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We propose a single carrier frequency domain equalization scheme for data transmission systems with two transmit antennas and two receive antennas. The scheme is shown to achieve the same diversity gains as that of the system with one transmit antennas and four receive antennas at low complexity over frequency selective fading channels. We analyze the impact of channel estimate error on the frequency domain equalization, which is critical when the signal noise ratio is low as in a zero forcing based time domain linear equalization system. Without extra power consumption, system performance can be achieved by channel coding with longer code length. The performance of the proposed scheme is evaluated over block fading Rayleigh distribution channel model. The justification and the performance are demonstrated by numerical simulation.