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This paper studies the performance of two major space-time trellis code (STC) transmission and detection schemes over frequency selective fading channels: (1) maximum likelihood equalization and detection (MLED), and (2) orthogonal frequency division multiplexing (OFDM). Their performance is evaluated and compared both analytically and empirically. It shows that the maximum achievable diversity order for MLED and OFDM approaches are both identical as NML, where N, M is the number of transmit and receive antennas respectively, and L is the channel tap length. To achieve a certain amount of diversity order, the MLED approach requires a weaker code, but the decoding trellis complexity for both MLED (with combined trellis detector) and OFDM are the same. For codes that do not achieve the maximum diversity order, MLED always achieves higher diversity order than OFDM. Moreover, the use of interleaver in STC OFDM is essential in avoiding rank deficiency caused by clustering of path arrivals, which reduces the diversity order of the system. Simulation results support these arguments, and show that the MLED approach outperforms OFDM when the same maximum diversity order achievable code is used.