A semi-blind maximum likelihood approach for resolving linear convolutive mixtures

We introduce a new technique to separate a linear convolutive mixture of discrete-time sources, emitting uncorrelated data samples. The proposed approach works in the reduced dimension space of the (channel) whitened data samples, where the data matrix is highly structured: it is the product of an orthogonal and generalized Toeplitz matrices embedded in additive Gaussian noise. By itself, this factorization does not unambiguously determine the sources (even in the absence of noise), but uniqueness is restored if short fragments (inadequate for training) of the emitted messages are known beforehand. We present a locally convergent iterative algorithm which implements the joint maximum likelihood (ML) estimator of both the orthogonal mixing matrix and the user signals, subject to the known side information. We also discuss a simple (sub-optimal) adaptation of the proposed algorithm to the class of finite-alphabet (FA) sources. Computer simulations show that the proposed technique outperforms an alternative subspace approach, specially in low signal-to-noise ratio (SNR) scenarios