Covariance matrix reconstruction method based on amplitude and phase constraints with application to extend array aperture

The angular resolution has always been a concern in the underwater direction of arrival (DOA) estimation. The resolution of the uniform linear array will worsen if the array aperture decreases. When the element spacing is determined, increasing the number of array elements (NAE) can improve the resolution. However, the NAE cannot be greatly increased in practical applications. To address this problem, we propose an array aperture extension method. For this method, we design an optimization algorithm to reconstruct the covariance matrix of the extended array by using that of the original array. Moreover, to make the extended array resemble the actual array, the reconstructed covariance matrix is constrained with a pure signal covariance matrix. The solution method of the optimization algorithm is described in detail. The function of this method is to improve the array aperture by increasing the virtual array elements without changing the element spacing. Therefore, when the array elements are insufficient, this method helps to improve the DOA estimation performance, such as the estimation precision and resolution probability of dual targets. Experiments including simulations and real lake experiments are implemented to validate the effectiveness of the proposed method.