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The rapid growth within the field of digital communication during the recent years expanded the need for high-speed data transmission to support a wide range of services such as: video, data and voice in wireless communication systems, etc. Orthogonal frequency division multiplexing (OFDM) and a multicarrier modulation scheme are employed to achieve the high data rates. Since OFDM is very much sensitive to carrier frequency offsets, which cause the Inter-carrier Interference (ICI) leads to mitigation of this ICI is necessary. The objectives of this paper are to, proposed an efficient ICI self-cancellation scheme to mitigate the effect of ICI on OFDM systems. For this purpose, a redundant data is transmitted onto adjacent sub-carriers such that the ICI between adjacent sub-carriers cancels out at the receiver side. One data symbol is modulated into a group of adjacent sub carriers with a group of weighting coefficients. At the receiver side, the received signals are linearly combined on these sub carriers with proposed coefficients. The residual ICI contained in the received signals can then be further reduced. This study provides significant carrier-to-interference power ratio (CIR) improvement, which has been studied theoretically and supported by simulations. Since no channel equalization is required to reduce ICI, so the proposed scheme doesnt increase the system complexity.