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Group Information Geometry Approach for Ultra-Massive MIMO Signal Detection

Jiyuan Yang, Yan Chen, Xiqi Gao, Xiang-Gen Xia, Dirk Slock

TL;DR

GIGA reframes ultra-massive MIMO signal detection as an approximate marginals problem under an information-geometry lens. By grouping received-signal components into auxiliary manifolds and performing $m$-projections onto an independent-component objective manifold, it yields tractable approximate marginals used in MPM detection. The method introduces a Berry-Esseen-based approximation to compute $m$-projections efficiently, offering favorable BER performance with scalable per-iteration complexity; the grouping level $U$ trades off convergence speed and cost, with practical settings delivering improvements over state-of-the-art detectors. This group-geometry framework provides a scalable, high-performance detector for ultra-massive MIMO systems and can extend to varying group sizes."

Abstract

We propose a group information geometry approach (GIGA) for ultra-massive multiple-input multiple-output (MIMO) signal detection. The signal detection task is framed as computing the approximate marginals of the a posteriori distribution of the transmitted data symbols of all users. With the approximate marginals, we perform the maximization of the {\textsl{a posteriori}} marginals (MPM) detection to recover the symbol of each user. Based on the information geometry theory and the grouping of the components of the received signal, three types of manifolds are constructed and the approximate a posteriori marginals are obtained through m-projections. The Berry-Esseen theorem is introduced to offer an approximate calculation of the m-projection, while its direct calculation is exponentially complex. In most cases, more groups, less complexity of GIGA. However, when the number of groups exceeds a certain threshold, the complexity of GIGA starts to increase. Simulation results confirm that the proposed GIGA achieves better bit error rate (BER) performance within a small number of iterations, which demonstrates that it can serve as an efficient detection method in ultra-massive MIMO systems.

Group Information Geometry Approach for Ultra-Massive MIMO Signal Detection

TL;DR

GIGA reframes ultra-massive MIMO signal detection as an approximate marginals problem under an information-geometry lens. By grouping received-signal components into auxiliary manifolds and performing -projections onto an independent-component objective manifold, it yields tractable approximate marginals used in MPM detection. The method introduces a Berry-Esseen-based approximation to compute -projections efficiently, offering favorable BER performance with scalable per-iteration complexity; the grouping level trades off convergence speed and cost, with practical settings delivering improvements over state-of-the-art detectors. This group-geometry framework provides a scalable, high-performance detector for ultra-massive MIMO systems and can extend to varying group sizes."

Abstract

We propose a group information geometry approach (GIGA) for ultra-massive multiple-input multiple-output (MIMO) signal detection. The signal detection task is framed as computing the approximate marginals of the a posteriori distribution of the transmitted data symbols of all users. With the approximate marginals, we perform the maximization of the {\textsl{a posteriori}} marginals (MPM) detection to recover the symbol of each user. Based on the information geometry theory and the grouping of the components of the received signal, three types of manifolds are constructed and the approximate a posteriori marginals are obtained through m-projections. The Berry-Esseen theorem is introduced to offer an approximate calculation of the m-projection, while its direct calculation is exponentially complex. In most cases, more groups, less complexity of GIGA. However, when the number of groups exceeds a certain threshold, the complexity of GIGA starts to increase. Simulation results confirm that the proposed GIGA achieves better bit error rate (BER) performance within a small number of iterations, which demonstrates that it can serve as an efficient detection method in ultra-massive MIMO systems.
Paper Structure (17 sections, 2 theorems, 115 equations, 10 figures, 1 table, 2 algorithms)

This paper contains 17 sections, 2 theorems, 115 equations, 10 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Configuration and Problem Formulation
  3. System Configuration
  4. Problem Formulation
  5. GIGA
  6. Signal Detection in Information Geometry Perspective
  7. Factorization of $p\left(\mathbf{s}|\mathbf{y}\right)$ by Grouping the Components of the Received Signal
  8. GIGA
  9. Calculation of the $m$-projection from onto the OBM
  10. Direct Calculation
  11. Approximate Calculation
  12. Computational Complexity
  13. Simulation Results
  14. BER Performance
  15. Complexities
  16. ...and 2 more sections

Key Result

Lemma 1

Given $N$ independent random vectors $\left\lbrace \mathbf{x}_n\right\rbrace_{n=1}^N$, where $\mathbf{x}_n \in \mathbb{R}^{d}$, and $d \ge 1$ is finite. Each $\mathbf{x}_n$ has finite mean ${\boldsymbol\mu}_n \in \mathbb{R}^{d}$ and finite positive-definite covariance matrix ${\boldsymbol\Sigma}_n \ holds. Then, $\mathbf{x}_s$ converges in distribution to a real Gaussian random vector $\tilde{\mat

Figures (10)

  • Figure 1: Illustration of the $m$-projection of $p_u\left(\mathbf{s};{\boldsymbol\theta}_{u}\right)$ onto the OBM.
  • Figure 2: BER performance of GIGA compared with AMP, EP and LMMSE under $4$-QAM.
  • Figure 3: Convergence performance of GIGA compared with EP and AMP at SNR = $4$ dB under $4$-QAM.
  • Figure 4: BER performance of GIGA compared with AMP, EP and LMMSE under $16$-QAM.
  • Figure 5: BER performance of GIGA compared with AMP, EP and LMMSE under $64$-QAM.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Lemma 1: Berry–Esseen theorem
  • Theorem 1