In this paper, a non-data-aided maximum a posteriori (MAP) channel estimation technique for OFDM systems employing M-PSK modulation scheme is proposed. The technique requires a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve orthogonal expansion and estimates the complex channel parameters of each subcarriers iteratively in frequency domain using the Expectation-Maximization (EM) algorithm. Pilot symbols are employed to choose reliable initial values of the unknown channel parameters. An analytical expression is derived for the exact Cramer-Rao lower bound of the proposed MAP channel estimator. Moreover, robustness of estimator to changes in channel correlation and signal-to-noise ratio is also analyzed. The performance is presented in terms of the mean-square error and the uncoded symbol error rate for a system employing QPSK signaling. Computer simulations demonstrate that the performance of OFDM systems using coherent demodulation based on our channel estimation can be significantly improved.