Research On Adaptive Filtering Algorithm Based On Kronecker Product Decomposition And Echo Cancellation

The echo phenomenon often occurs in communication scenarios,which is that the user hears his/her voice from the signal transmitted from the far-end through communication equipment.It seriously affects the quality of communication and the user’s comfort,so we need to eliminate it.Echo with long delay leads to the need to set many filter taps when using the adaptive filter to identify the path of echo.When processing such echoes,the adaptive filter needs to set many taps to achieve a better elimination effect.However,increasing the number of filter taps will increase the computational complexity of the adaptive filtering algorithm,while reducing the convergence rate of the algorithm.Based on the Kronecker product decomposition and low rank approximation method,the identification of a long echo path is transformed into the identification of two short sub-paths by using the property of the non-full rank of the matrix when the coefficient vector is converted to a high-dimensional matrix.This method can reduce the total number of filter taps,and this advantage is particularly obvious when dealing with low-rank systems.In addition,researches have shown that both linear and nonlinear echo paths exhibit sparsity,which means that the coefficient vector of such echo paths have obvious low-rank characteristics when it is transferred to a high-dimensional matrix.Therefore,this paper will focus on the adaptive filtering algorithms and echo cancellation problem based on Kronecker product decomposition.The main work is as follows:1)In response to the sparse characteristics of echo paths,the proportional algorithm is first studied,and the mean and mean-square theoretical analysis of the proportionate normalized least mean M-estimate algorithm is carried out,and the step-size to achieve the fastest convergence and the relationship between the steady-state error and the step-size are given.The adaptive decorrelation proportionate normalized least mean M-estimate algorithm is proposed by introducing an adaptive decorrelation method,which can converge faster when processing highly correlated input signals.Furthermore,based on the minimum criterion of mean-square posterior error,a variable step-size adaptive decorrelation proportionate normalized least mean M-estimate algorithm is derived,which can achieve fast convergence and low steady-state error.2)Aiming at the problem of long and sparse echo paths,the sub-paths obtained by decomposing them based on Kronecker product decomposition and low-rank approximation are analyzed,and it is found that their sub-paths still have a certain degree of sparsity,so the proportional strategy is introduced to accelerate the convergence rate of the algorithm,and a proportional normalized least mean square algorithm based on Kronecker product decomposition is proposed.The combined step-size strategy is introduced,and a combined step-size proportionate normalized least mean square algorithm based on Kronecker product decomposition with better convergence performance is proposed.In addition,the M-estimate strategy is further introduced to enhance the robustness of the algorithm to impulsive noise,and a proportionate normalized least mean M-estimate algorithm Kronecker product decomposition is proposed.3)In response to the problem of longer and sparse echo paths in nonlinear systems,inspired by the proportionate algorithm based on Kronecker product decomposition,a Kronecker product decomposition based proportionate normalized least mean square algorithm for second-order Volterra filter is proposed with faster convergence rate.Finally,in the context of system identification and echo cancellation,the correctness of the theoretical analysis and the effectiveness of the proposed algorithm in this paper are verified.