Joint maximum-likelihood frequency offset and channel estimation for multiple-input multiple-output-orthogonal frequency-division multiplexing systems

The problem of joint maximum-likelihood estimation of the carrier-frequency offset (CFO) and channel coefficients in multiple-input multiple-output orthogonal frequency-division multiplexing systems is investigated, assuming that a training sequence is available. The exact solution to this problem turns out to be too complex for practical purposes. To overcome this difficulty, the authors resort to the expectation-maximisation (EM) algorithm and propose an iterative scheme which iterates between estimating the channel parameters and the frequency offset. This results in an estimation algorithm of a reasonable complexity which is suitable for practical applications. Moreover, the Cramer-Rao bounds (CRB) for both CFO and channel estimators are developed to evaluate the performance of the proposed scheme. Simulation results show that the proposed algorithm achieves almost ideal performance compared with the CRBs in all ranges of signal-to-noise ratio for both channel and frequency offset estimates.