On the theory of space-time codes for PSK modulation

The design of space-time codes to achieve full spatial diversity over fadin g channels has largely been addressed by handcrafting example codes using c omputer search methods and only for small numbers of antennas. The lack of more general designs Is in part due to the fact that the diversity advantag e of a code is the minimum rank among the complex baseband differences betw een modulated codewords, which Is difficult to relate to traditional code d esigns over finite fields and rings. In this paper, we present general bina ry design criteria for PSK-modulated space-time codes. For linear BPSK/QPSK codes, the rank of (binary projections of) the unmodulated codewords, as b inary matrices over the binary field, is a sufficient design criterion: ful l binary rank guarantees full spatial diversity. This criterion accounts fo r much of what is currently known about PSK-modulated space-time codes, we develop new fundamental code constructions for both quasi-static and time-v arying channels, These are perhaps the first general constructions-other th an delay diversity schemes-that guarantee full spatial diversity for an arb itrary number of transmit antennas.