Research On Nonlinear Channel Equalization Algorithms In Alpha Stable Noise

In the field of communication signal processing,most people assume that the noise subjects to the Gauss distribution.However,more and more studies have found that some noise in actual communication has more remarkable impulsiveness than Gauss due to man-made factors,lightning electromagnetic equipment and magnetic storm etc.natural factors,which can't be described by Gauss model.For example,man-made noise,marine environment noise in underwater acoustic communication system and the noise in satellite communication system when lightning or storm appears,at this time,Alpha stable distribution is often used to describe this kind of noise.In addition,in underwater acoustic communication system,because of the effects of reverberation,scattering and acoustic medium,acoustic channel often exhibits nonlinear characteristics;And in the satellite communication system,in order to improve the utilization rate of the power,people usually makes its internal high power amplifier works near the saturation point,which leads to the nonlinear characteristics.Alpha stable distribution noise and the nonlinear characteristics of the channel will affect the performance of the transmission system.Equalization technique is an important method to overcome intersymbol interference and to effectively compensate channel distortion.Based on the kernel method,this paper studies the nonlinear channel equalization algorithm in Alpha stable distribution noise.First of all,in order to improve the performance of nonlinear channel equalization in Alpha stable distribution noise,this paper studies and summarizes the kernel adaptive equalization algorithm,and introduces the least mean p-norm algorithm on this basis,then a kernel adaptive equalization algorithm is presented for the Alpha stable distribution noise,namely the kernel least mean p-norm algorithm.The algorithm firstly uses kernel function to map the received signal to a high-dimensional space,as the input signal of equalizer in high dimensional space;then the tap coefficients of equalizer is self-adjusted by the kernel least mean p-norm algorithm in high dimensional space,and the output of the equalizer is expressed as inner product form by mathematical operations;the equalizer output expressed in inner product form in high dimensional space is transformed into low dimensional space for the calculation finally.The simulation results show that the proposed algorithm has faster convergence rate and less steady-state error compared with existing algorithms.Secondly,in order to further improve the convergence rate of the equalizer and reduce the steady-state error,this paper puts forward two kinds of variable step kernel least mean p-norm algorithm based on the Sigmoid function and the Tanhx function,and compares the complexity of the two algorithms.The simulation results show that the convergence rate of two kinds of variable step size algorithm is significantly improved and the steady-state error is reduced.In addition,the equalization performance of the two variable step size algorithms is basically same,and the calculation of the variable step algorithm based on Tanhx function is less than the variable step algorithm based on Sigmoid function.Finally,in order to overcome the adverse effects of signal distortion ?intersymbol interference etc.caused by the multipath fading in actual communication,this paper propose spatial diversity nonlinear channel equalization algorithm and variable step algorithm based on the equal-gain combining in Alpha stable distribution noise,utilizing the good anti-fading performance of the diversity technology and combining the kernel least mean p-norm algorithm and the variable step kernel least mean p-norm algorithm based on the Tanhx function Simulation.Simulation results show that these algorithms can achieve stable and good equalization performance compared with the algorithm of signal equalizer.