On transmit diversity with imperfect channel state information

The optimal transmission strategy of a multiple-input single-output wireless communication link is studied. The receiver has full channel state information and the transmitter has only long-term channel state information in terms of the channel covariance matrix. A necessary and sufficient condition for the optimal eigenvalues of the transmit covariance matrix is presented. A necessary and sufficient condition for achieving capacity when transmitting in m directions is developed. The main questions regarding the system design are answered using these conditions. It is shown how the optimal number of transmit antennas can be computed to achieve full spatial diversity given the channel covariance matrix. The maximum number of required parallel data streams is computed and a transmit diversity function is defined in order to obtain a measure for the available spatial diversity