Research On Proportionate Adaptive Filtering Algorithm Under Non-gaussian Noise

Adaptive filter has the characteristics of real-time tracking channel change,the core of which is adaptive filtering algorithm.Algorithm is the biggest factor determining filter performance.Algorithm affected by the environment,result in different convergence speed and steady-state error filters.Communication systems are often sparse.The traditional adaptive filtering algorithm does not use sparse features,resulting in unsatisfactory convergence performance.In order to solve this problem,scholars have proposed a variety of improved algorithms,in which the proportionate improvement is a simple and effective way.The most typical is to improve the LMS algorithm to PNLMS algorithm.In fact,the interference of Non-Gaussian impulse noise is very common,which will make the algorithm sensitive and the performance deteriorates.This problem can be solved by selecting the appropriate error criterion.Both least mean p-power error criterion(MPE)and maximum correntropy criterion(MCC)have good performance under Non-Gaussian impulse noise.MPE criterion has been successfully applied in adaptive filtering fields,since it is robust to larger outliers.In this thesis,the PLMP algorithm is introduced,and then the PLMP algorithm is normalized,called the PNLMP algorithm.The PNLMP algorithm has a good effect when it has a large strong impulse noise.And the -law method is introduced to the MPNLMP algorithm,which can track the change of weight coefficients,assign the suitable proportional steps with the large weight coefficients to improve the convergence speed to reduce the steady-state error.However,the filtering performance of MPNLMP algorithm decreases slightly when the sparse degree is small.Therefore,the CIM method is introduced to the CIM-PNLMP algorithm,which can obtain the optimal proportional step size.The CIM-PNLMP algorithm can keep good filtering performance,even if the sparsity is small,but its computational complexity is high.The MCC criterion also has good application value in Non-Gaussian noise environment.In this thesis,-law function and the CIM function are introduced into PMCC algorithm to derive two new PMCC algorithms,called MPMCC algorithm and CIMPMCC algorithm,respectively.Both of them have good filtering performance under sparse channels.Although CIMPMCC algorithm has the best filtering performance,the computational complexity is too large to be applied.Next,the new algorithm SMPMCC is simplified by the MPMCC algorithm,which is simple and can keep fast convergence speed,and increases convergence error.SPMCC algorithm converges rapidly,but it loses a certain steady-state disorder.PMCC algorithm converges slowly,but its steady-state disorder is low.In order to solve the tradeoff between the convergence speed and steady-state error,we develop an adaptive convex combination SMPMCC(CSMPMCC)algorithm,which has good convergence speed and steady state error.Finally,the DMPMCC algorithm is introduced,which uses a decorrelation method to remove the correlation of the input signals.When the input signal is related,DMPMCC algorithm has better filtering performance than others.The simulations verify the effectiveness of the various improved proportionate adaptive filtering algorithms.