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We derive vector transmission models for OFDM-based systems: pure OFDM, multiuser OFDM (OFDMA), CDM-OFDMA and MC-CDMA. Two kinds of OFDMA systems, conventional OFDMA and interleaved OFDMA are studied and the effects of frequency offset and multipath propagation are investigated. For each system both downlink and uplink transmission models are described. The models allow multiuser detection as a means to cope with carrier frequency offsets, which is especially useful for the uplink. The possibility of frequency offset estimation is discussed briefly.