Single-channel phaseless blind source separation

In this letter, we consider a novel problem of blind source separation from observed magnitude-only measurements of their convolutive mixture in different communication systems. The problem setups correspond to a blind receiver architecture that either does not have phase information in the measurements or has excessive phase noise that cannot be easily recovered. We have formulated the problem as a matrix recovery problem by using the lifting technique and proposed a convex programming-based solution for joint recovery of the unknown channel and source signals. We have implemented the proposed solution using the alternating direction method of multipliers (ADMM). We have plotted a phase transition diagram for random Gaussian subspaces that shows, for s source signals each of length n and channel of length k, the minimum measurements required for exact recovery are $$m \ge 1.19 (sn+k) \log ^{2}m$$ m ≥ 1.19 ( s n + k ) log 2 m that is in accord with our theoretical result. We have also plotted a phase transition diagram for the case where the channel delays matrix is deterministic (consisting of the first k columns of the identity matrix) that shows the minimum measurements required for exact recovery are $$m \ge 2.86 (sn+k) \log ^{2}m$$ m ≥ 2.86 ( s n + k ) log 2 m which are higher than random subspaces.