Maximum likelihood frequency offset estimation for frequency selective MIMO channels: An average periodogram interpretation and iterative techniques

We provide exact and approximate maximum likelihood solutions and the corresponding Cramer Rao Lower Bounds (CRLBs) for the estimation of channel fading coefficients and frequency offsets (FOs) for a MIMO frequency selective channel. In our problem we considered estimation of parameters of data observed over a number of frames, and assumed FOs during those frames do not vary significantly as compared to the channel fading coefficients that change between frames according to Rayleigh fading profile. We show the resulting estimator for the FO is an average periodogram maximizer. We also provide an approximation to the estimator to reduce the data storage complexity. Since FO estimator requires a large set of data for satisfactory performance, we provided an iterative technique which combines very short pilot symbols with the soft estimate of the transmitted data symbols to iteratively refine the performance of the estimator.