Research On Performance Analysis Of The Adaptive Least Mean Square Algorithm

As a kind of adaptive filtering algorithm,Least Mean Square(LMS)algorithm which has the advantages of simple structure and easy implementation,is widely used in real life,but the traditional LMS algorithm has two defects: first,it uses fixed step size,which leads to the algorithm steady-state performance and convergence performance cannot be satisfied at the same time;second,it needs to determine the filter order in advance,and Second,the filter order needs to be determined in advance,and the filter order has a great influence on the steady-state and convergence performance of the algorithm.In practice,the system order cannot be determined in advance,and the design of LMS filters with larger orders is usually considered first,which increases the computational effort to implement the algorithm and makes the algorithm application process more complicated.For the problem that the steady-state performance and convergence performance of the algorithm cannot be satisfied at the same time,this paper proposes a parameterfree variable-step LMS algorithm based on hyperbolic tangent function.The average value of the error signal is used to update the step size,and the product of the input signal power and the accumulated value of the error signal and the average value of the accumulated value of the error signal is added together,and the calculated results are used to normalize the algorithm in order to prevent the algorithm from scattering due to the sudden increase of the signal power.The convergence of the proposed algorithm is demonstrated,and the superiority of the performance of the algorithm is analyzed by simulating and comparing it with several existing variable-step LMS algorithms.The core of this method is to take a larger step size when the algorithm first converges to improve the convergence speed,and to take a smaller step size after the algorithm converges to reduce the steady-state error,which greatly alleviates the contradiction that the fast convergence and high convergence accuracy of the algorithm cannot be satisfied at the same time.For the problem of order uncertainty of the unknown system and the order fluctuation caused by the unreasonable choice of iteration parameters and error width of the fractional variable-order LMS algorithm,the fractional variable-order LMS algorithm is improved by using the method of variable iteration parameters and variable error width to solve the problem.In the variable iteration parameter method,the absolute value of the fragment error and the complete mean square error is used to update the iteration parameter to eliminate the interference of the systematic error,and the fractional order iterative is updated using the limit function to suppress the algorithm order fluctuation.In the variable error width method,the difference between the fragment error and the complete error mean square is used to update the iterative error width,which better reflects the convergence of the algorithm and enhances the robustness of the algorithm,and the improved dynamic scaling factor qualifying function is used to further suppress the order fluctuations.The numerical simulation results are compared with the traditional fractional variable-order LMS algorithm to analyze the superiority of improving the performance of the algorithm using variable iteration parameters and variable iteration errors.