A Gridless Fourth-Order Cumulant-Based DOA Estimation Method Under Unknown Colored Noise

To reduce the adverse impacts of the unknown colored noise on the performance degradation of the direction-of-arrival (DOA) estimation, we propose a new gridless DOA estimation method based on fourth-order cumulant (FOC) in this letter. We first introduce the non-redundancy single measurement vector (SMV) through FOC, which is capable of suppressing the Gaussian colored noise. Next, we analyze the distribution of the estimation error and design an estimation error tolerance scheme for it. We then combine the atomic norm minimization of the non-redundancy SMV with the above constraint scheme. This combination poses the stability of the sparsest solution. Finally, the DOA estimation is retrieved through rotational invariance techniques. Moreover, this method extends the gridless DOA estimation to the sparse linear array. Numerical simulations validate the effectiveness of the proposed method.

I. Introduction

Direction-of-arrival (DOA) estimation algorithms have received extensive research attention in many engineering fields such as radar and wireless communication [1]–[4]. These algorithms commonly assume that the background noise is white Gaussian. However, it is a noteworthy phenomenon that occurs in these fields, where colored noise is output as white noise after passing through linear components. This phenomenon inevitably mismatches the signal model proposed by second-order statistics-based DOA estimation methods [5], [6], which is the primary cause of the performance deterioration in practical applications.