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We consider orthogonal frequency-division multiplexing systems with intercarrier interference (ICI) due to insufficient cyclic prefix and/or temporal variations. Intersymbol interference (ISI) and ICI lead to an error floor in conventional receivers. We suggest two techniques for the equalization of ICI. The first, called "operator-perturbation technique" is an iterative technique for the inversion of a linear system of equations. Alternatively, we show that serial or parallel interference cancellation can be used to drastically reduce the error floor. Simulations show that, depending on the SNR and the origin of the ICI, one of the schemes performs best. In all cases, our schemes lead to a drastic reduction of the bit error rate.