We consider an iterative ML channel estimator for MC-CDMA systems with code-multiplexed training. Its performance has been studied by using results from the asymptotics of Fourier matrices with dimensions growing without bound with a certain constant ratio between them. Our results are then more representative of real non-asymptotic situations because, as in practical scenarios, different quantities in the signal model are assumed to have the same order of magnitude. This asymptotic analysis allows us to characterize the estimator analitically in terms of a parameter related to the evolution through the iterations of the symbol estimate. The results can efficiently be used for detection purposes, whereby a larger performance gain could be attained if employed for nonconstant-amplitude M-ary-QAM modulations.