Carrier frequency offset (CFO) is a serious drawback in orthogonal frequency division multiplexing (OFDM) systems. It must be estimated and compensated before demodulation to guarantee the system performance. In this paper, we examine the performance of a blind minimum output variance (MOV) estimator. Based on the derived probability density function (PDF) of the output magnitude, its mean and variance are obtained and it is observed that the variance reaches the minimum when there is no frequency offset. This observation motivates the development of the proposed MOV estimator. The theoretical mean-square error (MSE) of the MOV estimator over an AWGN channel is obtained. The analytical results are in good agreement with the simulation results. The performance evaluation of the MOV estimator is extended to a frequency-selective fading channel and the maximal-ratio combining (MRC) technique is applied to enhance the MOV estimator's performance. Simulation results show that the MRC technique significantly improves the accuracy of the MOV estimator.