Parameter estimation and equalization techniques for MIMO frequency selective channels with multiple frequency offsets

In this work, we focus upon the estimation of the channel parameters of a multiple input and multiple output (MIMO) model, allowing for more than one path between the transmit and the receive antennas, with each path possibly having different frequency offsets (FOs). Such a scenario may arise due to Doppler shifts associated with various multipaths. In particular, we derive an approximate maximum likelihood estimator (AML) for the channel parameters by exploiting the correlation property of the pilot signal. The resulting AML is realised as the sum of n_TL one-dimensional maximizations, where n_T is the number of transmit antennas and L is the total number of paths, and is validated by comparison with the Cramér-Rao lower bound (CRLB), which is also derived. Furthermore, a minimum mean square error recursive (MMSER) equalizer is proposed which exploits the estimated parameters, the performance of which is shown to be much improved on an equalizer not accounting for FOs.