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Traditional communication systems like AM and FM were essentially single carrier systems because the information modulated just one carrier and was transmitted. There was just one oscilator which fed the carrier signal.
In multicarrier systems there are oscilator banks (eg. fdm very old way, collins radio kineplex system I think used this) where different signals modulated different carrier frequencies and then were transmitted by one transmitter. On the receiver side there was another oscilator bank to demodulate the signal and separate them. Ofcourse the carriers were spaced apart enough in frequency to reduce or prevent ICI.
Nowadays, OFDM and MC-CDMA are multiple carrier systems. OFDM uses IFFT to cleverly convert a single carrier system to a multiple carrier which ofcourse is a different story.