This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on the uplink performance of single-cell massive MIMO (multiple-input multiple-output) in practical Rician fading environments. First, Bussgang decomposition-based effective channels and distortion characteristics are analytically derived and the spectral efficiency (SE) achieved by several receivers are explored for third-order non-linearities. Next, two deep feedforward neural networks are designed and trained to estimate the effective channels and the distortion variance at each BS antenna, which are used in signal detection. We compare the performance of the proposed methods with state-of-the-art distortion-aware and -unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise. Using the data generated by the derived effective channels for general order of non-linearities at both the BS and UEs, it is shown that the deep learning-based estimator provides better estimates of the effective channels also for non-linearities more than order three.

中文翻译：

---

硬件非线性下大规模MIMO中的信道估计：贝叶斯方法与深度学习

本文考虑了基站（BS）和用户设备（UE）的非线性硬件损伤对实际Rician衰落环境中单小区大规模MIMO（多输入多输出）的上行链路性能的共同影响。首先，分析得出基于Bussgang分解的有效信道和失真特性，并探索由多个接收器实现的频谱效率（SE），以获取三阶非线性。接下来，设计并训练了两个深度前馈神经网络，以估计每个BS天线的有效信道和失真方差，并将其用于信号检测。我们将提出的方法的性能与最新的失真感知和不感知贝叶斯线性最小均方误差（LMMSE）估计量进行比较。提出的深度学习方法通​​过利用损伤特征来提高估计质量，而LMMSE方法则将失真视为噪声。使用由导出的有效信道生成的数据来估计BS和UE处的非线性的一般顺序，表明基于深度学习的估计器还为非线性提供了比三阶更好的有效信道估计。