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A hybrid ARQ scheme for multiple transmit antennas systems is presented. Space-diversity is achieved through the use of random signal mapping (RSM). The use of RSM instead of other typical space-time coding schemes, as space-time trellis codes or space-time block codes, allows that more antennas may be added to the system with negligible complexity increase at the receiver. Coding gain is achieved with a standard parallel turbo code. Numerical results for frame error rate, throughput and number of required retransmissions for a varying number of transmit antennas are presented. The impact of the proposed scheme in the performance of a higher layer protocol, as TCP, is also investigated through computer simulations.