Research On DOA Estimation Algorithms Under Unknown Mutual Coupling

As an important branch of array signal processing,spatial spectrum estimation aims to determine the direction of arrival(DOA)for the incident sources.Most typical DOA estimation algorithms suffer severe performance degradation in practical applications for they rely on precise manifold and don't consider the mutual coupling effect which can't be neglected.Thus,it is of great practical value to study the direction finding algorithm in the case of mutual coupling.In addition,according to the statistical characteristics of the incident sources,they can be divided into circular sources and non-circular sources.The assumption that radiating sources are complex circular is implicit in most DOA estimation algorithms,and they only use the sources' non-zero covariance to complete direction finding,resulting in the maximum number of detectable incident sources less than the number of array elements.The covariance and elliptical covariance of non-circular sources are non-zero,so it is hopeful that the noncircularity of the incident sources can be used to improve the performance of direction finding algorithm.For the scenario where the incident sources are impinging upon a uniform linear array(ULA)with unknown mutual coupling,this paper proposes a gridless super-resolution DOA estimation algorithm based on atomic norm minimization framework.Firstly,a transformation function is adopted to convert the estimated angles to the estimated frequencies.Based on the banded symmetric Toeplitz structure of the mutual coupling matrix,a selection matrix is formed to truncate the original received data and a new steering vector is obtained by assimilating the unknown mutual coupling coefficients into the signal part.Then a semidefinite programming problem is derived to get the structured covariance matrix,which has the same Vandermonde decomposition form as the covariance matrix of the truncated signal but different coefficients.Finally,the traditional ESPRIT algorithm is applied to the structured covariance matrix to obtain the estimated frequencies.Verified by simulation results,the proposed algorithm achieves better performance in the case of lower SNR and fewer snapshots.For the scenario where a ULA is impinged by strictly noncircular sources in the presence of unknown mutual coupling,this paper proposes an extended ESPRIT algorithm by exploiting the noncircularity of impinging sources.Firstly,some auxiliary elements are added to each side of the original array to compensate the structure of the mutual coupling matrix.Then the received signal and its conjugate counterpart are combined to construct a new extended signal,in which the noncircularity of the sources is utilized.Finally,the ESPRIT algorithm is performed to the extended signal to obtain the estimated DOAs.The simulation results show that the proposed algorithm has larger virtual array aperture and lower computational complexity.