Localization for mixed far-field and near-field sources utilizing improved symmetric nested array

Abstract

Nested arrays exhibit higher spatial resolution (SR) and enhanced degrees-of-freedom (DOFs) with fewer sensors, and they have been utilized for direction-of-arrival (DOA) estimation of both far-field (FF) and near-field (NF) sources. In this study, an improved symmetric nested array configuration with a given number of sensors was developed, which achieved increased consecutive and unique lags and thus resolved more targets than the actual number of inherent array sensors. In particular, the analytical expressions of the number of consecutive lags, the number of unique lags, and the virtual array aperture were derived for quantitative evaluation and comparison, as well as the corresponding array composition parameters of the optimal array geometry were obtained. In the mixed sources localization scheme, a special cumulant matrix was constructed to eliminate the range parameter in the NF steer vectors by exploiting the symmetric feature. Both subspace and sparse reconstruction techniques were exploited in order to directly obtain the DOAs of both FF and NF sources. With the estimated DOAs and the covariance matrix of the array output, the NF sources could be identified, and the corresponding range parameters could also be obtained by a one-dimension (1-D) spectrum search scheme. Numerous simulation results demonstrated that the proposed array showed a remarkable performance in terms of estimation accuracy, SR capacity, and numerous DOFs compared to state-of-the-art symmetric nested arrays.