Systematic design of unitary space-time constellations

We propose a systematic method for creating constellations of unitary space–time signals for multiple-antenna communication links. Unitary space–time signals, which are orthonormal in time across the antennas, have been shown to be well-tailored to a Rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients. The signals can achieve low probability of error by exploiting multiple-antenna diversity. Because the fading coefficients are not known, the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum-Euclidean-distance norm. Our construction begins with the first signal in the constellation—an oblong complex-valued matrix whose columns are orthonormal—and systematically produces the remaining signals by successively rotating this signal in a high-dimensional complex space. This construction easily produces large constellations of high-dimensional signals. We demonstrate its efficacy through examples involving one, two, and three transmitter antennas.