In this paper, we present a weighted cyclic prefix orthogonal frequency-division multiplexing (WCP-OFDM) transceiver as a generalization of traditional cyclic prefix (CP)-OFDM. In time-variant channels, this multicarrier transmission scheme may mitigate inter-channel interference (ICI) thanks to the use of non-rectangular pulse shapes. A precoding step may be required in order to reduce the peak-to-average power ratio (PAPR) at the transmitter output. For instance, a discrete Fourier transform (DFT) precoder leads to a single carrier transmission scheme with frequency domain equalization. We analyze the consequences of such a precoding, in terms of performances, in the context of a time-frequency selective channel.