Maximum-likelihood CFO estimation for MIMO/OFDM uplink using superimposed trainings

We address the problem of superimposed training (ST)-based maximum-likelihood (ML) carrier frequency offset (CFO) estimation for multiple-input multiple-output/orthogonal frequency-division multiplexing (MIMO/OFDM) systems. With the specifically designed training signals, the effect due to the unknown information sequence is fully cancelled in time-domain and, the CFO estimation is performed by using one pilot sample of each distinct user. We also present a performance analysis of the CFOs estimation and derive an approximated closed-form CFO estimation variance. It is shown that with the judiciously designed training sequences, the performance of the proposed ST based-ML CFO estimator approaches the Cramer-Rao bound for high signal-to-noise ratio (SNR) scenario. Simulation results illustrate the merits of the proposed approach.