Communication Signal Processing New Algorithms And Performance Analysis In Stable Noise

In traditional signal processing, as its simple justification by the Central Limit Theorem, attractive analytic properties, and ability to lead to simple solutions, the Gaussian distribution and the signal processing based on second order statistics have received wide attention and been used in many areas. But in practice, especially in communication channels, many noises are not exactly Gauss distributed. Furthermore, spikes and impulsiveness often accompany these noises. If such noises are still modeled by Gaussian distribution and the associate signal processor are designed by second order statistics, then the system will degrade for the miss-match between the models and noises. As its excellent performance,α-stable distribution was introduced to model the noises, and gradually formed the signal processing methods based on the fractional lower order statistics.This dissertation focuses on the study of communication channel equalization algorithms, array signal processing algorithms and its performance analysis of relative algorithms under a-stable impulsive noise. The main researches and conclusions are listed as follows:(1) Blind channel identification and equalization of the communication system underα-stable implusiye noise environment is studied. The performance of the traditional blind identification and equalization algorithms degrade greatly, even they cannot work any more under impulsive channel noise enrionments. We firstly proposes a robust received signal covariance matrix estimation method which is based on the robust m-estimation underα-stable distribution model, then blind channel identification is realized using the noise subspace method. Secondly, in order to improve the convergence speed of the FLOS_CMA, a new quasi-Newton constant modulus algorithm based on fractional lower-order statistics (QNFLOS_CMA) is proposed by the exploitation of Hessian information within the weight update equation. We also propose a concurrent equalizer, in which a decision-directed Least Mean p Norm (DD_LMP) equalizer operates cooperatively with a FLOS_CMA equalizer, controlled through a non-linear link. This new algorithm not only has faster convergence rate and lower steady-state mean square error, but also can compensate the phase offset.As the introduced the pth order nonlinear operation in the estimation error signal of the FLOS_CMA, the steady-state mean square error (MSE) analysis method based on the energy-preservation equation can not be directly applied. In this paper, based on the Taylor series expansion of the estimation error signal and the energy-preserving relation under stationary and non-stationary environments, the steady-state MSE performance of the FLOS_CMA is studied, and the approximate analytical expressions for real- and complex-valued data are derived, respectively. Based on the derived expression, an estimate for the FLOS_CMA step-size interval to ensure its convergence and stability is obtained, when it is initialized sufficiently close to the zero-forcing solution. Furtherly, based on matrix inverse theorem, the steady-state MSE of the QNFLOS_CMA in stationary and nonstationary conditions are analysized. Simulation studies are undertaken to support the analysis.(2) The problem of blind source separation and equalization for multiple input and multiple output (MIMO) systems inα-stable impulsive noise is studied. In order to improve the performance of the traditional mutiuser constant modulus algorithm inα-stable noise, a generalized multi-user constant modulus cost function is proposed by employing the fractional lower-order constant modulus property of the equalizer input signals as well as the fractional lower-order cross-correlations between them. The associated adaptive blind equalization algorithm based on a stochastic gradient descent method is defined as fractional lower-order multi-user constant modulus algorithm (FMU_CMA), which is able to mitigate impulsive channel noise while recovering all input signals simultaneous. In order to improve its convergence performance, an approximation of the Hessian matrix is employed in the weighted update equation, and therefore the quasi-Newton fractional lower-order multi-user constant modulus algorithm (QNFMU_CMA) is formulated. Finally, the steady-state MSE of the FMU_CMA in stationary is studied.(3) The array singal processing underα-stable environment is anaylized. A space smoothing algorithm based on phased fractional lower order moment (PFLOM) is proposed in order to solve the DOA estimation of coherent sources in the presence ofα-stable impulsive noise. In order to solve the problem of robust subspace tracking, the rank one subspace tracking algorithms based on PFLOM, spatial sign function pretreatment and infinite norm normalization pretreatment are proposed, respectively. Finally, the performance degradation causes of the PAST algorithm inα-stable is analysized, a new cost function was proposed using the robust m-estimation method and then the robust PAST algorithm (RLM_PAST) was deducted based on the recursive least m-estimate.