On regularity and identifiability of blind source separation under constant-modulus constraints

We investigate the information regularity and identifiability of the blind source separation (BSS) problem with constant modulus (CM) constraints on the sources. We establish for this problem the connection between the information regularity [existence of a finite Crame´r-Rao bound (CRB)] and local identifiability. Sufficient and necessary conditions for local identifiability are derived. We also study the conditions under which unique (global) identifiability is guaranteed within the inherently unresolvable ambiguities on phase rotation and source permutation. Both sufficient and necessary conditions are obtained.