Research On Array Processing For Multi-parameter Estimation Of Non-stationary Signals

Nonstationary signals whose frequency contents evolve with time widely exist in our real life. When dealing with these signals, the performance of traditional methods in array signal processing may degrade heavily because of the narrowband and stationary signals assumptions. The aim of this dissertation is to make full use of the achievements in modern signal processing, and to combine nonstationary signal processing with array/multiple channel signal processing for joint spatial and time-frequency signatures estimation of nonstationary signals. This is also an advanced yet challenging problem to the signal processing community. We focus on array signal modeling and the application of nonstationary signal analysis tools, such as Cohen's class of bilinear time-frequency distribution and fractional fourier transform (FRFT), to array processing in the presence of nonstationary signals. The main contributions of this dissertation concentrate in a few aspects as follows: 1. The application of Cohen's class of time-frequency distribution to high -resolution direction finding (DF) for narrowband signals is discussed. We develop a time-frequency maximum likelihood (ML) estimator based on the spatial time-frequency distribution (STFD) matrices and derive the proof of it. The proposed estimator is shown to be effective in coherent signal environment and superior to the conventional ML estimator at low SNR. However, the evaluation of the STFD matrices suffers from high computational cost. To solve this problem, a novel time-frequency ML estimator, which is based on the STFD vectors, is presented. Compared with the STFD matrices-based methods, the proposed method is computationally much simpler and can make full use of the crossterm TFDs between signals. 2. Both the effect and role of the crossterms between signals when using quadratic TFDs in narrowband array processing are investigated. We propose a scheme for crossterm suppression by using the spatial signatures of the signals. The proposed scheme does not degrade the time-frequency resolution of the TFDs, and crossterm suppression is independent of the signal waveforms. Based on that, an algorithm for joint estimation of spatial and time-frequency signatures is proposed. 3. We consider the array signal modeling for wideband frequency modulated (FM) signals. Array signal models based on the time-varying narrowband assumption and symmetric array geometry are provided respectively. Direction finding techniques and joint estimation of spatial and time-frequency signatures based on spatial pseudo Wigner-Ville distributions are discussed. We analyze the time-frequency coherent signal subspace method (TF-CSM) for wideband signals that are localizable in the time-frequency domain and offer a modified scheme to improve the performance. The STFD vectors-based method and autoterm detection techniques are also presented. 4. Direction finding techniques based on FRFT preprocessing are developed. We propose two algorithms using FRFT domain second and fourth order statistics respectively. Besides signal selectivity, the subspace-based methods using FRFT domain fourth order cumulant possess very appealing features such as aperture extension and suppression of unknown additive Gaussian noise. In the case of wideband FM signals, an iterative DOA estimation algorithm based on phase compensation is proposed. The proposed algorithm is insensitive to initial estimates and converges fast to the true value. In addition, it is appropriate to handle signals over a wide frequency band.5. Multi-parameter estimation of nonstationary signals impinging on the antenna array over a very wide frequency band (such as 2-18GHz) is under investigation. We propose a scheme for joint estimation of chirp parameters and azimuth-elevation angle of the linear chirp signals based on spatio-temporal undersampling. Compared with the existing schemes, the proposed scheme is suitable for both linear chirp signals and the narrowband signals with time-invariant spectrum.