基于矩阵填充的随机步进频雷达高分辨距离-多普勒谱稀疏恢复方法

Random Stepped Frequency (RSF) radars can achieve high-range resolution with relatively low hardware complexity by synthesizing a wide bandwidth. Moreover, because of the random frequency agility of each pulse, the radars possess robust anti-interference and electromagnetic compatibility capabilities, rendering them invaluable for high-precision detection in complex electromagnetic environments. However, the inherent sparsity sensing of the radar waveform in the time-frequency domain, causes a lack of echo coherence information, leading to an underdetermined estimation of the traditional matched filter, which results in fluctuating high side lobes in the estimation spectrum and adversely deteriorating detection performance. This paper proposes a sparse recovery method based on Hankel matrix completion for the high-resolution range-Doppler spectrum of the RSF radars. Using the low-rank matrix completion concept, this method fills in the missing samples caused by sparse sensing for RSF radars, thereby restoring continuous coherence information and effectively addressing the underdetermined estimation issue. First, an undersampled data matrix of a single coarse-resolution range for RSF radar is constructed. Subsequently, the time-frequency data matrix is reconstructed into a double Hankel form, and its low-rank prior characteristics are analyzed and proven. Finally, the Alternating Direction Method of Multipliers (ADMM) algorithm is applied to restore the unsampled time-frequency data, ensuring sparse recovery of the high-resolution range-Doppler spectrum with low sidelobes. Simulations and real tests demonstrate the effectiveness and superiority of the proposed method.