Equiangular Frames for Quantized MIMO Beamforming


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


Submitted to Allerton Conf. on Comm., Control and Computing, 2004.


In an uncorrelated Rayleigh fading channel, multiple-input multiple-output (MIMO) beamforming-combining systems can attain full diversity using full channel knowledge at the transmitter. For practical implementation, such systems employ limited feedback by quantizing the beamforming vector at the receiver. This is done by using a °xed pre- determined mutually shared codebook of beamforming vectors and sending 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 Packing (GLP) have been proposed as possible solutions. In this paper, the codebook design problem is reformulated using an information-theoretic approach. A certain class of structured frames, equiangular unit norm tight frames (EUNTF), is shown to be optimal under the new design criterion. The Voronoi regions of EUNTFs are shown to contribute equal distortions. Simulations show that EUNTF codebooks result in signi°cantly higher receive signal-to-noise ratio compared to codebooks designed using VQ or GLP.

The manuscript is available on email request.