The Improvement And The FPGA Implementation About LMS Based Adaptive Filter

Adaptive filter are very common use in communications, signal processing, this paper analyzes and improves the adaptive LMS filter, the article finally achieved by means of simulation software LMS filter, and demonstrated its simple to use in the field of signal processing. This paper mainly based on the optimal Wiener filter theorem, how to solve the optimal solution under certain optimal criteria (also known as Wiener solution) elaborated; While the minimum mean square error as the optimal criteria for stochastic gradient method LMS algorithm as a method of updating the tap weights determined in the implementation process requires only a limited addition and multiplication limited and fully multi-iteration, we can get an approximation of the optimal solution; Although not the final solution obtained by Wiener but LMS algorithm to solve the approximate solution process simplicity it has been a very popular application and development. After that, the article uses a special method that weights and weights for solving the optimal solution (Wiener solution) the expected error methods to analyze the convergence and steady-state error of the step length parameter from the impact, but also to use MATLAB simulation software made the comparison; two results agree, they are verified the fixed-step algorithm can not make the same time has good convergence and steady-state error of good. Thus, in order to improve the performance of the algorithm can not have both of these two defects, VSLMS algorithm are leaded, which has the characteristics of step adjustable parameters; The iterative algorithm has a large initial step size parameter can get faster convergence, convergence after algorithm has a small step size parameter can get a small steady-state error; However, there are some differences in the performance with different VSLMS algorithms. This paper compares the variable step VSLMS algorithms and exponential expression with memory factor VSLMS algorithm, and using MATLAB software emulations of the two algorithms we proposed an improved algorithm; While the three algorithms MATLAB simulation results show that the improved algorithm set VSLMS excellent performance in one of the other two algorithms, both get a faster convergence, smaller steady-state error and get a good tracking performance. Finally, the article based on the derivation of the LMS algorithm, using Simulink modeling tools made LMS filter and its simulation; simulation tap input is a sine wave, the expected response is a superposition of Gaussian white noise sine wave, resulting estimation error is consistent with the theoretical value; LMS filter through after the simulation model, the code generated by Simulink related verilogHDL toolbar, ISE and Modelsim software reuse code for functional simulation and waveform simulation, modeling and simulation finally got the time and the basic simulation results agree.