Rate-diversity tradeoff of space-time codes with fixed alphabet and optimal constructions for PSK modulation

In this correspondence, we show that for any (Q x M) space-time code S having a fixed, finite signal constellation, there is a tradeoff between the transmission rate R and the transmit diversity gain V achieved by the code. The tradeoff is characterized by R less than or equal to Q - nu + 1, where Q is the number of transmit antennas. When either binary phase-shift keying (BPSK) or quaternary phase-shift keying (QPSK) is used as the signal constellation, a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain.