Eigenfunctions are widely used to characterize ker-nels in many data-driven analyses. In machine learning, eigen- function decomposition is primarily based on Mercer's theorem, which requires the kernel to be symmetric. This is difficult to satisfy in communication systems as the channel kernel is usually asymmetric due to the different downlink and uplink propagation environments. High Order Generalized Mercer's Theorem (HOGMT) provides a principled way to decompose any multi-dimensional asymmetric kernel into eigenfunctions. To manage the complexity of the eigen-decomposition, we propose an equivalent Neural Network (NN) for decomposing a gen-eral channel kernel. This is further improved by applying the Augmented Lagrangian Method (ALM) to reduce the training time and parameter tuning, which avoids additional tuning rounds when the size of the kernel or the number of eigen- components change depending on the wireless environment. We validate the adaptability of the proposed NN and its accu-racy using simulations in PyTorch. The code is available at https://github.com/ZBZou/HOGMT-ALM/tree/main.
Adaptive Neural Network for Eigen-Decomposition of Multi-Dimensional Channel Kernels
24.06.2024
807333 byte
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
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