Abstract Orthogonal frequency division multiplexing (OFDM) is a promising technique in modern high data rate wireless communication system. However, the serious problem in OFDM system is the inter-carrier-interference (ICI) that is produced by the carrier frequency offset (CFO). CFO destroys the orthogonal properties among the sub-carriers and introduces ICI. ICI is a major impairment in OFDM system as it can degrade the bit error rate (BER) performance of the system. In this paper we have proposed an optimal ICI self-cancellation scheme that can maximize the carrier-to-interference-ratio (CIR) of the system. This scheme is based on optimizing the data allocation and combining parameters where, for estimated CFO, the optimized values of these parameters are calculated using Nelder Mead simplex algorithm. An approach to calculate the sub-optimized values of data allocation and combining parameters is also proposed, where the knowledge of CFO estimation can be avoided. In this paper, we have carried out the complete performance analysis of ICI self-cancellation schemes. We have also derived the mathematical expressions for ICI coefficients and presented a comparative analysis of standard OFDM system with different ICI cancellation schemes. The mathematical expressions for CIR and BER performance are further derived. To confirm the validity of the results Monte Carlo simulations using Matlab are also performed. We have also done the comparison of peak-to-average power ratio (PAPR) of conventional ICI self-cancellation scheme and proposed scheme.