Complex Linear STBCs with Multiple Rates

Complex linear space-time block codes (STBCs) with multiple rates are investigated. First, the conditions for capacity-lossless STBC existence are derived and we prove that capacity-lossless complex linear STBCs exist if and only if there is one receive antenna. It is also proved that rate-one capacity-lossless complex linear STBCs exist if and only if there are two transmit antennas. We show that even though the Alamouti code and layered-Alamouti code are capacity-lossless for one receive antenna, better STBCs can still be found for two receive antennas by introducing the circular layered-Alamouti code. By analyzing the outage capacity, we also show that additional transmit antennas beyond the number of receive antennas can dramatically improve the performance. This analysis is supported by simulations