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Similar to other orthogonal frequency division multiplexing (OFDM)-based systems, carrier frequency offset (CFO) is a challenging problem in uplink communications of single carrier frequency division multiple access (SC-FDMA) system. It must be noticed that CFO, which is mainly due to oscillator instability and/or Doppler shift, would generate inter carrier interference (ICI) as well as multi-access interference (MAI) to disturb the received signals and seriously degrade system performance. Frequency synchronization in uplink communications is difficult because different users always experience different CFOs and one userÂ¿s CFO correction would misalign other users. In this paper, we proposed a suppression method to overcome the multi CFOs problem. To implement this algorithm, block type pilots would be exploited, which is also utilized in LTE uplink standard. The proposed algorithm is based on the following two assumptions. Firstly the proposed algorithm is applied in this scenario, where different users start to communicate with the base station at different symbol periods, and secondly, during the pilot block and the following data blocks, the CFO of each user is quasi static, which is feasible since CFO is slow varying. Compared with other interference suppression methods, the proposed method could directly estimate the interference components from the inverse pilot matrix, thus it does not need to do the CFO estimation. Further more, since block type pilots is a common pilot pattern in wireless communication system, this algorithm can be easily extended to other communication system. Simulation results show that the proposed suppression algorithm can significantly improved system performance.