Blind identification of linear channels using the data constellation geometry

We propose a novel geometric blind identification method based on the structure of the data constellation created from the output of an ISI-corrupted channel transmitting an M-ary PAM coded source. We formally establish that, in the absence of noise and under certain identification conditions, the covex hull of the constellation contains information sufficient for recovering the channel uniquely (up to the sign). In the noisy case the method must be preceeded by an unsupervised clustering procedure. Contrary to HOS- or SOS-based methods our approach is finite and does not require neither spatial nor temporal diversity. On the negative side, the complexity is higher than exponential with respect to the channel length and so the method is more suitable for short channels.