We investigate the application of the factor graph framework for blind joint channel estimation and symbol detection on time-variant linear inter-symbol interference channels. In particular, we consider the expectation maximization (EM) algorithm for maximum likelihood estimation, which typically suffers from high complexity as it requires the computation of the symbol-wise posterior distributions in every iteration. We address this issue by efficiently approximating the posteriors using the belief propagation (BP) algorithm on a suitable factor graph. By interweaving the iterations of BP and EM, the detection complexity can be further reduced to a single BP iteration per EM step. In addition, we propose a data-driven version of our algorithm that introduces momentum in the BP updates and learns a suitable EM parameter update schedule, thereby significantly improving the performance-complexity tradeoff with a few offline training samples. Our numerical experiments demonstrate the excellent performance of the proposed blind detector and show that it even outperforms coherent BP detection in high signal-to-noise scenarios.

翻译：我们研究了因子图框架在时变线性符号间干扰信道上进行盲联合信道估计与符号检测中的应用。具体而言，我们考虑了用于最大似然估计的期望最大化（EM）算法，但该算法通常因每次迭代需计算符号级后验分布而导致复杂度较高。我们通过在合适的因子图上采用置信传播（BP）算法高效近似后验分布来解决此问题。通过交织BP与EM的迭代流程，检测复杂度可进一步降低至每步EM仅需一次BP迭代。此外，我们提出了算法的数据驱动版本，在BP更新中引入动量项并学习合适的EM参数更新策略，从而通过少量离线训练样本显著优化了性能与复杂度的权衡。数值实验表明，所提出的盲检测器具有优异性能，且在高信噪比场景下甚至优于相干BP检测。