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

In this paper non-data-aided(NDA), maximum likelihood(ML) algorithms are de rived for the carrier frequency and phase offset, separately, for OFDM syst ems employing M-PSK modulation scheme. NDA ML estimation algorithm for freq uency offset estimation exploits the redundant information contained in the cyclic prefix preceeding the OFDM symbols, thus reducing the need for pilo ts. 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 tha t 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 ph ase estimator obtained reduces to the familiar Mth order power synchronizer which belongs to the class of NDA feedforward carrier synchronizers introd uced earlier in the literature. Its mean-squared performance is obtained an alytically and compared with simulation results. We observe that the result ing algorithm generates very accurate estimation even when the phase offset is high, that the self noise is absent and the performance of the algorith m is basically the same as the Cramer-Rao bound for moderate to high SNR. F inally we note that the error variance derived for the mean-squared perform ance of this NDA ML synchronizer is an extension of the approximate varianc e formula appeared in Reference 20,equation(14) for M-PSK.