Deep Learning and Latent Variables in Nonuniform Antenna Array Processing for Direction of Arrival

The problem of Direction of Arrival (DOA) in Antenna Array processing has been widely studied. Nonuniform spacing between consecutive elements of linear arrays gives particular advantages but is also challenging. Precedent solutions aimed to deal with it using standard and complex Deep Learning architectures. Given the simplicity of the complex DOA basic equations, we hypothesized that the intrinsic structure of DOA problems should correspond to well-defined manifolds in low-dimensional latent spaces and that this should also hold in nonuniform spatially distributed arrays. We benchmarked a variety of manifold learning estimators for DOA problems, namely, Principal Component Analysis, t-Distributed Stochastic Neighbor Embedding (tSNE), shallow and deep autoencoders (AE), and Uniform Manifold Active Projection (UMAP). The generated latent spaces exhibited intrinsic geometrical structures in one-dimensional manifolds with four branches. On the other hand, DOA recovery built upon fine-tuning these latent spaces exhibited better performance for nonuniform arrays using shallow AE architectures. Our results pave the way for using low-dimensional latent variable spaces in various electromagnetic problems based on the simplicity of the physical equations describing these technologies.