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.

DOA Estimation of Multiple LFM Sources Using a STFT-based and FBSS-based MUSIC Algorithm

“…As can be seen from the DOA simulation results of the STFT, SPWVD and FRFT, the estimation performance of the FRFT-based algorithms [10], [13], [15], [16], [32] is poor. Especially in the case that the LFM sources are t-f completely joint, the FRFT-FBSS-MUSIC algorithm even cannot work.…”

“…4(b)) that the performance of these algorithms is reduced if the LFM sources are t-f tiny joint compared to the t-f disjoint LFM sources. Especially for the FRFT-based MUSIC algorithms [10], [13], [15], [16], [32], in the case of high sources SNR, its estimation RMSE is still more than 1°. The simulation results also show the estimation performance of the STFT-FBSS-MUSIC algorithm and the TF-FBSS-MUSIC algorithm if they select the multiple-source t-f points.…”

“…In the simulations, we separately choose quadratic t-f analysis tools [18][19][20][21][22][23][24][25][26][27][28][29][30][31] and the linear t-f analysis tools [10], [13], [15], [16], [32] to estimate the DOAs of the LFM sources. In order to restrain the cross-terms of the quadratic t-f analysis tools, the smoothed pseudo WignerVille distribution (SPWVD) is considered in this paper [20].…”

“…Linear frequency-modulated (LFM), or chirp, signals are frequently encountered in applications such as radar, sonar, bioengineering, and so forth. So the DOA estimation of LFM signals also has become a hot issue in array signal processing [9][10][11][12][13][14][15][16][17]. As we know, time-frequency (t-f) analysis tools are effective tools to deal with LFM signals because of the concentration property of the signals in the t-f domain, so a series of DOA estimation algorithms based on spatial time-frequency distributions (STFDs) have been proposed [18][19][20][21][22][23][24].…”

“…Under this scenario, auto-terms t-f points [18], [20], [25], [27], [30] or cross-terms t-f points [19] have been considered to construct STFD matrices. Due to the computational complexity and the cross-terms of quadratic t-f analysis tools, the linear t-f analysis tools, e.g., the fractional Fourier transform (FRFT) [10], [13], [15], [16], [32] and the short-time Fourier transform (STFT) [33][34][35], also have been applied to the DOA estimation field. These algorithms also use the above two assumptions, which means they all cannot resolve the t-f completely or largely joint sources (the t-f points of the sources are all the same or the sources have a lot of the same t-f points), which limits their further developments.…”