A Consideration on Operations of Orthogonal Projection Algorithm onto Multi-Dimensional Subspace
Toshihiro Furukawa, Hajime Kubota, Yuji Kimura · IEEJ Transactions on Electronics Information and Systems · 1994
In adaptive algorithms, there are some problems, such as the improvement of the convergence property and the reduction of the computational requirements per sample time, to be resolved. This paper presents an adaptive algorithm which can solve these problems, and it is based on orthogonal projection onto Multi-Demensional Subspace. This is an algorithm in which a parameter called overlap length which is based on orthogonal projection onto multi-dimensional space is introduced. This parameter can be set in compliance with the priorities of the problems mentioned above and can realize various operations forms including the conventional algorithms (e. g. Affine Projection Algorithm, Block Orthogonal Projection Algorithm). By choosing suitable overlap length, this algorithm can reduce the number of multiplications per sample time and it is possible to obtain fast convergence speed. Therefore, using the proposed algorithm, various operations can be supplied according to user's specifications. Affine Projection Algorithm and Block Orthogonal Projection Algorithm correspond to the special case of the proposed method. Finally, it is shown by computer simulations that the performances of the proposed method are very good and that it is useful for such applications as echo canceller, automatic equalizer etc.