一种基于交互投影原理的快速自适应横向传播建模算法

Fast Adaptive Trans-Propagation Least Mean Square Algorithm Based on Principle of Alternative Projection

针对最小均方建模算法用于长记忆有限脉冲响应滤波器模型时收敛速度慢的问题,提出了基于交互投影原理的横向传播建模算法(简称为TPLMS算法).该算法将滤波器按质因数分解为多组滤波器组合,从最短的子滤波器分组开始迭代,逐步过渡到原滤波器,在每一时刻,采用最小均方算法顺序求解分组内各子滤波器的权系数.在迭代过程中,由于滤波器的长度缩短,从而可采用更大的步长,使权系数以更快的速度收敛.随着子滤波器长度的逐步增加,可以逐步减小迭代步长,从而得到较低的失调误差.仿真结果表明,TPLMS算法的收敛速度优于传统的最小均方算法和变步长最小均方算法.该算法收敛速度快,特别适用于长记忆有限脉冲响应滤波器模型的自适应建模.

A new fast adaptive algorithm, the TPLMS (Trans-Propagation Least Mean Square algorithm), was proposed for long finite impulse response (FIR) filters. Based on the iterative of alternative projection of two convex sets, a long FIR filter is decomposed into several sets of short sub-filters, and the iteration process is performed repeatedly from the set with the shortest sub-filters to the original filter. At each moment, the least mean square algorithm is performed sequentially in every set of sub-filters. Since the length of sub-filters is shorter than the original filter, the convergence rate is higher than the standard least mean square algorithm even by using a larger permissible iteration step-size. With the increase of the length of sub-filters step by step, the iteration step-size is reduced accordingly, which leads to a lower misadjust-ment. The simulation results indicate that the proposed TPLMS algorithm can remarkably speed up convergence rate, and is particularly suitable for long FIR filters.