This paper discusses the effect of carrier frequency offset on the performance of OFDM communications systems. The sensitivity of OFDM systems to frequency offset compared with single carrier systems is a major disadvantage. In general, Frequency offset is defined as the difference between the nominal frequency and actual output frequency. In OFDM, the uncertainty in carrier frequency, which is due to a difference in the frequencies of the local oscillators in the transmitter and receiver, gives rise to a shift in the frequency domain. This shift is also referred to as frequency offset. The frequency offset disturbs the orthogonality of the sub-carriers and eventually gives rise to lower SNR and ISI which affects the overall performance of the OFDM system. The demodulation of a OFDM signal with an frequency offset in the carrier frequency can cause large bit error rate and it may to make contemptible the performance of a symbol synchronizer. It is therefore important to estimate the frequency offset and minimize/eliminate its impact. In this paper we will study the effects of CFO upon signal to noise ratio (SNR) for an OFDM system, and also estimate the amount of frequency offset. In the first part of paper we discusses Conjugate ICI Cancellation scheme. method for estimating of frequency offset. In second part we will discuss another method i.e Extended Kalman Filtering (EKF) for estimating CFO and then Simulation results illustrate comparison of performance of these two methods for BPSK modulation scheme for different values of frequency offset.