Sparse Reconstruction Algorithm for Extended Targets in Frequency-Agile Radar Based on ADMM-MFOCUSS

Frequency-agile radar can achieve high resolution reconstruction of multiple scattering points from a given target. However， for extended targets， the scattering points are distributed across multiple range bins， and the range-phase factors of these points in adjacent bins may interfere with each other. This interference often leads to redundant reconstructions. To address this limitation， a sparse signal processing model was developed for extended targets. The causes and characteristics of the positional distribution of redundant reconstructions were analyzed， and a sparse reconstruction algorithm is proposed that integrates the alternating direction method of multipliers （ADMM） and multi focal underdetermined system solver （MFOCUSS） algorithms. Therefore， the proposed method is referred to as the ADMM-MFOCUSS algorithm. ADMM-MFOCUSS first performs sparse reconstruction via ADMM， followed by suppression of repeated responses via analysis of the energy of the solutions as well as the consistency of the indicated positions. Reliable support sets are adaptively selected， and the amplitudes of sparse solutions are further refined within the support sets using MFOCUSS to enable accurate scene reconstruction for extended targets. Simulation results demonstrate that the proposed method achieves accurate parameter estimation for extended targets in frequency-agile radar scenarios involving multiple range gates. Compared with existing approaches such as regularized adaptive matching pursuit （RAMP）， ADMM， and MFOCUSS， the proposed algorithm yields higher reconstruction accuracy and lower false alarm rates.