Blind separation of linear mixtures of digital signals using successive interference cancellation iterative least squares

We consider blind separation of linear mixtures of digital communication signals in noise. When little or nothing can be assumed about the mixing matrix, signal separation may be achieved by exploiting structural properties of the transmitted signals. ILSP and ILSE are two iterative least squares (ILS) separation algorithms that exploit the finite-alphabet property. ILSE is monotonically convergent and performs very well, but its complexity is exponential in the number of signals; ILSP is computationally cheaper, but is not guaranteed to converge monotonically, and leaves much to be desired in terms of BER-SNR performance relative to ILSE. We propose two computationally efficient and provably monotonically convergent ILS blind separation algorithms based on an optimal scaling Lemma. The signal estimation step of both algorithms is reminiscent of Successive Interference Cancellation (SIC) ideas. For well-conditioned data and moderate SNR, the proposed algorithms attain the performance of ILSE at the complexity cost of ILSP.