Sequential Estimation of Frequency and Direction-of-Arrival Based on the Relaxed Coprime Array for Multiple Targets

Recently, extensive researches focus on the joint estimation of carrier frequency and direction-of-arrival, whereas the heavy computation burden and affordable hardware cost are always required therein. To alleviate the problem, we propose a relaxed coprime array based two-stage estimator, which can sequentially detect the frequencies and direction-of-arrival for multiple targets. Guided by the closed-form robust algorithm, this relaxation yields a higher array sparsity compared with existing sparse arrays. Specifically, the first stage aims to achieve the classification of the frequency and angle remainders arising from temporal-spatial undersampling, which is realized by combining spectrum correction with pattern clustering. By incorporating the closed-form robust Chinese Remainder Theorem into the remainder classification result, we obtain all the frequencies and direction-of-arrival in the second stage. Both performance analysis and numerical results were conducted to verify the effectiveness of the proposed estimator in the multi-target case.