Adaptive Beamforming Based on Complex Quaternion Processes

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.