Existence and construction of noncoherent unitary space-time codes

We consider transmission using N transmit and reception using M receive antennas in a wireless environment assuming that neither the transmitter nor the receiver knows the channel coefficients. For the scenario that the transmission employs noncoherent T × N unitary space-time codes and for a block-fading channel model where the channel is static during T channel uses and varies from T channel uses to the other, we establish the bound r ≤ min(T-N, N) on the diversity advantage rM provided by the code. In order to show that the requirement r ≤ min(T-N, N) cannot be relaxed, for any given R, N, T, and r ≤ min(T-N, N), we then construct unitary T × N space-time codes of rate R that guarantee diversity advantage rM. Two constructions are given that are also amenable to simple encoding and noncoherent maximum-likelihood (ML) decoding algorithms.