| The LMS(The Least Mean Square)algorithm is widely used in system identification,adaptive noise cancellation(ANC)systems,adaptive channel equalization and other fields because of its simplicity,effectiveness and ease of implementation.Fractional calculus,as the promotion of integer-order calculus,plays an important role in the modeling of fractional-order systems in practical engineering applications.In recent years,scholars have introduced fractional calculus into the design of the LMS algorithm,and found that the fractional LMS algorithm has more superior performance,and has been successfully applied to areas such as adaptive channel equalization,nonlinear time series prediction,and speech enhancement.Therefore,this thesis studies the step factor,convergence speed and steady-state error of the fractional LMS algorithm based on the fractional step descent method,and then proposes an improved algorithm and analyzes the performance of the algorithm.Since the step size factor of the fractional LMS algorithm is fixed,if the algorithm step size is set unreasonably,the algorithm is easy to diverge.Using the fractional variable step size LMS algorithm can improve the performance of the algorithm.The analysis is mainly conducted from two aspects:First,an algorithm combining fractional LMS and SVSLMS is proposed.The core of this algorithm is to replace the fixed step length in the fractional LMS algorithm with a variable step length,and establish the step length factor and The function relationship between the output errors,simulation experiments prove that the algorithm improves the convergence speed of the fractional LMS algorithm;secondly,an algorithm combining fractional LMS,fractional normalized LMS and fractional SVSLMS is proposed.In the initial convergence stage,the step size should be larger in order to have a faster convergence speed and tracking speed of the time-varying system,and keep a small step size after the algorithm converges to achieve a small steady-state error.Simulation experiments prove that the algorithm not only improves the convergence speed of the fractional LMS algorithm,but also balances the contradiction between the convergence speed of the algorithm and the steady-state error,thereby achieving low steady-state error under high convergence speed and improving the performance of the fractional LMS algorithm;Finally,the improved algorithm is applied to the filtering of real speech signals.The improved algorithm’s filtering,noise reduction and anti-interference performance are significantly better than the original traditional LMS algorithm. |
