Frame theoretic quantization for limited feedback MIMO beamforming systems

In an uncorrelated Rayleigh fading channel, multiple-input multiple-output (MIMO) beamforming-combining systems can attain full diversity and significant array gain using channel knowledge at the transmitter. In the absence of channel knowledge at the transmitter, a beamforming vector can be quantized at the receiver using a fixed pre-determined codebook of beamforming vectors and the codeword index can be sent to the transmitter. Designing optimal codebooks (that maximize expected SNR) is an open problem and vector quantization (VQ) and Grassmannian line packings (GLP) have been proposed as possible solutions. In this paper, a mutual information based codebook design criterion is introduced and equiangular frames (EF) are proposed as beamforming codebooks satisfying this criterion. Besides providing a systematic way to design codebooks, EFs result in higher receive signal-to-noise ratio compared to codebooks designed using VQ or GLP.