Exploiting Sparse Recovery Algorithms for Semi-Supervised Training of Deep Neural Networks for Direction-of-Arrival Estimation

Abstract

This paper proposes a semi-supervised training approach for a direction-of-arrival (DoA) estimation based on a convolutional neural network (CNN). We apply a sparse recovery algorithm called optMGD-ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -SVD on the training dataset consisting of only unlabeled observed data to obtain binarized pseudo-spectra regarded as the CNN training targets (labels). The estimated DoAs are obtained at test time by performing peak picking on the CNN outputs. optMGD-ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -SVD has been shown to perform well with a few sensors under low signal-to-noise ratio (SNR) conditions (up to −6 dB) by optimally reweighting the pseudo-spectra of ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -SVD based on the application of group delay function on the pseudo-spectra of MUSIC. Since its hyperparameters are noise-sensitive, we assume that the SNR levels of the training dataset are known such that we can use the optimal ones. We also consider multi-condition training using data of multiple SNR levels to improve the robustness towards different noisy environments. We evaluated the trained networks, named optMGD-ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -SVD-CNN and MGD-ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -SVD-CNN, in terms of the average root-mean-square error and the resolution probability under low SNR conditions (up to −20 dB). We demonstrated that it performed well with a few sensors and snapshots, including at SNR levels unseen in the training data.