A parallel binary structured LMS algorithm for transversal adaptive filters

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 everys steps, whereas in the recursive algorithms, the tap weights are updated at each step. Fors step update, bit strings of lengths 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 timen+s as a function of the tap weights at timen, the inputs from timen+1 ton+s−1, and the desired output from timen+1 ton+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.