Identifiability is a fundamental issue in blind signal processing. It is well known that there are two types of inherent ambiguities: the scalar and permutation ambiguities. However, this is obtained under the condition that no a priori information of input signals is assumed. We show that if the information of source constellation is exploited, with a general constellation, there is an inherent discrete phase ambiguity, which is uniformly spaced on the unit circle. We also illustrate our identifiability results to blind channel estimation in orthogonal frequency division multiplexing (OFDM) systems.