Channel estimation for orthogonal frequency division multiplexing (OFDM) system at the presence of carrier frequency offset (CFO) and phase noise is discussed in this paper. A CFO estimation algorithm is developed by exploiting the time-frequency structure of training symbols, and it provides a very accurate estimation of CFO at the presence of both unknown frequency selective fading and phase noise. Based on the estimated CFO, the phase noise and frequency selective fading are jointly estimated by employing the maximum a posteriori (MAP) criterion. Specifically, the fading channel is estimated in the form of frequency domain channel transfer function (CTF). The estimation of CTF eliminates the requirement of the priori knowledge of channel length, and it is simpler compared to the time domain channel impulse response (CIR) estimation method in the literature. Theoretical analysis with Cramer-Rao lower bound demonstrates that the joint phase noise and CTF estimation can achieve near optimum performance
