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Optimum space-time turbo trellis codes (ST turbo TCs) with 4-PSK and 8-PSK for two, three and four transmit antennas on multi-input/multi-output (MIMO) fading channels are presented. The component codes of the turbo schemes are designed by choosing feedforward coefficients to maximize coding gain and feedback coefficients to minimize iterative decoding threshold. Performance comparison of ST turbo TCs with various memory orders, feedback coefficients, transmit antennas and interleaver structures is illustrated. For four transmit antennas, ST turbo TCs offer a gain of 3.75 dB over the one with two transmit antennas and is 2 dB better than the space-time trellis codes (STTCs) at an FER of 10-3 on slow Rayleigh fading channels.