On the non-uniqueness problem and the semi-blind source separation

Semi-blind source separation (SBSS) is a special case of the well-known source separation problem when some partial knowledge of the source signals is available to the system. In particular, a batch-wise adaptation in the frequency domain based on the independent component analysis (ICA) can be effectively used to jointly perform source separation and multi-channel acoustic echo cancellation (MCAEC) without double-talk detection. However, the non-uniqueness problem due to the correlated far-end reference signals still affects the SBSS approach. In this paper, we analyze the structure of the SBSS de-mixing matrix and the behavior of a batch on-line adaptation algorithm under two most common far-end mixing conditions. We show that with a proper constraint on the de-mixing matrix, high echo reduction can be achieved just as the misalignment remains relatively low even for the worst-case scenario of single far-end talker and also without any pre-processing procedure to decorrelate the far-end signals.