We compare four different multi-carrier schemes in a discrete-time, oversampled domain over doubly-selective channels. We find that all the schemes can be implemented in a reduced complexity way, resorting to suitable fast transforms like DFT, DCT, or DST. For all models we assume either a rectangular base pulse or a properly designed prototype pulse, well-localized in both time and frequency domains, and we show that such a technique can be applied to our discrete-time block-based model. We highlight the similarities and the differences between some recently proposed multi-carrier modulations based on DCT and DST to mathematical concepts such as the Wilson base, that in turn will be used to develop a novel and effective multi-carrier format, ready to be employed in practical communication systems. All analyzed modulations will be compared in terms of spectral efficiency and BER performance in practical implementations.
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