In this paper, we propose to combine multi-user detection with channel estimation for synchronous Multi-Carrier Direct Sequence Code Division Multiple Access (MC-DS-CDMA) systems, over time-varying Rayleigh fading channels. In particular, our scheme operates in three steps: 1/the decorrelating filter is carried out along each carrier to eliminate the multiple access interference (MAI) 2/ the fading channels responses modelled by AR processes are estimated using Kalman filtering.3/ The channels estimates are fed into the Frequency diversity Maximum Ratio Combining (MRC) rule to obtain the data symbol estimate. A comparative study is carried out under realistic Jakes' fading model, with slow and fast fading scenarios. THe simulation results confirm that using 1st and 2nd order AR model in the Kalman filter based channel estimator depends on the fading rate. For low fading rate, a 1st order AR model is enough whereas a 2nd order AR model provides lower Bit Error Rate (BER) for moderate and high fading rates.