Subspace analysis of spatial time-frequency distribution matrices

Abstract

Spatial time-frequency distributions (STFDs) have been recently introduced as the natural means to deal with source signals that are localizable in the time-frequency domain. Previous work in the area has not provided the eigenanalysis of STFD matrices, which is key to understanding their role in solving direction finding and blind source separation problems in multisensor array receivers. The aim of this paper is to examine the eigenstructure of the STFDs matrices. We develop the analysis and statistical properties of the subspace estimates based on STFDs for frequency modulated (FM) sources. It is shown that improved estimates are achieved by constructing the subspaces from the time-frequency signatures of the signal arrivals rather than from the data covariance matrices, which are commonly used in conventional subspace estimation methods. This improvement is evident in a low signal-tonoise ratio (SNR) environment and in the cases of closely spaced sources. The paper considers the MUSIC technique to demonstrate the advantages of STFDs and uses it as grounds for comparison between time-frequency and conventional subspace estimates.

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

“…where U n denotes the noise eigenvectors of the forward/ backward smoothed STFDs matrix D fb in (21), which replaced by the covariance matrix of x(t) in the conventional MUSIC algorithm [6] and the STFDs matrix in the traditional t-f based MUSIC algorithm [9,20].…”

“…In the t-f DOA estimation field, the algorithm always makes the best of reducing the effect of noise and ensuring the full column rank property of the STFD matrix. Joint diagonalization [31], [40], [41] and t-f averaging [20], [27] are two main approaches that have been used for this purpose. In this paper, however, we only consider averaging over multiple t-f points.…”

“…Compared to the traditional algorithms, the t-f based algorithms can provide better DOA estimation performance since the t-f analysis tools spread the noise power while localizing the source energy in the t-f domain. Moreover, the selection of t-f points belonging to a specific set of sources allows these algorithms estimate more sources with a small number of sensors [20], [25], [26]. By selecting auto-source t-f points, these algorithms can also solve the DOAs of closely-spaced sources [25][26][27].…”

“…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]. These algorithms use the STFD matrices instead of the covariance matrices in the traditional subspace algorithms [6][7][8].…”

“…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.…”