A Multi-Dimensional Newtonized Orthogonal Matching Pursuit Algorithm for Phased Array Radar

Traditional pulse-Doppler radar employs linear signal processing methods for target detection and state estimation， offering advantages such as low complexity and high processing efficiency. However， in complex scenarios as in closely spaced targets， traditional methods encounter challenges such as weak targets being obscured by the sidelobes of strong targets and limitations imposed by the Rayleigh resolution. The compressed sensing （CS） approach effectively leverages the sparsity of targets across four domains： fast time， slow time， azimuth， and elevation. By discretizing these domains into grids， it reconstructs targets through sparse inversion. However， since parameters such as radial distance， radial velocity， azimuth angle， and elevation angle are inherently continuous， grid-based methods face issues that include grid mismatch， resolution constrained by grid spacing， and non-constant false alarm rates. In this study， a multidimensional Newtonized orthogonal matching pursuit algorithm for phased array radar （MDNOMP-PAR） customized for multitarget scenarios is proposed for linear frequency modulation pulse signals. The algorithm iteratively refines the radial distance， radial velocity， azimuth angle， and elevation angle of multiple targets using Newton’s method and block coordinate descent. It also employs a constant false alarm rate （CFAR） criterion to design the stopping condition， ultimately determining the number of targets. Numerical experiments demonstrate that compared with conventional methods—such as digital beamforming （DBF）， windowed pulse compression （WPC）， and moving target detection （MTD）—MDNOMP-PAR not only retains the CFAR detection characteristics but also improves estimation accuracy by at least 100%； With a spatial resolution of 37.5 m， this method achieved a resolution of 45 m， offering a 50 m improvement in resolution compared to the windowed pulse compression MTD method. Furthermore， in scenarios involving adjacent strong and weak targets， when the false alarm rate was set to 10^-6， the weak target detection performance of the MDNOMP-PAR method improved by 4 dB.