BG']}.
  • Figure 4: Performance metrics versus pilot sequence length for $L=25$, $N=1$, $K=40$, $\lambda=0.3$, and $T=60$.
  • Figure 5: CDF of performance metrics for $L=25$, $N=1$, $K=40$, $\lambda=0.3$, $T=60$, and $T_p=6$.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Corollary 1: Bernoulli-Gaussian Product Lemma
  • proof