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The performance of an adaptive modulation system in Rayleigh fading channels exploiting spatial diversity through transmit antenna selection is analysed for the case of delay constrained networks. The system combines maximal ratio combining at the receiver and a transmit antenna selection system which switches between available antennas and modulation schemes at the transmitter. In a practical system, a delay between the channel being sampled at the receiver and acted upon by the transmitter will tend to degrade system performance. In this paper, a channel prediction scheme is employed at the receiver to provide estimates of future best transmission states, which includes selecting the best transmission antenna as well as the best supported M-QAM modulation scheme. The Shannon capacity for optimal rate and constant power is derived and presented, and used as a benchmark to evaluate the spectral efficiency of the discrete rate system optimised for instantaneous BER (bit error rate) and constant power constraint.