Blind source separation in the presence of Doppler frequency shifts

We address the problem of blind separation of sources, mixed subject to possible Doppler frequency-shifts, differing between sources and between sensors. This situation is likely to occur, e.g. in scenarios involving mobile sensors and/or sources, but so far the multiple sources case does not seem to have been addressed (at least not in open literature, to our knowledge). We propose a batch-type iterative procedure for the estimation of the (static) mixing parameters and the frequency-shifts, followed by application of the inverse system to reconstruct the sources. The estimation procedure can be regarded as parameterized joint diagonalization of a bulk of rank-one matrices. Somewhat surprisingly, correlation matrices at zero lag are generally sufficient for separation, and consequently, the separation of white Gaussian sources is generally possible in this framework - unlike the situation in classical static mixing - as we demonstrate in simulation.