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Trainable Joint Channel Estimation, Detection and Decoding for MIMO URLLC Systems

Yi Sun, Hong Shen, Bingqing Li, Wei Xu, Pengcheng Zhu, Nan Hu, Chunming Zhao

TL;DR

This work addresses URLLC challenges arising from short packets and limited pilots by proposing joint channel estimation, detection, and decoding (JCDD) under MAP criteria for both Gaussian MIMO and sparse mmWave channels. It develops ADMM-based solutions and unfolds them into two model-driven networks, JCDDNet-G for Gaussian MIMO and JCDDNet-S for sparse mmWave, enabling end-to-end trainable receivers that leverage LDPC constraints and pilot data. The networks demonstrate superior performance to traditional turbo receivers while maintaining significantly lower complexity per layer, and show robustness to channel statistics and moderate mismatches. The framework extends to multiuser scenarios and various code families, offering a practical, low-latency alternative for URLLC deployments with short codes and few pilots.

Abstract

The receiver design for multi-input multi-output (MIMO) ultra-reliable and low-latency communication (URLLC) systems can be a tough task due to the use of short channel codes and few pilot symbols. Consequently, error propagation can occur in traditional turbo receivers, leading to performance degradation. Moreover, the processing delay induced by information exchange between different modules may also be undesirable for URLLC. To address the issues, we advocate to perform joint channel estimation, detection, and decoding (JCDD) for MIMO URLLC systems encoded by short low-density parity-check (LDPC) codes. Specifically, we develop two novel JCDD problem formulations based on the maximum a posteriori (MAP) criterion for Gaussian MIMO channels and sparse mmWave MIMO channels, respectively, which integrate the pilots, the bit-to-symbol mapping, the LDPC code constraints, as well as the channel statistical information. Both the challenging large-scale non-convex problems are then solved based on the alternating direction method of multipliers (ADMM) algorithms, where closed-form solutions are achieved in each ADMM iteration. Furthermore, two JCDD neural networks, called JCDDNet-G and JCDDNet-S, are built by unfolding the derived ADMM algorithms and introducing trainable parameters. It is interesting to find via simulations that the proposed trainable JCDD receivers can outperform the turbo receivers with affordable computational complexities.

Trainable Joint Channel Estimation, Detection and Decoding for MIMO URLLC Systems

TL;DR

This work addresses URLLC challenges arising from short packets and limited pilots by proposing joint channel estimation, detection, and decoding (JCDD) under MAP criteria for both Gaussian MIMO and sparse mmWave channels. It develops ADMM-based solutions and unfolds them into two model-driven networks, JCDDNet-G for Gaussian MIMO and JCDDNet-S for sparse mmWave, enabling end-to-end trainable receivers that leverage LDPC constraints and pilot data. The networks demonstrate superior performance to traditional turbo receivers while maintaining significantly lower complexity per layer, and show robustness to channel statistics and moderate mismatches. The framework extends to multiuser scenarios and various code families, offering a practical, low-latency alternative for URLLC deployments with short codes and few pilots.

Abstract

The receiver design for multi-input multi-output (MIMO) ultra-reliable and low-latency communication (URLLC) systems can be a tough task due to the use of short channel codes and few pilot symbols. Consequently, error propagation can occur in traditional turbo receivers, leading to performance degradation. Moreover, the processing delay induced by information exchange between different modules may also be undesirable for URLLC. To address the issues, we advocate to perform joint channel estimation, detection, and decoding (JCDD) for MIMO URLLC systems encoded by short low-density parity-check (LDPC) codes. Specifically, we develop two novel JCDD problem formulations based on the maximum a posteriori (MAP) criterion for Gaussian MIMO channels and sparse mmWave MIMO channels, respectively, which integrate the pilots, the bit-to-symbol mapping, the LDPC code constraints, as well as the channel statistical information. Both the challenging large-scale non-convex problems are then solved based on the alternating direction method of multipliers (ADMM) algorithms, where closed-form solutions are achieved in each ADMM iteration. Furthermore, two JCDD neural networks, called JCDDNet-G and JCDDNet-S, are built by unfolding the derived ADMM algorithms and introducing trainable parameters. It is interesting to find via simulations that the proposed trainable JCDD receivers can outperform the turbo receivers with affordable computational complexities.
Paper Structure (26 sections, 1 theorem, 78 equations, 12 figures, 2 tables, 2 algorithms)

This paper contains 26 sections, 1 theorem, 78 equations, 12 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. JCDD for Gaussian MIMO Channels
  4. Problem Formulation
  5. ADMM-Based Solution
  6. Network Design
  7. JCDD for Sparse mmWave MIMO Channels
  8. Problem Formulation
  9. ADMM-Based Solution
  10. Optimization of ${\bf G}_s$
  11. Optimization of $\bf b$
  12. Network Design
  13. Extension for Multiuser Case
  14. Numerical Results
  15. Training Strategy
  16. ...and 11 more sections

Key Result

Proposition 1

Letting ${{\bf w}_{\bf b}} \triangleq {{\bf{X}}_{\bf b}^H}{\bf{y}}$ and ${{\bf R}_{\bf b}} \triangleq {{{\bf{X}}_{\bf b}^H}{{\bf{X}}_{\bf b}} + {\sigma ^2}{\bf{C}}_{\bf{g}}^{ - 1}}$, a surrogate problem of subproblem (eq20a) is given by where ${{\bf D}^{n-1}} = {\left( {\lambda ^{n - 1}}{{\bf{I}}_{{N_t}}} - {{\bf{V}}_{{{\bf{b}}^{n-1}}}^H}{{\bf{V}}_{{{\bf{b}}^{n-1}}}} \right)f({{\bf b}^{n-1}})} +

Figures (12)

  • Figure 1: The motivation of the proposed receiver design.
  • Figure 2: Block diagrams of (a) traditional turbo receivers and (b) proposed trainable JCDD receivers.
  • Figure 3: Block diagram of the $l$-th layer of JCDDNet-G.
  • Figure 4: Block diagram of the $l$-th layer of JCDDNet-S.
  • Figure 5: Comparison of JCDDNet-G and its corresponding ADMM algorithm in terms of (a) BLER performance and (b) average number of iterations/layers and time per codeword under i.i.d. Gaussian MIMO channels with QPSK modulation.
  • ...and 7 more figures

Theorems & Definitions (1)

  • Proposition 1