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This paper deals with a system combining orthogonal frequency division multiplexing (OFDM) and interleave-division multiple access (IDMA). OFDM makes the system robust against intersymbol interference, whereas IDMA combats the multiple access interference. Nevertheless, two problems have to be solved: 1/ carrier frequency offset (CFO) must be estimated/corrected to guarantee the orthogonality between subcarriers. 2/ the conventional IDMA receiver requires a priori knowledge of the channel. Therefore, the CFO and the channel must be estimated. Our contribution is twofold. Firstly, we suggest a sigma point Kalman filter to solve the estimation issue. In addition, we propose a new scheme where a CFO correction is no longer necessary, unlike common OFDM approaches. We show that without a CFO correction, the transmitted bits can be recovered by modifying the conventional IDMA receiver. When considering an OFDM-IDMA network over Rayleigh fading channels, simulation results show the efficiency of the proposed algorithm.