Learning to Decompose Asymmetric Channel Kernels for Generalized Eigenwave Multiplexing

Abstract

Learning the principal eigenfunctions of a kernel is at the core of many machine-learning problems. Common methods usually deal with symmetric kernels based on Mercer’s Theorem. However, in the communication systems, the channel kernel is usually asymmetric due to the inconsistencies between the uplink and the downlink propagation environment. In this paper, we propose an explainable Neural Network for extracting eigenfunctions from generic multi-dimensional asymmetric channel kernels based on a recent method called High Order Generalized Mercer’s Theorem (HOGMT), by decomposing it into jointly orthogonal eigenfunctions. The proposed neural network based approach is efficient and can be easily implemented compared to the conventional SVD based solutions used for eigen decomposition. We also discuss the effect of different hyperparameters on the training time, constraint satisfaction, and overall performance. Finally, we show that multiplexing using these eigenfunctions mitigates interference across all the available Degrees of Freedom (DoF), both mathematically as well as via neural network based system-level simulations.