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Optimization of Iterative Blind Detection based on Expectation Maximization and Belief Propagation

Luca Schmid, Tomer Raviv, Nir Shlezinger, Laurent Schmalen

TL;DR

This work tackles blind joint channel estimation and symbol detection for block-fading ISI channels using a factor-graph based BP detector augmented with EM for parameter learning. By unfolding EM and BP into a trainable architecture and introducing momentum-based updates, the authors learn efficient update schedules that reduce EM steps while preserving performance, and improve BP convergence. Empirical results show EMBP can surpass coherent BP in high SNR and with pilots, while achieving low complexity through selective, learned updates. The approach offers a scalable, robust receiver design for short-block transmissions in next-generation communications.

Abstract

We study iterative blind symbol detection for block-fading linear inter-symbol interference channels. Based on the factor graph framework, we design a joint channel estimation and detection scheme that combines the expectation maximization (EM) algorithm and the ubiquitous belief propagation (BP) algorithm. Interweaving the iterations of both schemes significantly reduces the EM algorithm's computational burden while retaining its excellent performance. To this end, we apply simple yet effective model-based learning methods to find a suitable parameter update schedule by introducing momentum in both the EM parameter updates as well as in the BP message passing. Numerical simulations verify that the proposed method can learn efficient schedules that generalize well and even outperform coherent BP detection in high signal-to-noise scenarios.

Optimization of Iterative Blind Detection based on Expectation Maximization and Belief Propagation

TL;DR

This work tackles blind joint channel estimation and symbol detection for block-fading ISI channels using a factor-graph based BP detector augmented with EM for parameter learning. By unfolding EM and BP into a trainable architecture and introducing momentum-based updates, the authors learn efficient update schedules that reduce EM steps while preserving performance, and improve BP convergence. Empirical results show EMBP can surpass coherent BP in high SNR and with pilots, while achieving low complexity through selective, learned updates. The approach offers a scalable, robust receiver design for short-block transmissions in next-generation communications.

Abstract

We study iterative blind symbol detection for block-fading linear inter-symbol interference channels. Based on the factor graph framework, we design a joint channel estimation and detection scheme that combines the expectation maximization (EM) algorithm and the ubiquitous belief propagation (BP) algorithm. Interweaving the iterations of both schemes significantly reduces the EM algorithm's computational burden while retaining its excellent performance. To this end, we apply simple yet effective model-based learning methods to find a suitable parameter update schedule by introducing momentum in both the EM parameter updates as well as in the BP message passing. Numerical simulations verify that the proposed method can learn efficient schedules that generalize well and even outperform coherent BP detection in high signal-to-noise scenarios.
Paper Structure (10 sections, 11 equations, 3 figures, 1 algorithm)

This paper contains 10 sections, 11 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. Channel Model
  4. Factor Graph-based Symbol Detection
  5. Blind Estimation and Detection via EM and BP
  6. Optimizing the EM Parameter Update Schedule
  7. Enhancing BP Accuracy
  8. The EMBP Algorithm
  9. Simulation Study
  10. Conclusion

Figures (3)

  • Figure 1: Factor graph representation of \ref{['eq:Ungerboeck_factorization']} for a channel with memory $L=2$.
  • Figure 2: BER over $\mathsf{snr}$ for various detection schemes, averaged over $10^7$ random channels with ${L=2}$. For the EMBP algorithm, a fixed serial EM update schedule is applied.
  • Figure 3: Mean squared estimation error ${\lVert \hat{\boldsymbol{h}} - \boldsymbol{h} \rVert^2}$ after each iteration of the EMBP algorithm with different EM parameter update schedules. The randomly sampled channels have ${\mathsf{snr}=10}$ dB and memory ${L=5}$, i.e., $7$ parameters to estimate (including $\sigma^2$).