Frame Theoretic Quantization for Limited Feedback MIMO Beamforming systems


B. Mondal , R. Samanta and Robert W. Heath Jr


Submitted to IEEE Info. Theory Workshop, 2004.


Assuming an uncorrelated Rayleigh fading channel, multiple-input multiple-output (MIMO) beamforming-combining systems can attain full diversity using the knowledge of the beamforming vector at the transmitter. For practical implementation, such systems employ limited feedback by quantizing the beamforming vector at the receiver using a fixed pre-determined mutually shared codebook of beamforming vectors and send the index of the codeword to the transmitter. Designing optimal codebooks (that maximize average SNR) is an open problem and vector quantization (VQ) and Grassmannian Line Packings (GLP) have been proposed as possible solutions. In this paper, frames are introduced as codebooks and the geometric structure of a ``good" codebook is studied. It is proven that an optimal codebook is a frame. It is justified using quantum information theoretic results that unit norm tight frames are candidates for ``good" codebooks. Then it is proved that equiangular unit norm tight frames (EUNTF) minimize an upper bound on average distortion. Simulations show that codebooks that are EUNTFs result in significantly higher receive signal-to-noise ratio compared to codebooks designed using VQ or GLP.

The manuscript is available on email request.