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 just 4 EM iterations, which is 8 iterations less than a separate system design for a signal-to-noise ratio (SNR) of 6 dB. Additionally, the joint system provides improved estimation accuracy with a mean square error (MSE) of $10^{-4}$. We also identify scenarios where a joint design is not preferable, especially when the channel is noisy (e.g., SNR=2 dB) and the turbo decoder is unable to provide reliable extrinsic information for a BW-based estimator.

翻译：基于Baum-Welch（BW）算法的符号间干扰信道盲估计（该算法是用于训练隐马尔可夫模型的期望最大化（EM）算法的一种具体实现）具有鲁棒性，且无需标注数据。然而，该算法以计算成本高、收敛速度慢且常收敛于局部极值而著称。本文通过将信道参数与两个连续状态相关联，修改了BW算法的网格结构。此修改使得我们能够在保持相同性能的同时，将所需状态数减半。此外，为提高收敛速度和估计性能，我们利用Turbo译码器产生的外在信息，在每次EM迭代中优化基于BW的估计器，从而构建了一个联合Turbo-BW均衡系统。实验表明，在信噪比（SNR）为6 dB的条件下，该联合系统仅需4次EM迭代即可收敛，比分离式系统设计减少了8次迭代。同时，联合系统提供了更高的估计精度，其均方误差（MSE）达到$10^{-4}$。我们还指出了联合设计并非更优的场景，特别是当信道噪声较大（例如SNR=2 dB）且Turbo译码器无法为基于BW的估计器提供可靠外在信息时。