Analysis of vector quantizers using transformed codebook with application to feedback-based multiple antenna systems

Transformed codebooks are often obtained by a transformation of a codebook, potentially optimum for a particular set of statistical conditions, to best match the statistical environment at hand. The procedure, though suboptimal, has recently been suggested for feedback MISO systems because of their simplicity and effectiveness. We first consider in this paper the analysis of a general vector quantizer with transformed codebook. Bounds on the average distortion of this class of quantizers are provided to characterize the effects of sub-optimality introduced by the transformed codebook on system performance. We then focus our attention on the application of the proposed general framework to providing capacity analysis of a feedback-based MISO system over correlated fading channels using channel quantizers with both optimal and transformed codebooks. In particular, upper and lower bounds on the channel capacity loss of MISO systems with transformed codebooks are provided and compared to that of the optimal quantizers. Numerical and simulation results are presented which confirm the tightness of the theoretical distortion bounds.