Noncoherent space--time coding: an algebraic perspective

The design of space--time signals for noncoherent block-fading channels where the channel state information is not known a priori at the transmitter and the receiver is considered. In particular, a new algebraic formulation for the diversity advantage design criterion is developed. The new criterion encompasses, as a special case, the well-known diversity advantage for unitary space--time signals and, more importantly, applies to arbitrary signaling schemes and arbitrary channel distributions. This criterion is used to establish the optimal diversity-versus-rate tradeoff for training based schemes in block-fading channels. Our results are then specialized to the class of affine space--time signals which allows for a low complexity decoder. Within this class, space--time constellations based on the threaded algebraic space--time (TAST) architecture are considered. These constellations achieve the optimal diversity-versus-rate tradeoff over noncoherent block-fading channels and outperform previously proposed codes in the considered scenarios as demonstrated by the numerical results. Using the analytical and numerical results developed in this paper, nonunitary space--time codes are argued to offer certain advantages in block-fading channels where the appropriate use of coherent space--time codes is shown to offer a very efficient solution to the noncoherent space--time communication paradigm. Index Terms--Diversity-versus-rate tradeoff, generalized likelihood ratio test (GLRT) receivers, noncoherent channels, space--time coding.