Underwater localization with binary measurements: From compressed sensing to deep unfolding

1-bit compressive sensing (1-bit CS) refers to reconstructing a sparse signal from the sign of its measurements. Unlike compressive sensing measurements, the binary measurements in 1-bit CS can be realized using a simple comparator, thereby reducing the hardware complexity and the cost of the receiving array. Many recovery algorithms have been proposed for 1-bit CS, including recently methods based on deep learning. In this paper, we design a new method for underwater source localization by combining the matched field processing method (MFP) with 1-bit CS. We use the Fixed Point Continuation (FPC) method and a deep neural network designed by unfolding its iterations to solve the 1-bit recovery problem and evaluate their performance in the associated source localization problem. Furthermore, in order to improve the robustness of the signal recovery to noise added in the binary measurements, we propose to preprocess the received data with a simple average technique; this formulates the proposed Average FPC-ℓ₁ (AVG-FPC-ℓ₁) method. Our experiments show that an underwater target can be successfully located by using the sign of the measurements. Moreover, with the aid of the noise immunity method and the deep neural network (DNN) structure, the accuracy of the location estimates is greatly improved.