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.
In this study, the problem of spatio-temporal-polarisation filtering based on hypercomplex processes is considered for an electromagnetic (EM) vector-sensor array. The quaternion domain facilitates modelling and processing of four-dimensional real signals (or two-dimensional complex signals). Based on the quaternion model of linear symmetric array with twocomponents EM vector-sensors, an interference and noise canceller (INC) is presented for polarised signals. Then, the output signal to interference-plus-noise ratio (SINR) expression of INC is derived and its performance is analysed. The performance analysis reveal explicitly the fact that even though no separation between the direction of arrival (DOAs) of the desired signal and interference, the maximum value of output SINR can be obtained employing the orthogonality between the polarisations of the desired signal and interference. Simulation results show that if sample size N is large enough, the INC has larger output SINR and better robustness against the DOA mismatch.
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