Existence and construction of noncoherent unitary space-time codes

We consider transmission using transmit and reception using 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 unitary space–time codes and for a block-fading channel model where the channel is static during channel uses and varies from channel uses to the other, we establish the bound min( ) on the diversity advantage provided by the code. In order to show that the requirement min( ) cannot be relaxed, for any given , , , and min( ), we then construct unitary space–time codes of rate that guarantee diversity advantage . Two constructions are given that are also amenable to simple encoding and noncoherent maximum-likelihood (ML) decoding algorithms.