Deep Learning for MIMO Channel Estimation: Interpretation, Performance, and Comparison
This work addresses the black-box problem in deep learning for wireless communication, offering interpretability that could aid further improvements, though it is incremental as it builds on existing DL methods.
The paper tackles the lack of interpretability in deep learning methods for MIMO channel estimation by providing a theoretical analysis showing that DNNs with ReLU activation approximate piecewise linear functions, enabling universal approximation and performance comparable to or better than traditional MMSE estimation without prior channel statistics.
Deep learning (DL) has emerged as an effective tool for channel estimation in wireless communication systems, especially under some imperfect environments. However, even with such unprecedented success, DL methods are often regarded as black boxes and are lack of explanations on their internal mechanisms, which severely limits further improvement and extension. In this paper, we present a preliminary theoretical analysis on DL based channel estimation for multiple-antenna systems to understand and interpret its internal mechanism. Deep neural network (DNN) with rectified linear unit (ReLU) activation function is mathematically equivalent to a piecewise linear function. Hence, the corresponding DL estimator can achieve universal approximation to a large family of functions by making efficient use of piecewise linearity. We demonstrate that DL based channel estimation does not restrict to any specific signal model and approaches to the minimum mean-squared error (MMSE) estimation in various scenarios without requiring any prior knowledge of channel statistics. Therefore, DL based channel estimation outperforms or is at least comparable with traditional channel estimation, depending on the types of channels. Simulation results confirm the accuracy of the proposed interpretation and demonstrate the effectiveness of DL based channel estimation under both linear and nonlinear signal models.