On Equivalence of Neural Network Receivers

Neural Network (NN) based receivers have seen limited adoption in practical systems due to a lack of explainability and performance guarantees, despite their efficacy as a data-driven tool for physical layer signal processing. In order to bridge this gap in explainability, we present an equivalent NN-based receiver that performs the same optimizations used by classical receivers for symbol detection. Achieving equivalence is crucial to explaining how a NN-based receiver classifies symbols in high-dimensional channels and determining its structure that is robust to the underlying channel with minimum training. We realize this by deriving the risk function that guarantees equivalence, which also provides a measure of the disparity between NN-based and classical receivers. Consequently, this information allows us to derive mathematically tight data-dependent bounds on the bit error rate of NN-based receivers, and empirically determine its structure that achieves minimum error rate. Extensive simulation results show the efficacy of the derived bounds and structure of NN-based receivers for single and multi-antenna systems over a variety of channels.