In this paper we study the expectation maximization (EM) technique for one-bit MIMO-OFDM detection (OMOD). Arising from the recent interest in massive MIMO with one-bit analog-to-digital converters, OMOD is a massive-scale problem. EM is an iterative method that can exploit the OFDM structure to process the problem in a per-iteration efficient fashion. In this study we analyze the convergence rate of EM for a class of approximate maximum-likelihood OMOD formulations, or, in a broader sense, a class of problems involving regression from quantized data. We show how the SNR and channel conditions can have an impact on the convergence rate. We do so by making a connection between the EM and the proximal gradient methods in the context of OMOD. This connection also gives us insight to build new accelerated and/or inexact EM schemes. The accelerated scheme has faster convergence in theory, and the inexact scheme provides us with the flexibility to implement EM more efficiently, with convergence guarantee. Furthermore we develop a deep EM algorithm, wherein we take the structure of our inexact EM algorithm and apply deep unfolding to train an efficient structured deep net. Simulation results show that our accelerated exact/inexact EM algorithms run much faster than their standard EM counterparts, and that the deep EM algorithm gives promising detection and runtime performances.

翻译：本文研究了期望最大化（EM）技术在单比特MIMO-OFDM检测（OMOD）中的应用。随着近期对采用单比特模数转换器的大规模MIMO系统兴趣的激增，OMOD成为一项大规模问题。EM作为一种迭代方法，能够利用OFDM结构，在每次迭代中高效处理该问题。本研究分析了一类近似最大似然OMOD公式（或更广义而言，涉及量化数据回归的问题）中EM的收敛速率，并揭示了信噪比与信道条件如何影响该收敛速率。通过建立EM与近端梯度方法在OMOD背景下的联系，我们得以构建新的加速和/或非精确EM方案。加速方案在理论上具有更快的收敛性，而非精确方案则提供了更高效实现EM的灵活性，同时保证收敛性。此外，我们开发了一种深度EM算法，通过提取非精确EM算法的结构并应用深度展开技术，训练出高效的深度结构化网络。仿真结果表明，我们提出的加速精确/非精确EM算法运行速度显著快于标准EM算法，且深度EM算法在检测性能与运行时间方面均表现出色。