MIMO frequency-selective channels with multiple-frequency offsets: estimation and detection techniques

Channel gains and frequency offsets are estimated in a multiple input and multiple output (MIMO) scenario, allowing for more than one path between the transmit and the receive antennas, with each path possibly having a different frequency offset. Such a scenario may arise due to Doppler shift associated with various multipaths. Here, the general case is examined and an approximate maximum likelihood (AML) estimator is derived by exploiting the correlation property of the pilot signal. The AML estimator can be written as the sum of n_TL one-dimensional maximisations, where n_T is the number of transmit antennas and L is the total number of paths. The proposed estimator is validated by comparing the results with the Crame´r-Rao lower bound (CRLB). Further, a minimum mean square error recursive (MMSER) equaliser is proposed for the considered scenario. Finally, the performance of the MMSER equaliser is compared with the equaliser not accounting for frequency offsets.