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Bayesian Learning for Pilot Decontamination in Cell-Free Massive MIMO

Christian Forsch, Zilu Zhao, Dirk Slock, Laura Cottatellucci

TL;DR

This work tackles pilot contamination in the uplink of cell-free massive MIMO by formulating a joint Bayesian estimation problem for channels and data. It introduces a novel expectation-propagation based joint channel estimation and data detection algorithm that augments the bilinear-EP framework with pilot information, enabling distributed and scalable operation. A new UE-level pilot contamination metric is proposed to quantify contamination and link it to NMSE and SER, and extensive simulations show that non-orthogonal (DFT) pilots coupled with the proposed EP method significantly outperform state-of-the-art Bayesian and linear detectors, approaching genie-aided performance in many settings. The results offer practical guidance on pilot design and demonstrate a principled, iterative approach to PC mitigation in distributed CF-MaMIMO deployments.

Abstract

Pilot contamination (PC) arises when the pilot sequences assigned to user equipments (UEs) are not mutually orthogonal, eventually due to their reuse. In this work, we propose a novel expectation propagation (EP)-based joint channel estimation and data detection (JCD) algorithm specifically designed to mitigate the effects of PC in the uplink of cell-free massive multiple-input multiple-output (CF-MaMIMO) systems. This modified bilinear-EP algorithm is distributed, scalable, demonstrates strong robustness to PC, and outperforms state-of-the-art Bayesian learning algorithms. Through a comprehensive performance evaluation, we assess the performance of Bayesian learning algorithms for different pilot sequences and observe that the use of non-orthogonal pilots can lead to better performance compared to shared orthogonal sequences. Motivated by this analysis, we introduce a new metric to quantify PC at the UE level. We show that the performance of the considered algorithms degrades monotonically with respect to this metric, providing a valuable theoretical and practical tool for understanding and managing PC via iterative JCD algorithms.

Bayesian Learning for Pilot Decontamination in Cell-Free Massive MIMO

TL;DR

This work tackles pilot contamination in the uplink of cell-free massive MIMO by formulating a joint Bayesian estimation problem for channels and data. It introduces a novel expectation-propagation based joint channel estimation and data detection algorithm that augments the bilinear-EP framework with pilot information, enabling distributed and scalable operation. A new UE-level pilot contamination metric is proposed to quantify contamination and link it to NMSE and SER, and extensive simulations show that non-orthogonal (DFT) pilots coupled with the proposed EP method significantly outperform state-of-the-art Bayesian and linear detectors, approaching genie-aided performance in many settings. The results offer practical guidance on pilot design and demonstrate a principled, iterative approach to PC mitigation in distributed CF-MaMIMO deployments.

Abstract

Pilot contamination (PC) arises when the pilot sequences assigned to user equipments (UEs) are not mutually orthogonal, eventually due to their reuse. In this work, we propose a novel expectation propagation (EP)-based joint channel estimation and data detection (JCD) algorithm specifically designed to mitigate the effects of PC in the uplink of cell-free massive multiple-input multiple-output (CF-MaMIMO) systems. This modified bilinear-EP algorithm is distributed, scalable, demonstrates strong robustness to PC, and outperforms state-of-the-art Bayesian learning algorithms. Through a comprehensive performance evaluation, we assess the performance of Bayesian learning algorithms for different pilot sequences and observe that the use of non-orthogonal pilots can lead to better performance compared to shared orthogonal sequences. Motivated by this analysis, we introduce a new metric to quantify PC at the UE level. We show that the performance of the considered algorithms degrades monotonically with respect to this metric, providing a valuable theoretical and practical tool for understanding and managing PC via iterative JCD algorithms.

Paper Structure

This paper contains 9 sections, 20 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation
  4. Bilinear-EP Algorithm
  5. Factor Graph Representation
  6. Message Updates and Scheduling
  7. Quantifying Pilot Contamination
  8. Numerical Results
  9. Conclusion

Figures (8)

  • Figure 1: Factor graph for bilinear-EP with $\mathcal{T}\coloneq T_p+1$. The numbered red dashed arrows show the message update scheduling according to Algorithm \ref{['alg:bilinear-EP']}.
  • Figure 2: CDF of $c_k$ for different pilot sequences.
  • Figure 3: SER versus transmit power.
  • Figure 4: NMSE versus transmit power.
  • Figure 5: NMSE versus iterations for $T_d=10$ and $\sigma_x^2=16\,$dBm.
  • ...and 3 more figures