On Understanding of Optimal Joint Transmit-receive Diversity from Eigenmode Beamforming in Correlated Fading Channels

Joint transmit-receive diversity (JTRD) is one of spatial diversity techniques to mitigate the communication quality degradation caused by multipath fading. In JTRD, the transmitter and the receiver cooperate so as to maximize the received signal-to-noise ratio (SNR). On the other hand, eigenmode beamforming (EMBF) technique is known to improve the spectrum efficiency by transmitting multiple data streams. The transmitter and receiver weight matrices of EMBF consist of the right- and left-singular vectors, respectively. In this paper, it is shown that optimal JTRD corresponds to the single-stream EMBF using the maximum singular value. In optimal JTRD, the achievable channel capacity improves as the fading correlation at the receiver becomes stronger. We try to understand such a behavior from a viewpoint of EMBF in correlated fading channels. By Monte-Carlo numerical computation assuming two-antenna receiver case, such a behavior of optimal JTRD is shown to result from the fact that as the fading correlation becomes stronger, the next maximum singular value (eigenvalue) fades rapidly and, in return, the maximum singular value (eigenvalue) becomes stronger.