Joint Target Recovery and Blind Calibration of Phased-Array Radar using Deep Unrolled Model

Digital phased array radar systems, widely used in air surveillance and weather monitoring, offer rapid beam steering and flexible receive beamforming strategies. Sparse signal processing methods have been proposed for target detection using phase array data, leveraging the sparsity of target returns across the range, Doppler, and angle domains. However, these methods often rely on gridding the search space, resulting in large-scale optimization problems that require iterative solvers, making them unsuitable for real-time applications. In this work, we present a novel framework for addressing the target detection problem through a deep-unrolled formulation of a sparse signal estimation algorithm over a finite horizon. Unlike previously proposed unrolled solvers for unconstrained least squares problems with sparsity penalties, our approach tackles the basis pursuit denoising (BPDN) problem. This method imposes a noise-floor constraint on the data fidelity term, eliminating the need for a tunable sparsity penalty term. In radar applications, the noise-floor variance can be directly estimated from the data, whereas the sparsity penalty requires frequent tuning to account for changes in the signal-tonoise ratio (SNR) of the scene. We demonstrate that the proposed unrolled network implemented on a GPU dramatically reduces computation time compared to traditional iterative nonlinear optimizers, as it optimizes step-size policy for finite horizon termination. Furthermore, we extend this framework to jointly address target detection and array calibration problems. Through both measured and simulated data experiments, we empirically validate the performance improvements of our approach when gain and phase perturbations are present in the array element responses.