Abstract
This paper presents a cumulant-based algorithm for near-field noncircular sources localization with a symmetric uniform linear array. It first constructs three extended matrices. Then, based on the rotational invariance property in extended cumulant-domain signal subspace, coarse direction-of-arrival (DOA) estimates are obtained. With the course results used as reference, the algorithm is able to disambiguate the cyclic phase ambiguities when the equivalent sub-array spacing exceeds a half wavelength. Thus, higher precision DOA estimates can be obtained. Finally, with the estimated DOAs, only one-dimensional searching is needed to obtain the range estimates via rank-reduction algorithm. The proposed algorithm avoids two-dimensional searching and parameters pairing. In addition, compared with the existing near-field noncircular sources localization algorithm, the significant characteristic of the proposed algorithm is that it exploits cumulant and the noncircularity of signal to achieve extended steering vector. Cumulant is insensitive to Gaussian (white or color) noise. Consequently, the proposed one provides DOA estimates with improved precision especially at low signal-to-noise ratios. Furthermore, it doubles the number of detectable sources. Total least square ESPRIT algorithm is exploited to yield search free estimates of near-field bearing parameters. Computer simulations are carried out to demonstrate the superiority of the proposed algorithm.
Highlights
Estimation of source localization has received significant attention in array signal processing fields such as radar, sonar, wireless communication, guiding systems, seismic detection, medical imaging and so on over t he past decades [1]–[4]
Since each is is obtained via eigenvalue decomposition (EVD), and the EVDs are accompanied by an unknown permutation matrix, the diagonal elements of R1 are not in one-to-one correspondence with those of R2
In this paper, for a symmetric uniform linear array (ULA), a cumulant-based algorithm is presented for parameter estimation of noncircular sources in the near-field
Summary
Estimation of source localization has received significant attention in array signal processing fields such as radar, sonar, wireless communication, guiding systems, seismic detection, medical imaging and so on over t he past decades [1]–[4]. Based on the isotropic uniform linear array (ULA), as the maximum number of detectable sources is less than the number of array elements, it is necessary to develop under-determined parameter estimation algorithm for near-field sources by exploiting the noncircularity of signals. By utilizing the noncircularity of the signals to extend the virtual array aperture, the DOA estimation accuracy and the maximum number of detectable sources can be improved [21]–[26]. To get the near-field noncircular information more precisely, we present a fourth-order cumulant-based algorithm with scalar symmetric ULA in this paper. Course DOA estimates are obtained based on the rotational invariance property of extended cumulant-domain signal subspace These course results are further used as reference to disambiguate the cyclic phase ambiguities induced by the large equivalent spacing of sub-arrays which exceeds a half wavelength. Notation: Upper(lower)bold symbols denote matrix (vector). (·)∗, (·)T ,(·)H , (·)† denote complex conjugation, transpose, conjugate transpose, and pseudo-inverse, respectively; E {·} represents the statistical expectation, cum {·} stands for the fourth-order cumulant, arg(·) means the argument of a complex number
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