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Optimal Bilinear Equalizer for Cell-Free Massive MIMO Systems over Correlated Rician Channels

Zhe Wang, Jiayi Zhang, Emil Björnson, Dusit Niyato, Bo Ai

TL;DR

This work addresses spectral efficiency in cell-free massive MIMO under spatially correlated Rician channels by introducing optimal bilinear equalizers (OBE) that are BE-structured, leveraging channel statistics to avoid high-cost per-coherence-block inversions. It develops a unified SE framework for centralized and distributed processing, producing closed-form SE expressions under the UatF bound and designing three OBEs: Centralized OBE (C-OBE), Distributed OBE based on Global statistics (DG-OBE), and Distributed OBE based on Local statistics (DL-OBE). The paper shows that OBEs can closely approach C-MMSE performance with significantly reduced complexity and reveals regime-dependent guidance: C-OBE for limited fronthaul, DG-OBE when LoS phase shifts are negligible, and DL-OBE when LoS phase shifts are present. Numerical results confirm exact match between closed-form and Monte Carlo SE, and highlight OBEs’ robustness to pilot contamination and phase-shift effects, offering practical, scalable processing options for CF mMIMO deployments.

Abstract

In this paper, we explore the low-complexity optimal bilinear equalizer (OBE) combining scheme design for cell-free massive multiple-input multiple-output networks with spatially correlated Rician fading channels. We provide a spectral efficiency (SE) performance analysis framework for both the centralized and distributed processing schemes with bilinear equalizer (BE)-structure combining schemes applied. The BE-structured combining is a set of schemes that are constructed by the multiplications of channel statistics-based BE matrices and instantaneous channel estimates. Notably, we derive closed-form achievable SE expressions for centralized and distributed BE-structured combining schemes. We propose one centralized and two distributed OBE schemes: Centralized OBE (C-OBE), Distributed OBE based on Global channel statistics (DG-OBE), and Distributed OBE based on Local channel statistics (DL-OBE), which maximize their respective SE expressions. OBE matrices in these schemes are tailored based on varying levels of channel statistics. Notably, we obtain new and insightful closed-form results for the C-OBE, DG-OBE, and DL-OBE combining schemes. Numerical results demonstrate that the proposed OBE schemes can achieve excellent SE, even in scenarios with severe pilot contamination.

Optimal Bilinear Equalizer for Cell-Free Massive MIMO Systems over Correlated Rician Channels

TL;DR

This work addresses spectral efficiency in cell-free massive MIMO under spatially correlated Rician channels by introducing optimal bilinear equalizers (OBE) that are BE-structured, leveraging channel statistics to avoid high-cost per-coherence-block inversions. It develops a unified SE framework for centralized and distributed processing, producing closed-form SE expressions under the UatF bound and designing three OBEs: Centralized OBE (C-OBE), Distributed OBE based on Global statistics (DG-OBE), and Distributed OBE based on Local statistics (DL-OBE). The paper shows that OBEs can closely approach C-MMSE performance with significantly reduced complexity and reveals regime-dependent guidance: C-OBE for limited fronthaul, DG-OBE when LoS phase shifts are negligible, and DL-OBE when LoS phase shifts are present. Numerical results confirm exact match between closed-form and Monte Carlo SE, and highlight OBEs’ robustness to pilot contamination and phase-shift effects, offering practical, scalable processing options for CF mMIMO deployments.

Abstract

In this paper, we explore the low-complexity optimal bilinear equalizer (OBE) combining scheme design for cell-free massive multiple-input multiple-output networks with spatially correlated Rician fading channels. We provide a spectral efficiency (SE) performance analysis framework for both the centralized and distributed processing schemes with bilinear equalizer (BE)-structure combining schemes applied. The BE-structured combining is a set of schemes that are constructed by the multiplications of channel statistics-based BE matrices and instantaneous channel estimates. Notably, we derive closed-form achievable SE expressions for centralized and distributed BE-structured combining schemes. We propose one centralized and two distributed OBE schemes: Centralized OBE (C-OBE), Distributed OBE based on Global channel statistics (DG-OBE), and Distributed OBE based on Local channel statistics (DL-OBE), which maximize their respective SE expressions. OBE matrices in these schemes are tailored based on varying levels of channel statistics. Notably, we obtain new and insightful closed-form results for the C-OBE, DG-OBE, and DL-OBE combining schemes. Numerical results demonstrate that the proposed OBE schemes can achieve excellent SE, even in scenarios with severe pilot contamination.
Paper Structure (21 sections, 8 theorems, 47 equations, 10 figures, 1 table)

This paper contains 21 sections, 8 theorems, 47 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Fundamentals of CF mMIMO Networks
  3. Channel Model
  4. Channel Estimation
  5. Data Transmission
  6. Spectral Efficiency Analysis
  7. Centralized Processing
  8. Distributed Processing
  9. Optimal Bilinear Equalizer Design
  10. C-OBE Combining Scheme Design
  11. DG-OBE Combining Scheme Design
  12. DL-OBE Combining Scheme Design
  13. Numerical Results
  14. Conclusions
  15. Useful Results
  16. ...and 6 more sections

Key Result

Theorem 1

With the combining scheme in Centrlized_Wg, the achievable SE for UE $k$ in SE_centrlized_UatF can be computed in closed-form as $\overline{\mathrm{SE}}_{k}^{\mathrm{c},\mathrm{UatF}}=\frac{\tau _c-\tau _p}{\tau _c}\log _2( 1+\overline{\mathrm{SINR}}_{k}^{\mathrm{c},\mathrm{UatF}} )$ with $\overline $\omega _k$ is given in LoS_Closed on the top of this page, $\overline{\mathbf{G}}_{kk}=\mathrm{dia

Figures (10)

  • Figure 1: Average SE per UE measured by the UatF bound against the number of antennas per AP for the FCP scheme over different combining schemes with $M=20$, $K=20$, and $\tau_p=1$.
  • Figure 2: CDF of the SE per UE measured by the standard, UatF, and genie-aided capacity bounds for the FCP scheme with $M=20$, $K=10$, $N=4$, and $\tau_p=1$.
  • Figure 3: CDF of the SE per UE measured by the standard bound for the FCP scheme with different numbers of pilot signals $\tau_p$ over $M=20$, $K=20$ and $N=4$.
  • Figure 4: Average SE per UE measured by the standard bound against the number of UEs for the FCP scheme with $M=20$, $N=2$, and $\tau_p=\{1,5\}$.
  • Figure 5: Average SE per UE versus the number of APs over the EWDP and LSFD schemes with $K=20$, $N=4$, and $\tau_p=1$.
  • ...and 5 more figures

Theorems & Definitions (19)

  • Remark 1
  • Theorem 1
  • Remark 2
  • Theorem 2
  • Remark 3
  • Remark 4
  • Corollary 1
  • Theorem 3
  • Remark 5
  • Corollary 2
  • ...and 9 more