A clustering approach for the blind separation of multiple finite alphabet sequences from a single linear mixture

Abstract

In this paper, we treat the blind separation problem of binary signals and multilevel PAM signals from a single real mixture or a single complex mixture, respectively. Our approach is based on the clustering of the observation values and the close relationship between the position of the cluster centers and the mixing coefficients. Under mild assumptions, our mathematical formulation yields two deterministic algorithms for the blind estimation of the mixing operator. In the real mixture case we derive a finite, recursive algorithm exploiting the arrangement of the centers along the 1-D line, while in the complex mixture case we exploit the properties of the convex hull of the 2-D data cloud to estimate the mixing parameters. In the absence of noise and for any number of sources, both methods yield perfect results. Following the parameter estimation step, the source symbols can be estimated using a nearest neighbor rule. In the noisy case, our error analysis shows that the parameter estimation error increases smoothly with the noise power, while the source estimate bit error rate depends on relative size of the noise power and the minimum distance between the cluster centers.