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Fast and Robust Expectation Propagation MIMO Detection via Preconditioned Conjugated Gradient

Luca Schmid, Dominik Sulz, Laurent Schmalen

TL;DR

The paper tackles the high computational burden of expectation propagation (EP) for MIMO detection, which stems from the required matrix inversion in each EP iteration. It introduces EPiCG, an inversion-free EP variant that decouples marginal inference into mean and variance tasks, using a preconditioned conjugate gradient (pCG) method with a Jacobi preconditioner for the mean and a regression-informed Neumann-series variance approximation. Two EPiCG implementations are proposed: EPiCG (mean via pCG, variance approximated) and EPiCG-Sigma0 (initialization from the inverse at iteration zero, then standard EPiCG steps). Experiments on Rayleigh and 3GPP 3D MIMO UMa NLOS channels show that EPiCG achieves favorable performance-complexity tradeoffs, with improved stability in highly correlated, high-MUI scenarios and even outperforms the original EP detector in some challenging regimes.

Abstract

We study the expectation propagation (EP) algorithm for symbol detection in massive multiple-input multiple-output (MIMO) systems. The EP detector shows excellent performance but suffers from a high computational complexity due to the matrix inversion, required in each EP iteration to perform marginal inference on a Gaussian system. We propose an inversion-free variant of the EP algorithm by treating inference on the mean and variance as two separate and simpler subtasks: We study the preconditioned conjugate gradient algorithm for obtaining the mean, which can significantly reduce the complexity and increase stability by relying on the Jacobi preconditioner that proves to fit the EP characteristics very well. For the variance, we use a simple approximation based on linear regression of the Gram channel matrix. Numerical studies on the Rayleigh-fading channel and on a realistic 3GPP channel model reveal the efficiency of the proposed scheme, which offers an attractive performance-complexity tradeoff and even outperforms the original EP detector in high multi-user inference cases where the matrix inversion becomes numerically unstable.

Fast and Robust Expectation Propagation MIMO Detection via Preconditioned Conjugated Gradient

TL;DR

The paper tackles the high computational burden of expectation propagation (EP) for MIMO detection, which stems from the required matrix inversion in each EP iteration. It introduces EPiCG, an inversion-free EP variant that decouples marginal inference into mean and variance tasks, using a preconditioned conjugate gradient (pCG) method with a Jacobi preconditioner for the mean and a regression-informed Neumann-series variance approximation. Two EPiCG implementations are proposed: EPiCG (mean via pCG, variance approximated) and EPiCG-Sigma0 (initialization from the inverse at iteration zero, then standard EPiCG steps). Experiments on Rayleigh and 3GPP 3D MIMO UMa NLOS channels show that EPiCG achieves favorable performance-complexity tradeoffs, with improved stability in highly correlated, high-MUI scenarios and even outperforms the original EP detector in some challenging regimes.

Abstract

We study the expectation propagation (EP) algorithm for symbol detection in massive multiple-input multiple-output (MIMO) systems. The EP detector shows excellent performance but suffers from a high computational complexity due to the matrix inversion, required in each EP iteration to perform marginal inference on a Gaussian system. We propose an inversion-free variant of the EP algorithm by treating inference on the mean and variance as two separate and simpler subtasks: We study the preconditioned conjugate gradient algorithm for obtaining the mean, which can significantly reduce the complexity and increase stability by relying on the Jacobi preconditioner that proves to fit the EP characteristics very well. For the variance, we use a simple approximation based on linear regression of the Gram channel matrix. Numerical studies on the Rayleigh-fading channel and on a realistic 3GPP channel model reveal the efficiency of the proposed scheme, which offers an attractive performance-complexity tradeoff and even outperforms the original EP detector in high multi-user inference cases where the matrix inversion becomes numerically unstable.
Paper Structure (17 sections, 19 equations, 3 figures, 1 table)

This paper contains 17 sections, 19 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. System Model
  4. Rayleigh-fading Channel Model
  5. 3GPP 3D MIMO UMa NLOS Channel Model
  6. Expectation Propagation for MIMO Detection
  7. The EPiCG Algorithm
  8. Marginal Inference: Mean
  9. Krylov Subspace Methods
  10. pCG Method
  11. Marginal Inference: Variance
  12. The Proposed EPiCG Algorithm
  13. Experimental Study
  14. Approximation of the Marginal Mean
  15. Detection Performance
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Median RRE of various approximative solvers over the steps $k$. The plots vary the EP iteration $\ell$, in which the linear system \ref{['eq:linear_system']} is solved.
  • Figure 2: SER over $\mathsf{snr}$ for various MIMO detectors on the Rayleigh-fading channel with ${N_\text{t}=64,128}$ and ${N_\text{r}=128}$.
  • Figure 3: SER over $\mathsf{snr}$ for various MIMO detectors on the 3GPP 3D MIMO UMa NLOS channel with ${N_\text{t}=64,128}$ and ${N_\text{r}=128}$.