Research On Adaptive Filtering Algorithms Based On The Constraint Of Low Order Norm In Sparse System

Adaptive filter is widely used in engineering practice,such as system identification,prediction,reverse modeling and interference canceling.The traditional Least Mean Square?LMS?algorithm has the advantages of low computational complexity,fast convergence and easy implementation among common adaptive filtering algorithms.However,when the LMS algorithm encounters a sparse system,its performance degraded seriously,which is mainly reflected in a slow convergence speed and a poor steady-state performance.After studying and comparing the sparse adaptive filtering algorithm,this thesis carries research on the following problems in the norm-constrained algorithm:1.the sparse adaptive filtering algorithm based on ₁l norm and l₀ norm constraints applies extra attraction to large tap coefficients and insufficient attraction to small tap coefficients,which can lead to a poor steady-state performance.This is especially evident when the sparsity of the system is reduced.2.When the step size is fixed,the algorithm cannot guarantee both a fast convergence speed and a low steady-state error.Firstly,theory of adaptive filtering is briefly discussed in this thesis.And the classical low-order norm-constrained sparse adaptive filtering algorithm is also analyzed.Secondly,aiming at the poor steady-state performance caused by the constraint term itself for the norm-constrained sparse adaptive algorithm,a sparse adaptive algorithm based on the modified Cauchy distribution function is proposed,which is called Cauchy distribution function-penalized LMS algorithm?C-LMS?.The algorithm modifies the traditional norm-based constraint to the modified Cauchy distribution function.Theoretically,it reduces the attraction to the large tap coefficients and expands the attraction to the small tap coefficients further,which can reduce the steady-state error.After analyzing the convergence and computational complexity of the C-LMS algorithm,two experiments are designed to test its performance.The simulation results confirm that the C-LMS algorithm has lower steady-state error than the other sparse adaptive algorithms.And when the system sparsity is reduced,the algorithm still maintains fine performance.Finally,for the problem of sparse adaptive filtering algorithm under fixed step size,this thesis proposes a new variable step-size method based on?-function.The method uses the derived?-function to map the normalized noiseless prior error power to the step-size interval which satisfies the algorithm requirements.The normalized noiseless prior error power can reduce the dependence of the algorithm on the environment by eliminating environmental noise,theoretically.The simulation results show that the new variable step size algorithm can effectively alleviate the contradiction between convergence speed and steady-state error.To a certain extent,it reduces the impact of noise factors on the filtering results.