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This paper considers pilot-based parameter estimation for bandlimited MC-DS-CDMA systems relying on long spreading codes. Three different schemes are proposed and compared. The two so-called unstructured algorithms, namely the Least Squares Estimator (LS-E) and the Least Absolute Shrinkage and Selection Operator Estimator (LASSOE) first estimate the composite channel impulse response, and then extract the propagation delay, amplitude and phase. By contrast, the third algorithm namely the Structured LS Search Estimator (SLSS-E) exploits the a priori knowledge of the chip waveform and directly estimates the channel parameters. Parallel interference cancelation (PIC) is incorporated in the SLSS-E for the sake of mitigating the effect of multiple access interference and hence to further improve the performance. The complexity of PIC assisted SLSS-E and LS-E only increases linearly with the number of users, with the number of subcarriers and with the length of the pilot sequence. Simulation results indicate that the PIC assisted structured estimator outperforms its unstructured counterparts.