A parallel binary structured LMS algorithm for transversal adaptive filters

Abstract

Abstract. The adaptation process in digital filters requires extensive calculation. This computation makes adaptation a slow and time consuming process. Simple, but versatile, parallel algorithms for adaptive filters, suitable for VLSI implementation, are in demand. In this paper a regular and modular parallel algorithm for an adaptive filter is presented. This parallel structure is based on the Gradient Vector Estimation Algorithm, which minimizes the Mean Square Error. In the parallel method, the tap weights of the adaptive filter are updated every s steps, whereas in the recursive algorithms, the tap weights are updated at each step. For s step update, bit strings of length s are used to derive the terms with which the tap weights of the adaptive filter are calculated. The algorithm presented computes the tap weights at time n + s as a function of the tap weights at time n, the inputs from time n + 1 to n + s -1, and the desired output from time n + 1 to n + s -1. The algorithm also can be mapped to a VLSI architecture that is both regular and modular and allows either expansion of the order of the filter or the degree of parallelism obtainable. A comparison between the performance of the sequential LMS algorithm, Fast Exact LMS algorithm, and the parallel binary structured LMS algorithm is presented.

Design and implementation of a fast active noise control system on FPGA

“…Researchers in [7] proposed a Parallel Binary Structured LMS Algorithm for Transversal Adaptive Filters.…”

Implementation of PBS/spl I.bar/LMS algorithm for adaptive filters on FPGA

“…There are several approaches for implementing these blocks [1]. In this paper we have selected the X, C, P and D methods that are suitable for implementing on a FPGA chip.…”

“…LMS algorithm is an iterating method, called Gradient Vector Estimation, in which at each time step 1 n , the tap weights vector, is the convergence step size, and H denotes the Hermitian transposed of a vector. After that, other adaptive methods based on LMS algorithm are developed as P_LMS [3], FE_LMS [4] and PBS_LMS [1] algorithms. The author in [3] present a simple parallel architecture for the LMS algorithm, called it Parallel LMS or P_LMS.…”

“…The total number of multiplications and additions per iteration in their proposed algorithm is less than the total number of multiplications and additions requires in sequential LMS algorithm. PBS_LMS [1] algorithm (parallel binary structured _LMS) is a parallel algorithm for implementing adaptive filters. The basic advantage of this algorithm from other parallel algorithm as P_LMS or FE_LMS is that in P_LMS or FE_LMS, coefficient vector is update at any time step, thus performing parallelism for increasing speedup are applying in through two time step.…”