When is limited feedback for transmit beamforming beneficial?

Transmit beamforming and receive combining are low complexity techniques that help in achieving the full diversity afforded by the multi-antenna channel. Complete channel state information at the transmitter may be possible only under rare instances. Thus quantized beamforming with limited feedback on a reverse link has been a topic that has attracted great attention recently. But almost all of the work to date has focussed on modeling the channel with independent, identically distributed (i.i.d.) Rayleigh fading between antenna pairs. In this paper, we consider the correlated channel case, and show that Grassmannian line packing is an artificial artifact of the i.i.d. assumption. We show that there are dominant peaks in the eigen-domain when correlation is imposed and the codebook construction should be matched to the correlation in the channel, which renders the problem in this case easier than for i.i.d. channels