Iterative (turbo) expectation - maximisation-based time and frequency synchronisation for multiple-input multiple-output-orthogonal frequency-division multiplexing systems

An iterative expectation-maximisation time-frequency synchronisation algorithm joint with channel estimation for multiple-input multiple-output-orthogonal frequency-division multiplexing (OFDM) systems in frequency-selective fading channels is addressed. The receiver iterates between detection and estimation stages. For each iteration, the expectation of ODFM symbols is calculated first by using a posteriori probabilities provided by maximum a posteriori (MAP) decoder, and second, a proposed metric is maximised to obtain both frequency offset and symbol timing. The channel can be identified by means of these estimates. This algorithm can work in transmission mode, and thus, can be used to estimate the residual errors or track the change of the parameters. The performance of the proposed synchronisation approach, in terms of bit-error rate and mean-square error, is shown.