Coprime arrays have shown potential advantages for direction-of-arrival (DOA) estimation by increasing the number of degrees-of-freedom in the difference coarray domain with fewer physical sensors. In this paper, a new DOA estimation algorithm for coprime array based on the estimation of signal parameter via rotational invariance techniques (ESPRIT) is proposed. We firstly derive the observation vector of the virtual uniform linear array but the covariance matrix of this observation vector is rank-deficient. Different from the traditional Toeplitz matrix reconstruction method using the observation vector, we propose a modified Toeplitz matrix reconstruction method using any non-zero row of the covariance matrix in the virtual uniform linear array. It can be proved in theory that the reconstructed Toeplitz covariance matrix has full rank. Therefore, the improved ESPRIT method can be used for DOA estimation without peak searching. Finally, the closed-form solution for DOA estimation in coprime array is obtained. Compared to the traditional coprime multiple signal classification (MUSIC) methods, the proposed method circumvents the use of spatial smoothing technique, which usually results in performance degradation and heavy computational burden. The effectiveness of the proposed method is demonstrated by numerical examples.

Coprime array exhibits many advantages over the uniform linear array (ULA) with the same number of physical sensors in resolution performance and interference suppression capability. In this study, the authors take the advantages of coprime array to improve the robustness of adaptive beamformer. In the coprime virtual ULA (CV‐ULA), they prove that a constructed Toeplitz matrix can be taken as the sample covariance matrix from the perspective of virtual signal characteristics. The CV‐ULA Capon spectrum estimator is modified to obtain the directions and powers of all impinging signals. Since the real directions of all impinging signals are located at different angular sectors, they form independent signal subspace for each impinging signal. They also assign independent steering vector mismatches for different impinging signals to obtain their real steering vectors. The steering vector mismatch of each impinging signal is independently obtained by solving its own convex optimisation problem. They reconstruct the interference‐plus‐noise covariance matrix (INCM) with precise steering vectors and powers of interference signals. The proposed weight vector is computed by combining the desired signal steering vector and the reconstructed INCM. Extensive simulations show that the proposed algorithm provides robustness against many types of model mismatches.

Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed $l_0$ -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-complexity high-order cumulants based data matrix. Then, the proposed algorithm designs a joint smoothed function tailored for the MMV case, based on which joint smoothed $l_0$ -norm sparse representation framework is constructed. Finally, for the MMV-based joint smoothed function, the corresponding gradient-based sparse signal reconstruction is designed, thus the DOA estimation can be achieved. The proposed method is a fast sparse representation algorithm, which can solve the MMV problem and perform well for both white and colored Gaussian noises. The proposed joint algorithm is about two orders of magnitude faster than the $l_1$ -norm minimization based methods, such as $l_1$ -SVD (singular value decomposition), RV (real-valued) $l_1$ -SVD and RV $l_1$ -SRACV (sparse representation array covariance vectors), and achieves better DOA estimation performance.