A Fast Projection Algorithm for Adaptive Filtering

Masashi TANAKA  Yutaka KANEDA  Shoji MAKINO  Junji KOJIMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A   No.10   pp.1355-1361
Publication Date: 1995/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
adaptive filtering,  projection algorithm,  complexity reduction,  

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This paper proposes a new algorithm called the fast Projection algorithm, which reduces the computational complexity of the Projection algorithm from (p+1)L+O(p3) to 2L+20p (where L is the length of the estimation filter and p is the projection order.) This algorithm has properties that lie between those of NLMS and RLS, i.e. less computational complexity than RLS but much faster convergence than NLMS for input signals like speech. The reduction of computation consists of two parts. One concerns calculating the pre-filtering vector which originally took O(p3) operations. Our new algorithm computes the pre-filtering vector recursively with about 15p operations. The other reduction is accomplished by introducing an approximation vector of the estimation filter. Experimental results for speech input show that the convergence speed of the Projection algorithm approaches that of RLS as the projection order increases with only a slight extra calculation complexity beyond that of NLMS, which indicates the efficiency of the proposed fast Projection algorithm.