New Algorithms For Time Delay Estimation And Beamforming Under Stable Distribution Noise

Time delay estimation and beamforming are two important topics in the signal processing. The noise components of the received data in the receivers or array sensors for time delay esti-mation and beamforming are often assumed to obey Gaussian distributions. In most cases,this assumption is reasonable. However, there is some type non-Gaussian impulsive noise which encountered in the wireless communication,radar,underwater acoustic and biomedicine. This types of noise have heavy-tailed probability density function and they are usually modeled by the stable distribution. In this paper, we continue to discuss the time delay estimation and beam-forming in stable distribution noise using the Renyi entropy,correntropy,modified Mahalanobis distance,Parzen kernel estimation of the probability density function based on the previous work-s. The main work of the dissertation is as follows:(1) New cost functions with Renyi entropy and correntropy for the time delay estimation in stable distribution noise are presented and their rational explanations are also provided. The parametric representations of Renyi entropy and correntropy for symmetric stable random vari-able are presented. We show that there exists an equivalence between the minimum error entropy criterion and the minimum dispersion criterion where symmetric stable distribution random vari-ables are considered as the errors of the adaptive signal processing. We also provide the equiv-alency of the maximum correntropy and the minimum dispersion for zero location symmetric stable distribution random variables. As applications, we propose novel time delay estimation algorithms by the minimum error entropy criterion and maximum correntropy criterion under the stable distribution noise respectively. We also modify the time delay estimation algorithm based on average magnitude difference function using the similarity property with correntropy. A modified version of Mahalanobis distance is defined and linear transformation invariance of this distance is proved in this dissertation. Joint estimation of time-difference of arrival/frequency-difference of arrival is presented using the modified Mahalanobis distance to determine the pa-rameter adaptively.(2) To solve signal mismatch and the stable distribution noise, we proposed new beamform-ers with the techniques which combine the variable diagonal loading and general rank model to fractional lower order statistics. Firstly,the fractional lower order covariance linear constrained minimum variance beamforming and fractional lower minimum power distortionless response (FrMPDR) beamforming are generalized. The relationship of these two generalized beamform-ing is discussed. Then,the white noise gain of the FrMPDR beamforming is analyzed. The analysis and simulations show that the white noise gain of the FrMPDR beamforming is small-er than that of the traditional minimum power distortionless response beamforming because the dispersion of the eigenvalues of the fractional lower order covariance matrix is smaller than that of the traditional covariance matrix. A variable diagonal loading beamforming in the frame-work of generalized sidelobe canceller implemented by the recursive least p norm is presented. Simulations show the proposed variable diagonal loading algorithm has higher signal interfer-ence noise ratio for the pointing errors and random perturbations when the noise obeys the stable distribution. A new fractional lower order covariance beamforming based on the general-rank signal model is presented. The nonsingularity of the fractional lower order covariance is also discussed. The simulations demonstrate the superiority of the proposed beamforming compared to the traditional methods against the stable distribution noise and steering vector mismatches.(3) Constant modulus beamformers in the stable distribution noise are proposed by maxi-mum matching of the probability density functions. The Parzen kernel estimation of the probabil-ity density function is utilized to propose constant modulus beamforming based on the maximum matching of the probability density functions between the desired signal and output signal. The linear constraint conditions are added to the proposed constant modulus beamforming cost func-tion and the linear constrains version of the constant modulus beamforming is also derived to suppress the interference and enhance the signal of interest simultaneously.