Super-resolution DOA estimation methods based on element multiplication and summation

In this article, we propose two direction-of-arrival (DOA) estimation methods to further improve the resolution and performance of subspace-based algorithms. While most subspace-based algorithms employ either noise or signal subspaces, we utilize the signal and noise subspaces jointly. First, we project the steering vectors to the estimated signal and noise subspaces respectively to obtain the projection vectors, then, by investigating the numerical characteristics behind the inner products between the steering vectors and the estimated eigenvectors of the sample covariance matrix, an initial estimator is proposed based on the multiplication of elements of the projection vectors instead of the summation. Though the initial estimator achieves higher resolution than most existing subspace-based methods, the appearance of pseudo peaks, especially in high SNR, may affect the estimation accuracy. By analyzing the main elements in the initial objective function that cause pseudo peaks, two improved algorithms incorporating element summation are proposed to balance the resolution capacity and estimation accuracy, which are especially suitable for small sample size, low SNR and closely spaced sources. The numerical simulations verify the effectiveness and superiority of the proposed algorithms.