A New Atomic Norm for DOA Estimation With Gain-Phase Errors

The problem of direction of arrival (DOA) estimation has been studied for decades as an essential technology in enabling radar, wireless communications, and array signal processing related applications. In this paper, the DOA estimation problem in the scenario with gain-phase errors is considered, and a sparse model is formulated by exploiting the signal sparsity in the spatial domain. By proposing a new atomic norm, named as GP-ANM, an optimization method is formulated via deriving a dual norm of GP-ANM. Then, the corresponding semidefinite program (SDP) is given to estimate the DOA efficiently, where the SDP is obtained based on the Schur complement. Moreover, a regularization parameter is obtained theoretically in the convex optimization problem. Simulation results show that the proposed method outperforms the existing methods, including the subspace-based and sparse-based methods in the scenario with gain-phase errors.

I. Introduction

The estimation problem of the direction of arrival (DOA) has been studied for decades in different applications encompassing radar, wireless communications, and array signal processing [1]. Traditionally, the DOA is estimated by the discrete Fourier transform (DFT)-based methods [2]–[4], where the antenna arrays provide spatial samplings. The DFT-based methods realize the DOA estimation via the DFT of received signals spatially sampled by the antenna array, with its inherent sampling resolution characterized by the Rayleigh criterion [5].