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In this paper, the authors 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.
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