Deep learning has seen a rapid adoption in a variety of wireless communications applications, including at the physical layer. While it has delivered impressive performance in tasks such as channel equalization and receive processing/symbol detection, it leaves much to be desired when it comes to explaining this superior performance. In this work, we investigate the specific task of channel equalization by applying a popular learning-based technique known as Reservoir Computing (RC), which has shown superior performance compared to conventional methods and other learning-based approaches. Specifically, we apply the echo state network (ESN) as a channel equalizer and provide a first principles-based signal processing understanding of its operation. With this groundwork, we incorporate the available domain knowledge in the form of the statistics of the wireless channel directly into the weights of the ESN model. This paves the way for optimized initialization of the ESN model weights, which are traditionally untrained and randomly initialized. Finally, we show the improvement in receive processing/symbol detection performance with this optimized initialization through simulations. This is a first step towards explainable machine learning (XML) and assigning practical model interpretability that can be utilized together with the available domain knowledge to improve performance and enhance detection reliability.
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