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Low Complexity Detector for XL-MIMO Uplink: A Cross Splitting Based Information Geometry Approach

Wenjun Zhang, An-An Lu, Xiqi Gao

TL;DR

This work tackles the high computational burden of uplink signal detection in XL-MIMO by introducing CS-IGA, a cross-splitting information geometry detector whose per-iteration cost scales favorably with the number of users. By factorizing the a posteriori precision into diagonal and low-rank components and enforcing e- and m-conditions, CS-IGA achieves convergence rates comparable to Bayes-optimal AMP while reducing complexity to $ ext{O}(T N^2)$. The authors further extend the framework to nonlinear, discrete-prior detection via NCS-IGA, which incorporates an extra auxiliary manifold to yield symbol-wise Bayesian estimates with low overhead. Extensive simulations on realistic 3GPP channels demonstrate that CS-IGA and NCS-IGA deliver faster convergence and BER performance close to or surpassing AMP and IGA, at substantially lower computational cost, making them practical for next-generation XL-MIMO uplink detection.

Abstract

In this paper, we propose the cross splitting based information geometry approach (CS-IGA), a novel and low complexity iterative detector for uplink signal recovery in extralarge-scale MIMO (XL-MIMO) systems. Conventional iterative detectors, such as the approximate message passing (AMP) algorithm and the traditional information geometry algorithm (IGA), suffer from a per iteration complexity that scales with the number of base station (BS) antennas, creating a computational bottleneck. To overcome this, CS-IGA introduces a novel cross matrix splitting of the natural parameter in the a posteriori distribution. This factorization allows the iterative detection based on the matched filter, which reduces per iteration computational complexity. Furthermore, we extend this framework to nonlinear detection and propose nonlinear CSIGA (NCS-IGA) by seamlessly embedding discrete constellation constraints, enabling symbol-wise processing without external interference cancellation loops. Comprehensive simulations under realistic channel conditions demonstrate that CS-IGA matches or surpasses the bit error rate (BER) performance of Bayes optimal AMP and IGA for both linear and nonlinear detection, while achieving this with fewer iterations and a substantially lower computational cost. These results establish CS-IGA as a practical and powerful solution for high-throughput signal detection in next generation XL-MIMO systems.

Low Complexity Detector for XL-MIMO Uplink: A Cross Splitting Based Information Geometry Approach

TL;DR

This work tackles the high computational burden of uplink signal detection in XL-MIMO by introducing CS-IGA, a cross-splitting information geometry detector whose per-iteration cost scales favorably with the number of users. By factorizing the a posteriori precision into diagonal and low-rank components and enforcing e- and m-conditions, CS-IGA achieves convergence rates comparable to Bayes-optimal AMP while reducing complexity to . The authors further extend the framework to nonlinear, discrete-prior detection via NCS-IGA, which incorporates an extra auxiliary manifold to yield symbol-wise Bayesian estimates with low overhead. Extensive simulations on realistic 3GPP channels demonstrate that CS-IGA and NCS-IGA deliver faster convergence and BER performance close to or surpassing AMP and IGA, at substantially lower computational cost, making them practical for next-generation XL-MIMO uplink detection.

Abstract

In this paper, we propose the cross splitting based information geometry approach (CS-IGA), a novel and low complexity iterative detector for uplink signal recovery in extralarge-scale MIMO (XL-MIMO) systems. Conventional iterative detectors, such as the approximate message passing (AMP) algorithm and the traditional information geometry algorithm (IGA), suffer from a per iteration complexity that scales with the number of base station (BS) antennas, creating a computational bottleneck. To overcome this, CS-IGA introduces a novel cross matrix splitting of the natural parameter in the a posteriori distribution. This factorization allows the iterative detection based on the matched filter, which reduces per iteration computational complexity. Furthermore, we extend this framework to nonlinear detection and propose nonlinear CSIGA (NCS-IGA) by seamlessly embedding discrete constellation constraints, enabling symbol-wise processing without external interference cancellation loops. Comprehensive simulations under realistic channel conditions demonstrate that CS-IGA matches or surpasses the bit error rate (BER) performance of Bayes optimal AMP and IGA for both linear and nonlinear detection, while achieving this with fewer iterations and a substantially lower computational cost. These results establish CS-IGA as a practical and powerful solution for high-throughput signal detection in next generation XL-MIMO systems.

Paper Structure

This paper contains 26 sections, 2 theorems, 31 equations, 10 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation and Information Geometry
  3. System Model
  4. Problem Statement
  5. Linear Detection Scheme
  6. Non‑Linear Detection Scheme
  7. Definitions from Information Geometry
  8. Statistical Manifold of Complex Gaussians
  9. Objective Manifold of Complex Gaussians
  10. Kullback–Leibler (KL) Divergence and m-Projection
  11. Auxiliary Manifolds
  12. CS-IGA for Linear Detection
  13. Construction of Auxiliary Manifolds with Cross Splitting
  14. CS-IGA for signal detection
  15. Information Geometrical Interpretation
  16. ...and 11 more sections

Key Result

Theorem 1

For the $n$-th auxiliary manifold with natural parameters $(\boldsymbol{\theta}_n,\boldsymbol{\Theta}_n)$, the expectation parameters are calculated as where $\check{\boldsymbol{\Lambda}}_n$, $r_n$, $\mathbf{m}_n$ and $v_n$ are given by

Figures (10)

  • Figure 1: BER versus iteration number for different approaches at SNR=13dB under 16QAM modulation.
  • Figure 2: BER versus SNR for different approaches at 3 and 4 iterations under 16QAM modulation.
  • Figure 3: BER versus iteration number for different approaches at SNR=19dB under 64QAM modulation.
  • Figure 4: BER versus SNR for different approaches at 5 and 6 iterations under 64QAM modulation.
  • Figure 5: BER versus iteration number for different approaches at SNR=5dB under QPSK modulation.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof