This paper proposes a new gradient-descent algorithm for complex independent component analysis and presents its application to the Multiple-Input Multiple-Output communication systems. Algorithm uses the Lie structure of optimization landscape and toral decomposition of gradient matrix. The theoretical results are validated by computer simulation and compared to several classes of algorithms, gradient descent, quasi-Newton as well as complex JADE. The simulations performed showed excellent results of the algorithm in terms of speed, stability of operation and the quality of separation. A characteristic feature of gradient methods is their quick response to changes in the input signal. The good results of the proposed algorithm indicate potential use in on-line applications.
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