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Hybrid Message Passing-Based Detectors for Uplink Grant-Free NOMA Systems

Yi Song, Yiwen Zhu, Kun Chen-Hu, Xinhua Lu, Peng Sun, Zhongyong Wang

TL;DR

This work tackles uplink grant-free NOMA detection under temporally correlated user activity. It introduces a Bernoulli-Gaussian-Markov chain prior to jointly model sparsity and slow activity evolution, and develops a GAMP-based detector (GAMP-BG-MC) that leverages bidirectional time-slot messages. The detector employs Hybrid Message Passing with HMP-TSGM to integrate BP/MF on a mixed factor graph and adaptively learn the BG-MC parameters during estimation. Experimental results show improved detection accuracy over existing methods while maintaining the same order of computational complexity, highlighting the approach's potential for low-latency, high-reliability scenarios in 6G and beyond.

Abstract

This paper studies improving the detector performance which considers the activity state (AS) temporal correlation of the user equipments (UEs) in the time domain under the uplink grant-free non-orthogonal multiple access (GF-NOMA) system. The Bernoulli Gaussian-Markov chain (BG-MC) probability model is used for exploiting both the sparsity and slow change characteristic of the AS of the UE. The GAMP Bernoulli Gaussian-Markov chain (GAMP-BG-MC) algorithm is proposed to improve the detector performance, which can utilize the bidirectional message passing between the neighboring time slots to fully exploit the temporally-correlated AS of the UE. Furthermore, the parameters of the BG-MC model can be updated adaptively during the estimation procedure with unknown system statistics. Simulation results show that the proposed algorithm can improve the detection accuracy compared with the existing methods while keeping the same order complexity.

Hybrid Message Passing-Based Detectors for Uplink Grant-Free NOMA Systems

TL;DR

This work tackles uplink grant-free NOMA detection under temporally correlated user activity. It introduces a Bernoulli-Gaussian-Markov chain prior to jointly model sparsity and slow activity evolution, and develops a GAMP-based detector (GAMP-BG-MC) that leverages bidirectional time-slot messages. The detector employs Hybrid Message Passing with HMP-TSGM to integrate BP/MF on a mixed factor graph and adaptively learn the BG-MC parameters during estimation. Experimental results show improved detection accuracy over existing methods while maintaining the same order of computational complexity, highlighting the approach's potential for low-latency, high-reliability scenarios in 6G and beyond.

Abstract

This paper studies improving the detector performance which considers the activity state (AS) temporal correlation of the user equipments (UEs) in the time domain under the uplink grant-free non-orthogonal multiple access (GF-NOMA) system. The Bernoulli Gaussian-Markov chain (BG-MC) probability model is used for exploiting both the sparsity and slow change characteristic of the AS of the UE. The GAMP Bernoulli Gaussian-Markov chain (GAMP-BG-MC) algorithm is proposed to improve the detector performance, which can utilize the bidirectional message passing between the neighboring time slots to fully exploit the temporally-correlated AS of the UE. Furthermore, the parameters of the BG-MC model can be updated adaptively during the estimation procedure with unknown system statistics. Simulation results show that the proposed algorithm can improve the detection accuracy compared with the existing methods while keeping the same order complexity.
Paper Structure (14 sections, 26 equations, 3 figures, 1 algorithm)

This paper contains 14 sections, 26 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Factor Graph
  3. System Model
  4. Probabilistic Formulation
  5. Factor Graph Representation
  6. Adaptive detector based on the HMP rule
  7. Computation of the HMP for GAMP-BG-MC algorithm
  8. GAMP part messages
  9. MC part messages
  10. Transition probability update part
  11. Variance update part
  12. Message Passing Scheduling
  13. Simulation Results
  14. Conclusion

Figures (3)

  • Figure 1: The left part of the figure denotes the uplink transmission from to the ; The right part of the figure indicates the sparse and temporally correlated structures of the transmit signal $\boldsymbol{B}$.
  • Figure 2: Factor graph representation for the detectors.
  • Figure 3: Performance of proposed GAMP-BG-MC algorithm.