Differential space-time codes with four transmit antennas

We give near optimal differential unitary space-time codes using Bruhat decomposition and Weyl group for four transmit antennas. In case of two transmit antennas, it has been assumed that the two channels are uncorrelated. However, for four transmit antennas, the assumption is no longer justified. Therefore the new codes are found by examination of the average of the minimum squared Euclidean distance between all of the unitary matrices multiplied by various fading coefficients. The performance of the codes are simulated by computer and compared with the well-known cyclic group codes. The near optimal codes are about 2 dB better than the cyclic codes.