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For transmitted-reference impulse radio, it has been experimentally shown that multiple transmit antennas can provide an energy boost in the received signal. Here, we propose a 2-transmit and Q-receive differential space-time block coded impulse radio with autocorrelation receiver. A mathematical model for predicting the system bit-error-rate (BER) performance is derived for intersymbol interference-free transmission over an ultra-wideband channel, and validated with computer simulated results. From the results, it is observed that in migrating from 1-transmit to 2-transmit antennas, a signal-to-noise ratio gain of 3 dB, 2 dB and 1 dB at BER = 10-5 can be achieved, respectively, for the case of 1-, 2- and 4-receive antennas.