DeepFPC: A Deep Unfolded Network for Sparse Signal Recovery from 1-Bit Measurements With Application to DOA Estimation

In this paper, we introduce a novel deep neural network, coined DeepFPC, and investigate its application to tackling the problem of direction-of-arrival (DOA) estimation. DeepFPC is designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided 1 -norm (FPC- 1 ), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates prior knowledge about the signal structure (i.e., sparsity), thereby offering interpretability by design. Once DeepFPC is properly trained, a sparse signal can be recovered fast and accurately from quantized measurements. The proposed model is then applied in DOA estimation and is shown to outperform state-of-the-art solutions; namely, the iterative FPC- 1 algorithm and the deep convolution network (DCN) model.