Efficient direction-of-arrival estimation via annihilating-based denoising with coprime array

Abstract

Although the coprime array provides the possibility for performing underdetermined direction-of-arrival (DOA) estimation, its applicable high-performance algorithm is still in demand. In this paper, we propose a new DOA estimation method for coprime array. This method is motivated by the possibility of applying the annihilating filter theory to the non-uniform samples of the complex exponential sum. The non-uniform coarray array is transformed into a uniform linear array by introducing the concept of interpolating via denoising. The model noise caused by finite snapshots is taken into account, and the array noise variance is included as an unknown variable. The annihilating filter is designed by forming a nonlinear annihilating relation constrained least squares problem, which is solved by sequential quadratic programming. The final DOA can be obtained by the rooting method or spectral method, based on the designed filter. This method makes full use of the degree of freedom and signal information and is proved to be an asymptotic conditional maximum likelihood estimator, which leads to high accuracy under both underdetermined and overdetermined scenarios. It is gridless, free of regularization parameter, and even more computationally efficient than the coarray MUSIC method. Its performances are verified by simulations and compared with representative algorithms.