As one of the most important components of the wideband wireless access technique,orthogonal frequency division multiplcxing (OFDM) has a high usage rate of spectrum and combats inter-symbol interference (ISI) in multi-path fading channel. However,when there are frequency offsets during the signal transmission,the inter-carrier interference (ICI) is introduced,which significantly degrades the performance. The existing ICI self-cancellation schemes such as PCC-OFDM are not optimum to minimize the interference considering both noise and ICI. In this paper,a new metric named SINR (signal-to-interference-and-noise ratio) is proposed. We discuss the optimization issue when a constant frequency offset exists and in time-varying channels. The optimum weighting-coefficient-pair (OWCP) is obtained,which maximizes SINR theoretically through the alter-nant iteration algorithm. Simulations show that the performance of OWCP-OFDM is better than that of PCC-OFDM,especially when the frequency offset is large. Although the ICI sell-cancellation scheme suffers bandwidth inefficiency,from the simulation results we can also see that the performance of OWCP-OFDM is much better than that of the standard OFDM systems with the same bandwidth efficiency when a frequency offset exists. Moreover,since the redundant modulation provides the capability to suppress ICI as well as a receiving SNR gain,it can be considered as exchanging the bandwidth for SNR.