Optimality of multichannel beamforming for spatially correlated multiple-antenna Rayleigh fading channels with channel covariance information at transmitter

In this paper, we derive a closed form necessary and sufficient condition under which rank r multichannel beamforming achieves the capacity of a single user spatially correlated Rayleigh fading channel which employs multiple transmit antennas and a single receive antenna. It is assumed that the receiver has perfect channel side information (CSIR) while the transmitter only knows the channel distribution (CDIT). Additionally, a set of r independent closed form equation is derived that gives the r non-zero eigenvalues of transmit covariance associated to transmit power along each mode.