Investigation On Array Signal Processing Amid α-Stable Noise

Noise has been overwhelmingly modeled as Gaussian-distributed one in signal processingarea, although many real-world physical noises are in fact non-Gaussian. Variousexperiment measurements have shown that atmospheric noise, underwater acoustic noiseand electromagnetic disturbance noise have "impulsive" characteristics, which areinappropriatlly modeled as Gaussian noise in applications. With practical demands and thedevelopment of mathematical theory in impulsive statistics, there has been great interest insignal processing under the environment of the impulsive noise. Among different modelsof impulsive noises,α-stable distribution noise has acquired special attention in signalprocessing because of its wide applicability. Following the recent advances of array signalprocessing, this dissertation investigates the beamforming and direction-of-arrival (DOA)estimation issues of array signals in theα-stable distribution noise. This dissertationmainly consists of four parts: Background materials, beamforming algorithms, DOAestimation algorithms and DOA (DOA-polarization) estimation with vector-sensor array.PartⅠ: Background materialsThis part introduces fundamental materials onα-stable distribution noise and armysignal processing which are used in the following development. In theα-stabledistribution noise, the definitions and properties of the uni-vadate and muld-variateα-stable distributions are presented, the methods for estimatingα-stable distributionparameters are provided and the other related distributions for impulsive noises arediscussed. In the array signal processing, the array concept and data model are introduced,and the customary beamforming and DOA estimation algorithms are presentred.PartⅡ: Beamforming algorithmsEarlier beamforming algorithms under theα-stable distribution noise were mainlydeveloped based on the fractional lower order statistics (FLOM). However, the outputsignal to interference plus noise ratios (SINRs) decrease significantly as the noiseimpulsiveness increases, resulting in deterioration of the beamforming performance. Thispart presents three robust beamforming algorithms: the fractional lower order minimumvariance distortlessness response (FrMVDR) algorithm, the linear constrained minimumgeometric power (LCMGP) algorithm, and the minimum geometric power error (MGPE)algorithm. These algorithms are developed under different a prior knowledge of arraysignals and perform well especially for highly impulsive noise.FrMVDR is developed upon the conventional MVDR beamforming algorithm.Similar to the traditional array response, the fractional lower order array response isdefined. With the concept, the fractional lower array power is formulated and it is theoretically proved that the power is finite and reasonable for beamforming, provided thatthe fractional order does not exceed the half of the noise characteristic exponent.Theoretical analysis and simulation results show that FrMVDR algorithm is robust overrelated algorithms, especially when the noise is highly impulsive. FrMVDR algorithmextends the applications of the conventional MVDR algorithm to more general scenarios.CMGP and MGPE are developed based on zeros order statistics and geometricpower of theα-stable distribution noise. LCMGP determines its optimal beamformingweights by minimizing the beamformer's overall output geometric power with theconstraint on the desired signal from the specified DOA having unity amplitude. Comparedwith the FLOM-based beamforming algorithms, the LCMGP offers advantages such asrobustness to noise impulsiveness, computationally simple, and without need of a prioriinformation or estimation of the noise's characteristic exponent.MGPE is developed by minimizing the geometric power error between thebeamformer output signal and the desired signal. There is no close-form expression for theoptimal weights. An iteratively reweighted least squares (IRLS) algorithm is introduced forcalculating the MGPE weights. Compared with conventional FLOM-based beamformingalgorithms, the MGPE algorithm does not need a priori information or estimation of thenoise's characteristic exponent and has lower estimation error of the desired signal.PartⅢ: DOA Estimation AlgorithmsThe DOA estimation algorithms for stationary and non-stationary signals amidα-stable noise are investigated in this part. For stationary signals, the Screened-Ratiobased MUSIC (SR-MUSIC) and infinity-norm normalization pre-processing based MUSIC(IN-MUSIC) algorithms are developed. For non-stationary signals, time-frequencyanalyses of theα-stable distribution noise are firstly discussed and then the FLOM-basedspatial-time-frequency domain MUSIC (FLOM-TF-MUSIC) and FLOM-basedspatial-ambiguity domain MUSIC (FLOM-AD-MUSIC) algorithms are given.SR-MUSIC is developed upon on the eigen-decomposition of array correlation matrixconstructed from screened-ratio principle. The specially constructed matrix eliminates theselection of FLOM parameters as required in ROC-MUSIC and FLOM-MUSIC algorithms.Therefore, the SR-MUSIC suffers no DOA estimation errors from the estimates of thenoise characteristic exponent and the selections of the FLOM parameters.IN-MUSIC starts from the normalization of the array data by its infinite-norm. Theα-stable noise has infinite second order moments, however, it is theoretically proved thatthe infinity-norm normalizedα-stable noise becomes zero mean and finite variance.Therefore, the second order subspace based algorithm can be applied to the infinity-normnormalized array data. Compared with other related schemes, the infinity-normnormalization has adavantages such as the blindness in no requirement of any knowledge of the impulsive noise statistics, no need of the user-defined thresholds and controllingparameters, and computationally simple.FLOM-TF-MUSIC and FLOM-AD-MUSIC are developed for non-stationary signals.The conventional second order time-frequency analysis can not reveal the time-frequencycharacteristics of the signals under the impulsive noise. Therefore, the time-frequencybased algorithms can not be applied to theα-stable noise environment. Herein, a newsynergy between the FLOM and time-frequency analysis is devised. Firstly, theFLOM-based time-frequency distribution is defined and its properties are discussed. Thenthe distribution is extended to the case of the array signal and the spatialFLOM-time-frequency distribution is formulated. It is found that the spatialtime-frequency distribution is well structured and can be combined with MUSIC algorithmfor DOA estimation. As a counterpart to FLOM-TF-MUSIC, the spatial FLOM ambiguityfunction can be similarly formulated and used to perform DOA estimation. TheFLOM-TF-MUSIC (FLOM-AD-MUSIC) extends the applications of the TF-MUSIC(AD-MUSIC) algorithms to more general noise scenarios.PartⅣ: DOA-(Polarization) Estimation with Vector-Sensor ArrayThis part investigates DOA/DOA-polarization estimations using acoustic/electromagnetic vector arrays.For the acoustic vector array, a unitary acoustic vector doublet based ESPRIT(Uni-AUVD-ESPRIT) algorithm is presented. For the electromagenetic vector array, aunitary electromagnetic vector doublet based ESPRIT (Uni-EMVD-ESPRIT) algorithm isproposed. Uni-AUVD-ESPRIT and Uni-EMVD-ESPRIT can perform DOA andDOA-polarization estimnations under Gaussian noise, respectively. These two algorithmsare then combined with FLOM and infinity-norm normalization preprocessing to DOA andDOA-polarization estimations inα-stable impulsive noise.By fully exploiting the spatial invariants of two deployed vector sensors, Uni-AUVD-ESPRIT/Uni-EMVD-ESPRIT and can obtain the closed form DOA/DOA-polarizationestimations and are applicable to any time-varying signals.