Deep Learning of the Sparse Array Configurations in Optimum Beamforming

The article examines neural network learning of the sparse array configurations in optimum beamforming. Unlike iterative greedy, convex, and global optimization methods for optimum array design, deep learning enables fast reconfigurations of the sparse array in rapid dynamic propagation environments. We employ three different convolutional neural network architectures with varying simplification and parameter counts. The network is trained to select <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> out of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> uniformly spaced antennas to achieve maximum signal-to-interference and noise ratio (SINR) beamforming. Different values of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> are considered, including <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> = 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>, for studying network performance under an increased number of subarray classes. We consider one desired source and one interference of arbitrary angle, and delineate the learning results for the two cases where the network is trained with the desired source assuming fixed and varying angles. We discuss the benefits of reducing the number of possible configurations due to sidelobe level reductions. It is also shown that the network performance significantly improves with data augmentations and by removing redundant array configurations which produce the same SINR.