Transmit diversity as a combination of spatial and delay diversity

We present performance results of some of the algebraic space-time (ST) block codes based on the combination of Hadamard spreading sequences with rotated constellations. Given a vector x in a rotated constellation in dimension n that has full spatial diversity, we spread each component x_j of x by a different Hadamard sequence of length n and send the resulted sequence over n antennas at the time j. These codes transmit at a rate of 1 symbol/sec and have a maximum transmit diversity gain and near maximum coding gain but they only exist for n=1,2 and n multiple of 4. We also propose new schemes for the other dimensions to obtain maximum transmit diversity and near maximum coding gain based on the combination of delay and the spatial diversity of rotated constellations. We compare the proposed codes with some existing ST block codes and comment on the large improvement in performance at the detrimental of moderate increase of decoding complexity