Orthogonal projection algorithm for block adaptive signal processing and some of its properties

Abstract

AbstractWith the progress of hardware technology, the development of real‐time adaptive algorithms is becoming more and more important. The essential questions concerning adaptive algorithms are: 1) increasing the speed of the algorithm; and 2) speeding up the convergence. It seems that the block signal processing and the orthogonal projection on the subspace of state‐vectors are effective methods to solve the forementioned questions 1) and 2), respectively.This paper proposes a block orthogonal projection algorithm (BOPA) which combines the block processing with the orthogonal projection operation. Next, an analysis of this algorithm is presented and the fundamental properties of the relation between the block length and the convergence characteristics are shown. Also, the efficiency of the proposed algorithm is verified by computer simulation. This algorithm is based on a block‐by‐block adaptation where the operation of orthogonal projection on the state‐vector space is performed repetitively for arbitrary blocks.