Orthogonal Frequency Division Multiplexing (OFDM) is the technology which is used in 4G based high data rate applications. The standards like Long Term Evaluation (LTE), Long Term Evaluation Advanced (LTE-A) and Wi-MAX promise to offer a high data rate at high mobility. But the mobility destroys the orthogonality of OFDM systems and also reduces the spectral efficiency. The orthogonality loss due to frequency synchronization errors cause Inter Carrier Interference (ICI) which is a severe problem in OFDM based systems. In this paper we have discussed the effects of Carrier Frequency Offset (CFO) and various estimation techniques and compare their performance. The simulation results prove that Moose method of frequency domain estimation offers less Mean Square Error (MSE) when compared to other techniques.