A Fast Adaptive Algorithm Based on the Gradient Method and the Orthogonal Projection Matrix

Abstract

In adaptive signal processing, adaptive algorithms hold the important positions. There are mainly both the rapid convergence characteristics and the reduction of computational requirements as the essential items which are demanded to adaptive algorithms. The algorithms, based on the orthogonal projection onto the subspace spanned with the plural input signal vectors, are known as a method to satisfy the requirements above. The orthogonal projection algorithms result in solving the linear equations and the solutions of equations can be represented with Moore-Penrose type generalized inverse matrix. It is important to realize efficiently the orthgonal projection algorithms which include the inverse matrix above. For this problem, the algorithm has been already proposed which applies the Conjugate Gradient Method, called CGM-BOPA. The convergence characteristics of the CGM-BOPA, however, may degrade down when the recursive procedure of the CGM-BOPA are stopped midway due to some affairs, for example, the limitations of the hardware construction etc. Well, this paper presents a new recursive adaptive algorithm which can efficiently perform the orthogonal projection algorithms. Since the proposed algorithm is based on the orthogonal projection onto the direction vectors for the adjustment of the filter's coefficients at any step in one data block, the convergence characteristics of the proposed algorithm are prior to those of the CGM-BOPA if the recursive procedures are stopped midway.