Blind separation of complex-valued signals by real-valued in-phase and quadrature rotations

We propose a novel method for applying real-valued independent component analysis (ICA) to complex-valued multi-sensor data that comprises instantaneous linear mixtures of co-channel non-Gaussian independent signals. We examine, for non-ideal practical conditions, the optimahty of cumulant-based ICA and blind signal separation approaches in terms of the standard criterion for statistical independence and extend this theory to the complex-valued case. We show that this justifies estimation of in-phase and quadrature mixing parameters and, for finite data, avoids the difficulty of optimising a selected subset of real and complex-valued cumulants. Computational efficiency is also improved.