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Mathematical Problems in Engineering
Volume 2014, Article ID 291249, 10 pages
Research Article

Adaptive Beamforming Based on Complex Quaternion Processes

1Department of Flight Vehicle Control, Aviation University, Changchun 130022, China
2College of Communication Engineering, Jilin University, Changchun 130025, China

Received 20 February 2014; Accepted 21 May 2014; Published 12 June 2014

Academic Editor: Chunlin Chen

Copyright © 2014 Jian-wu Tao and Wen-xiu Chang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Motivated by the benefits of array signal processing in quaternion domain, we investigate the problem of adaptive beamforming based on complex quaternion processes in this paper. First, a complex quaternion least-mean squares (CQLMS) algorithm is proposed and its performance is analyzed. The CQLMS algorithm is suitable for adaptive beamforming of vector-sensor array. The weight vector update of CQLMS algorithm is derived based on the complex gradient, leading to lower computational complexity. Because the complex quaternion can exhibit the orthogonal structure of an electromagnetic vector-sensor in a natural way, a complex quaternion model in time domain is provided for a 3-component vector-sensor array. And the normalized adaptive beamformer using CQLMS is presented. Finally, simulation results are given to validate the performance of the proposed adaptive beamformer.