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.

中文翻译：

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深度学习以进行渠道估算：解释，性能和比较

在无线通信系统中，尤其是在某些不完善的环境下，深度学习（DL）已成为一种有效的信道估计工具。但是，即使取得了如此空前的成功，DL方法也经常被视为黑匣子，并且缺乏对其内部机制的解释，这严重限制了它们的进一步改进和扩展。在本文中，我们对基于DL的单输入多输出（SIMO）系统的信道估计进行了初步的理论分析，以了解和解释其内部机制。由于具有整流线性单位（ReLU）激活函数的深度神经网络（DNN）在数学上等同于分段线性函数，因此相应的DL估计量可以通过有效利用分段线性来实现对大功能族的通用逼近。我们证明基于DL的信道估计不限于任何特定的信号模型，并且在各种情况下都渐近地接近最小均方误差（MMSE）估计，而无需任何信道统计的先验知识。因此，取决于信道的类型，基于DL的信道估计优于或至少可与传统信道估计相比。仿真结果证实了所提出的解释的准确性，并证明了在线性和非线性信号模型下基于DL的信道估计的有效性。基于DL的信道估计优于或至少与传统信道估计相当，具体取决于信道的类型。仿真结果证实了所提出的解释的准确性，并证明了在线性和非线性信号模型下基于DL的信道估计的有效性。基于DL的信道估计优于或至少可与传统信道估计相比，这取决于信道的类型。仿真结果证实了所提出的解释的准确性，并证明了在线性和非线性信号模型下基于DL的信道估计的有效性。