Differential unitary space-time signal designs with improved performance using parametric equivalence

We present two unitary space-time signal designs for two or more transmit antennas. The first design is a reparametrisation of rotation matrices applied to diagonal matrices to form unitary space-time codes. The rotation matrices are applied as matrices similar to Alamouti-style block codes. The second design subsumes rotation matrices applied to diagonal matrices for two antennas. These designs are applied in a non-coherent/differential framework. Optimisation of constellations is performed using the union bound on block-error probability, for which a new exact closed-form expression is given. Both designs have superior block-error performance over previous designs, and have similar performance to each other.