Joint Maximum Likelihood Estimation of Integer Carrier Frequency Offset and Channel in OFDM Systems

For orthogonal frequency division multiplexing (OFDM) systems, the carrier frequency offset (CFO) between the carrier frequencies of the received signal and the receiver local oscillator is represented as the sum of the integer part and the fractional part by normalizing the CFO with subcarrier spacing. This paper focuses on the pilot-aided estimation of the channel gain and the integer part of the normalized CFO OFDM systems. For multipath channels, a simple estimator of the channel gain and the integer CFO is described, and the joint maximum likelihood (ML) estimator is developed. It is proved that the simple estimator becomes equivalent to the joint ML estimator when two OFDM symbols are observed. For the AWGN channel, this paper derives both the ML estimator of the integer CFO only and the joint ML estimator of the integer CFO and the phase offset. It is proved that the integer CFO estimation part of the joint ML estimator is the same as the ML estimator of the integer CFO only, and it is also shown by simulation that the ML estimator outperforms existing estimators significantly.