Modified Baum-Welch Algorithm for Joint Blind Channel Estimation and Turbo Equalization

TL;DR

This paper introduces a modified Baum-Welch algorithm with a new trellis structure and a joint turbo equalization system that significantly improves convergence speed and estimation accuracy in blind channel estimation for intersymbol interference channels.

Contribution

It proposes a novel trellis modification for the Baum-Welch algorithm and integrates it with turbo equalization to enhance convergence and performance in blind channel estimation.

Findings

Joint system converges in 10 EM iterations at 4dB SNR.

Achieves MSE of 10^{-4} at 6dB SNR.

Reduces computational complexity by halving the number of states.

Abstract

Blind estimation of intersymbol interference channels based on the Baum-Welch (BW) algorithm, a specific implementation of the expectation-maximization (EM) algorithm for training hidden Markov models, is robust and does not require labeled data. However, it is known for its extensive computation cost, slow convergence, and frequently converges to a local maximum. In this paper, we modified the trellis structure of the BW algorithm by associating the channel parameters with two consecutive states. This modification enables us to reduce the number of required states by half while maintaining the same performance. Moreover, to improve the convergence rate and the estimation performance, we construct a joint turbo-BW-equalization system by exploiting the extrinsic information produced by the turbo decoder to refine the BW-based estimator at each EM iteration. Our experiments demonstrate that the joint system achieves convergence in 10 EM iterations, which is 8 iterations less than a separate system design for a signal-to-noise ratio (SNR) of 4dB. Additionally, the joint system provides improved estimation accuracy with a mean square error (MSE) of $10^{-4}$ for an SNR of 6dB. We also identify scenarios where a joint design is not preferable, especially when the channel is noisy (e.g., SNR=2dB) and the decoder cannot provide reliable extrinsic information for a BW-based estimator.