Joint ML timing and phase estimation in OFDM systems using the EM algorithm

In this paper, a computationally efficient algorithm is presented for joint maximum likelihood (ML) timing and carrier phase estimation of OFDM systems employing M-PSK modulation scheme with additive Gauissian noise, based on the Expectation-Maximization (EM) algorithm. A nondata-aided(NDA) scheme is considered for the joint timing and phase synchronizer which maximizes the low SNR limit of the likelihood function averaged over the M-PSK signal costellation. For this, an Ehl algorithm is derived which estimates the timing offset and the phase rotations of each subcarrier iteratively and which converges to the true ML estimation of the unknown timing and phase. It is shown that the algorithm becomes independent of the signal-to-noise ratio for both low and high SNR cases. The algorithm is applied to the QPSK modulated OFDM systems and it is concluded that for SNR values greater than 10 dB the convergence is achieved in first iteration and for SNR values less than 10 dB, at most in three iterations. It is also concluded that the convergence is independent of the initial starting points.