Research And Application Of Adaptive Filtering Algorithm

At present, the adaptive filter plays an important role in communication and information processing. The core part of the adaptive filter is the adaptive filter algorithm, and the performance of the algorithm will directly affect the performance of the filter. The convergence rate and the steady-state error are the most important considerations in the performance of the algorithm. Therefore, it has been a hot research topic to find algorithms with fast convergence speed, low steady-state error and low computational complexity.At first, the classical LMS algorithm with its own advantages which has simple structure, stable performance and easy to implement in hardware, had been widely used. But there had been a contradiction between its convergence speed and steady-state error which made it cannot have fast convergence speed and low steady-state error at the same time. In order to improve the performance of LMS algorithm, in this paper we have studied the learning literature, and have also studied two branches of the algorithms which are the variable step size LMS algorithm and the constrained LMS algorithm, then three new algorithms are advanced. Specifically, there are the following three parts of the content.(1) This paper proposes a new variable step size LMS algorithm. First of all, a variety of common variable step size algorithms are studied. Secondly, On the basis of variable step ideas and thoughts on the block step, a new variable step size LMS algorithm is proposed. The algorithm uses the average of the error to control the change of step, so the contradiction between the convergence speed and the steady-state error is further solved. Finally, the algorithm is applied to the system identification model, and the simulation is carried out through Matlab, the new algorithm is verified that it significantly speeds up the convergence speed of the algorithm in the premise of without any increase of steady-state error.(2) A new variable step size CS-LMS algorithm is proposed. Firstly, The NLMS algorithm and relaxing constraints of CS- LMS algorithm have been carried on the related research. Two algorithms both make the normalized processing of the step length, which reduce the sensitivity of the algorithm to the noise and reduce the steady-state error of the algorithm to a certain extent in the case of small signal noise ratio. On the basis of the CS- LMS algorithm, firstly combined with the idea of variable step, we propose a new variable step size CS-LMS algorithm and finally we make it simulated in the application of the model of noise cancellation. Under the condition of the bad transmission environment, the algorithm still has good performance.(3) An improved NVSS algorithm is put forward. First, the NVSS and lambda NVSS algorithm is studied and we also learn the thoughts of original algorithm then introduce new appropriate forgetting factors and the correction parameters to establish a step function between factors, and then propose a new NVSS algorithm. The new algorithm significantly reduce the computational complexity of the algorithm, and through the analysis we conclude that algorithm in the time-varying system has good tracking ability. Finally, the simulation is carried out through Matlab, the improved algorithm is verified that it not only speeds up the convergence speed of the algorithm but also has good tracking ability in non-stationary environments.Compared with the algorithms in other literature, the four aspects--the convergence speed, computational complexity, steady-state error and tracking ability of the three improved algorithms in this paper have greatly improved. They also ease the contradiction between the convergence speed and steady-state error in a certain extent.