Coherent space-time codes for noncoherent channels

A new algebraic formulation for the diversity advantage design criterion for arbitrary space-time signals in noncoherent block fading channels is developed. It is shown that the new criterion encompasses, as a special case, the well-known diversity advantage criterion for unitary space-time signaling. Using the proposed criterion, the optimal diversity-vs-rate tradeoff is derived for training based noncoherent signaling schemes. Our results are then specialized to the class of affine space-time signals which allow for an efficient polynomial complexity decoder. Within this class, new space-time constellations based on the threaded algebraic space-time (TAST) framework are proposed. These codes achieve the optimal diversity-vs-rate tradeoff and outperform previously proposed codes in the considered scenarios as demonstrated by numerical results. Using these analytical and numerical results, we argue that non-unitary space-time codes offer certain advantages in block fading channels and the appropriate use of coherent space-time codes is shown to offer a very efficient solution to the noncoherent space-time communication paradigm.