Fast FRFT-Based Algorithm for 3-D LFM Source Localization With Uniform Circular Array

Localization of linear frequency modulation (LFM) source based on combination of time- frequency analysis and a spatial spectrum estimation technique has received extensive research. However, this scheme is always confined to far-field sources and suffers from high computational cost. In this paper, by performing the fractional Fourier transform to multiple incoherent LFM signals, a fast and closed-form algorithm based on phase difference is proposed for 3-D source localization under a uniform circular array. First, the phase relationship among sensors' maximum outputs in fractional Fourier domain is exploited to construct indefinite equations, and then the least square method is employed to estimate the source's azimuth angle, elevation angle, and range simultaneously. Finally, comparing with current approaches, the satisfactory performance of our proposed algorithm is demonstrated, and the effectiveness for dealing with mixed far-field and near-field sources is also confirmed.