Design and analysis of transmit-beamforming based on limited-rate feedback

We deal with the design and performance analysis of transmit-beamformers for multi-input multi-output (MIMO) systems, based on bandwidth-limited information that is fed back from the receiver to the transmitter. By casting the design of transmit-beamforming based on limited-rate feedback as an equivalent sphere vector quantization (SVQ) problem, we first consider multi-antenna beamformed transmissions through independent and identically distributed (i.i.d.) Rayleigh fading channels. We upper-bound the rate distortion function of the vector source, and also lower-bound the operational rate distortion performance achieved by the generalized Lloyd´s algorithm. A simple and valuable relationship emerges between the theoretical distortion limit and the achievable performance, and the average signal to noise ratio (SNR) performance is accurately quantified. Finally, we study beamformer codebook designs for correlated Rayleigh fading channels. and derive a low-complexity codebook design that achieves near optimal performance.