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Truncated Polynomial Expansion-Based Detection in Massive MIMO: A Model-Driven Deep Learning Approach

Kazem Izadinasab, Ahmed Wagdy Shaban, Oussama Damen

TL;DR

A deep learning (DL)-based approach for efficiently computing the inverse of Hermitian matrices using truncated polynomial expansion (TPE) outperforms the conventional TPE method with optimal coefficients in terms of asymptotic convergence speed and reduces the computational complexity of the online detection stage.

Abstract

In this paper, we propose a deep learning (DL)-based approach for efficiently computing the inverse of Hermitian matrices using truncated polynomial expansion (TPE). Our model-driven approach involves optimizing the coefficients of the TPE during an offline training procedure for a given number of TPE terms. We apply this method to signal detection in uplink massive multiple-input multiple-output (MIMO) systems, where the matrix inverse operation required by linear detectors, such as zero-forcing (ZF) and minimum mean square error (MMSE), is approximated using TPE. Our simulation results demonstrate that the proposed learned TPE-based method outperforms the conventional TPE method with optimal coefficients in terms of asymptotic convergence speed and reduces the computational complexity of the online detection stage, albeit at the expense of the offline training stage. However, the limited number of trainable parameters leads to a swift offline training process.

Truncated Polynomial Expansion-Based Detection in Massive MIMO: A Model-Driven Deep Learning Approach

TL;DR

A deep learning (DL)-based approach for efficiently computing the inverse of Hermitian matrices using truncated polynomial expansion (TPE) outperforms the conventional TPE method with optimal coefficients in terms of asymptotic convergence speed and reduces the computational complexity of the online detection stage.

Abstract

In this paper, we propose a deep learning (DL)-based approach for efficiently computing the inverse of Hermitian matrices using truncated polynomial expansion (TPE). Our model-driven approach involves optimizing the coefficients of the TPE during an offline training procedure for a given number of TPE terms. We apply this method to signal detection in uplink massive multiple-input multiple-output (MIMO) systems, where the matrix inverse operation required by linear detectors, such as zero-forcing (ZF) and minimum mean square error (MMSE), is approximated using TPE. Our simulation results demonstrate that the proposed learned TPE-based method outperforms the conventional TPE method with optimal coefficients in terms of asymptotic convergence speed and reduces the computational complexity of the online detection stage, albeit at the expense of the offline training stage. However, the limited number of trainable parameters leads to a swift offline training process.
Paper Structure (10 sections, 1 theorem, 18 equations, 2 figures, 2 tables)

This paper contains 10 sections, 1 theorem, 18 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Truncated Polynomial Expansion (TPE)
  4. TPE for Uplink Massive MIMO Detection
  5. The Proposed Learned TPE
  6. Complexity Analysis
  7. Simulations Results
  8. Training Setup
  9. BER Performance Evaluation
  10. Conclusion

Key Result

Lemma 1

For any positive definite Hermitian matrix $\bf X$, where the second equality holds when $0 < \alpha < \frac{2}{\lambda_{max} (\bf X)}$ such that $\lambda_{max} (\bf X)$ is the largest eigenvalue of $\bf X$. The parameter $\alpha$ is referred to as the normalization factor.

Figures (2)

  • Figure 1: BER performance for a massive MIMO system with $N = 128$, $K = 16$, and $16$-QAM modulation.
  • Figure 2: BER performance for a massive MIMO system with $N = 64$, $K = 16$, and $16$-QAM modulation.

Theorems & Definitions (1)

  • Lemma 1: Sessler2005