Separation and localization of multiple distributed wideband chirps using the fractional Fourier transform

Abstract

In this paper, we consider the problem of localizing the multiple distributed wideband chirp sources using the fractional Fourier transform. The model in the time domain and that in the fractional Fourier domain derived by the Taylor series expansion are presented respectively. The representation of location vector in the Dechirping domain is illustrated which is only related to the central angle. A novel direction of arrival (DOA) estimation algorithm in the Dechirping domain is proposed, which is extended from the conventional multiple signal classification (MUSIC) algorithm in the time domain. Using this algorithm, except for estimating the DOA, the incidence source number can be determined as well which is allowed to exceed the sensor number in the array. To demonstrate the performance of proposed algorithm, numerical results are conducted. Compared to the previous FrFT-MUSIC algorithm based on the assumption of point source model, the proposed algorithm performs a better estimation performance, especially for large angular spread and low signal-to-noise ratio.