This paper proposes a computationally efficient nondata-aided maximum a posteriori (MAP) channel-estimation algorithm focusing on the space-frequency (SF) transmit diversity orthogonal frequency division multiplexing (OFDM) transmission through frequency-selective channels. The proposed algorithm properly averages out the data sequence and requires a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve (KL) orthogonal expansion and estimates the complex channel parameters of each subcarrier iteratively, using the expectation maximization (EM) method. To further reduce the computational complexity of the proposed MAP algorithm, the optimal truncation property of the KL expansion is exploited. The performance of the MAP channel estimator is studied based on the evaluation of the modified Cramer-Rao bound (CRB). Simulation results confirm the proposed theoretical analysis and illustrate that the proposed algorithm is capable of tracking fast fading and improving overall performance.