Data-Driven Symbol Detection for Intersymbol Interference Channels with Bursty Impulsive Noise

TL;DR

The paper tackles data-driven MAP symbol detection for ISI channels afflicted by bursty impulsive noise, where full channel state information (CSI) is unavailable or impractical. It develops three detectors: NN-based BCJR for likelihood learning, HMM-based BCJR for unsupervised learning of state transitions, and a hybrid NN-HMM approach that jointly optimizes likelihoods and transitions. Results show that both NN-BJRR and HMM-BJRR achieve BERs close to the optimal full-CSI BCJR, significantly outperforming detectors that rely on inaccurate CSI, and demonstrating strong robustness to rapid ISI variations and non-Gaussian impulsive noise. The study highlights the practical viability of data-driven trellis detectors in digital broadcasting and vehicular scenarios, reducing reliance on precise CSI while maintaining near-optimal performance. A hybrid NN-HMM detector emerges as a particularly promising option when observation likelihoods are complex or non-Gaussian.

Abstract

We developed machine learning approaches for data-driven trellis-based soft symbol detection in coded transmission over intersymbol interference (ISI) channels in presence of bursty impulsive noise (IN), for example encountered in wireless digital broadcasting systems and vehicular communications. This enabled us to obtain optimized detectors based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm while circumventing the use of full channel state information (CSI) for computing likelihoods and trellis state transition probabilities. First, we extended the application of the neural network (NN)-aided BCJR, recently proposed for ISI channels with additive white Gaussian noise (AWGN). Although suitable for estimating likelihoods via labeling of transmission sequences, the BCJR-NN method does not provide a framework for learning the trellis state transitions. In addition to detection over the joint ISI and IN states we also focused on another scenario where trellis transitions are not trivial: detection for the ISI channel with AWGN with inaccurate knowledge of the channel memory at the receiver. Without access to the accurate state transition matrix, the BCJR- NN performance significantly degrades in both settings. To this end, we devised an alternative approach for data-driven BCJR detection based on the unsupervised learning of a hidden Markov model (HMM). The BCJR-HMM allowed us to optimize both the likelihood function and the state transition matrix without labeling. Moreover, we demonstrated the viability of a hybrid NN and HMM BCJR detection where NN is used for learning the likelihoods, while the state transitions are optimized via HMM. While reducing the required prior channel knowledge, the examined data-driven detectors with learned trellis state transitions achieve bit error rates close to the optimal full CSI-based BCJR, significantly outperforming detection with inaccurate CSI.

Figures (10)

• Figure 1: HMM representation as an undirected graph showing the factorization and conditional independencies implied by the model.
• Figure 2: State diagram representation of a 4-state HMM highlighting the model parameters: the observation likelihood function and the state transition matrix.
• Figure 3: Trellis diagram representation of a 4-state HMM illustrating the message passing mechanism in the forward-backward algorithm.
• Figure 4: Schematic of the communication system using channel model-based or data-driven symbol detector based on the forward-backward algorithm (BCJR detection). The neural network can be used in the data-driven estimation of the channel likelihoods, while both the channel likelihood estimation and the state transitions can be obtained by an HMM optimization.
• Figure 5: SER versus SNR for uncoded BPSK transmission over a time-invariant ISI ($L=2$ and $\sigma^2_h=0$) channel with AWGN for systems with channel model-based or data-driven BCJR detection.