Recursive complex BSS via generalized eigendecomposition and application in image rejection for BPSK

Under the assumptions of non-Gaussian, non-stationary, or non-white independent sources, linear blind source separation can be formulated as generalized eigenvalue decomposition. Here we provide an elegant method of doing this on-line, instead of waiting for a sufficiently large batch of data. This is done through a recursive generalized eigendecomposition algorithm that tracks the optimal solution that one would obtain using all the data observed. The algorithms proposed in this paper follow the well-known recursive least squares (RLS) algorithm in spirit. We also propose to employ this on-line approach for joint image rejection in separating audio signals with the linear mixing varying with time and in slow fading wireless receivers with successful results.