Non-data-aided ML carrier frequency and phase synchronization in OFDM systems

Abstract

In this paper non-data-aided(NDA), maximum likelihood(ML) algorithms are derived for the carrier frequency and phase offset, separately, for OFDM systems employing M-PSK modulation scheme. NDA ML estimation algorithm for frequency offset estimation exploits the redundant information contained in the cyclic prefix preceeding the OFDM symbols, thus reducing the need for pilots. Its mean-squared performance is obtained analytically and compared with simulation results. It is observed that the resulting algorithm generates very accurate estimation even when the offset is high. It is also shown that the frequency estimator may be used in a tracking mode. The ML algorithm derived for the carrier phase estimation is also a non-data-aided(NDA) and maximizes the low SNR limit of the likelihood function averaged over M-PSK signal constellation. It is shown that for sufficiently small SNR the ML phase estimator obtained reduces to the familiar Mth order power synchronizer which belongs to the class of NDA feedforward carrier synchronizers introduced earlier in the literature. Its mean-squared performance is obtained analytically and compared with simulation results. We observe that the resulting algorithm generates very accurate estimation even when the phase offset is high, that the self noise is absent and the performance of the algorithm is basically the same as the Cramer-Rao bound for moderate to high SNR. Finally we note that the error variance derived for the mean-squared performance of this NDA ML synchronizer is an extension of the approximate variance formula appeared in Reference 20,equation(14) for M-PSK.