Gaussian maximum likelihood blind multichannel multiuser identification

We consider a Spatial Division Multiple Access (S.D.M.A.) situation in which p users operate on the same carrier frequency and use the same linear digital modulation format. We consider in > p antennas receiving mixtures of these signals through multi-path propagation (equivalently, oversampling of the received signals of a smaller number of antenna signals could be used). Current approaches to multiuser blind channel identification include subspace-fitting techniques [7], deterministic Maximum-Likelihood (DML) techniques [13] and linear prediction methods [13]. The two first techniques are rather closely related and give the channel apart from a triangular dynamical multiplicative factor (see [7]), moreover, they are not robust to channel length overestimation. The latter approach is robust to channel length overestimation and yields the channel estimate apart from a unitary static multiplicative factor, which can be determined by resorting to higher order statistics. On the other hand, Gaussian Maximum Likelihood (GML) methods have been introduced in [5] for the single user case and have given better performances than DML. Extending GML to the multiuser case, we can expect good performances, and, as will be shown in the identifiability section, we will get the channel apart from a unitary static multiplicative factor.