Deep Learning for Channel Estimation: Interpretation, Performance, and Comparison

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 their further improvement and extension. In this paper, we present preliminary theoretical analysis on DL based channel estimation for single-input multiple-output (SIMO) systems to understand and interpret its internal mechanisms. As deep neural network (DNN) with rectified linear unit (ReLU) activation function is mathematically equivalent to a piecewise linear function, 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 asymptotically 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.