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In this work we present an equalization scheme for a multicarrier (MC) code division multiple access (CDMA) communication system that is operated in a frequency-selective time-variant (TV) channel. For block oriented data transmission we are interested to describe the TV channel for the duration of a data block with the smallest amount of parameters possible. Slepian showed that time-limited parts of band-limited sequences span a subspace with strongly reduced dimensionality. The discrete prolate spheroidal (DPS) sequences are the basis of this subspace. We exploit this property by using the Slepian basis expansion model (BEM) to describe a TV channel with a minimum amount of parameters. The mean squared error (MSB) of the Slepian BEM is 30 dB smaller than the MSE of the Fourier BEM for a frequency-flat TV channel. We present simulation results in terms of bit error rate (BER) versus Eb/N0 for a multiuser MC-CDMA forward link in a frequency-selective TV channel comparing the Fourier BEM and the Slepian BEM for channel equalization.