Blind and Semi-Blind FIR Multichannel Estimation: (Global) Identifiability Conditions

Two channel estimation methods are often opposed: training sequence methods that use the information induced by known symbols and blind methods that use the information contained in the received signal and, possibly, hypotheses on the input symbol statistics but without integrating the information from known symbols, if present. Semi-blind methods combine both training sequence and blind information and are more powerful than the two methods separately. We investigate the identifiability conditions for blind and semi-blind finite impulse response (FIR) multichannel estimation in terms of channel characteristics, received data length, and input symbol excitation modes, as well as number of known symbols for semi-blind estimation. Two models corresponding to two different cases of a priori knowledge on the input symbols are studied: the deterministic model in which the unknown symbols are considered as unknown deterministic quantities and the Gaussian model in which they are considered as Gaussian random variables. This last model includes the methods using the second-order statistics of the received data. Semi-blind methods appear superior to blind and training sequence methods and allow the estimation of any channel with only few known symbols. Furthermore, the Gaussian model appears more robust than the deterministic one as it leads to less demanding identifiability conditions.