Research On Sparse Impulse Response Adaptive Filtering Algorithm

The sparse impulse response filter has played an important role in modern communication system, because it can build a valid model for the reverb multipath phenomena. This kind of filters possesses two characteristics:the coefficients of the filter sparse and the length of the filter is large. As we know, the convergence rate and the convergence precision will be seriously affected by the length L of the filter, and the computational complexity will sharply increase with the increasing length L of the filter. Based on the improved PNLMS algorithms and Compressive Sampling, the new improved algorithms for project realization and the new algorithms with faster convergence rate are proposed. The research works are summarized as follows:Firstly, the block proportionate normalized least-mean-squares algorithm is proposed based on the coefficient blocks of the filter to reduce the calculation used to get scale factors. The calculation of the new algorithm is N/L (L is the length of the filter, N is the number of the coefficient blocks of the filter) times that of the SPNLMS algorithm. Thus the improved algorithm is more suitable for engineering application than SPNLMS algorithm. At the same time the theoretical analysis and the numerical simulation show that the improved algorithm is valid.Secondly,l∞-SPNLMS algorithm is proposed to reduce the multiplication between every coefficient of the filter and its scale factor in each iteration. Compared with the SPNLMS algorithm built on the standard LMS algorithm, l∞-SPNLMS algorithm is built on l∞-NLMS algorithm which replaces the multiplication operation with the symbolic operation. Thus the new algorithm can reduce L multiplications in each iteration. When the length L of the filters is very large, the part of the reduced amount of computation can effectively save the hardware resource and computing time. At the same time the theoretical analysis about the regulation between the convergence rate and Gaussian signal with different mean and variance is given. The numerical simulation shows that in certain requirements, the same convergence rate of SPNLMS algorithm can be achieved by a small amount of computation.Finally, the lp-LMS algorithm with variable balance parameter K is proposed to get a faster convergence rate. Based on the sparsity under different norm in compress sensing, the new algorithm builds a new convergence process of the parameter p which cooperates with the convergence process of the coefficients of the filter. Thus a faster convergence rate is obtained. To get a fast convergence rate and high convergence precision at the same time, the balance parameter K updated by the estimation error e(n) in every iteration is introduced in the algorithm. The numerical simulation shows that the improved algorithm is valid.