Near-Field Noncircular Sources Localization Based on Fourth-Order Cumulant

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-ofarrival (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 onedimensional 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. INDEX TERMS cumulant, near-field, noncircular sources, parameter estimation.

Analysis of the fourth-order co-array for a mixture of circular and noncircular signals

“…Moreover, two or all three of the approaches can be combined together to increase the DOFs further. Examples include algorithms combining the noncircular properties and the fourthorder cumulants [15,16,17,18,19], combining the noncircular properties and sparse arrays [20,21,22,23], or combining the fourth-order cumulants and sparse arrays [24,25,26,27,28]. In [29], all the three approaches are employed together.…”

“…3) The 'noncircular signal' mentioned in these works is mainly focused on the 'strictly noncircular signal', and the possible impact of the nonstrictly noncircular signals on the maximum number of signals to be estimated is often ignored [5,6,16,17,18,21].…”

An Improved Multiple-Toeplitz Matrices Reconstruction Algorithm for DOA Estimation of Coherent Signals

“…Many other matrix reconstruction methods based on higher-order cumulant [12][13][14] have been proposed to resolve coherent signals in the low SNR region. Unfortunately, these methods require large numbers of snapshots and suffer from burdensome computation.…”