Abstract
Transformed codebooks are obtained by a transformation of a given codebook to best match the
statistical environment at hand. The procedure, though suboptimal, has recently been suggested for
feedback of channel state information (CSI) in multiple antenna systems with correlated channels because
of their simplicity and effectiveness. In this paper, we first consider the general distortion analysis of
vector quantizers with transformed codebooks. Bounds on the average system distortion of this class of
quantizers are provided. It exposes the effects of two kinds of suboptimality introduced by the transformed
codebook, namely, the loss caused by suboptimal point density and the loss caused by mismatched
Voronoi shape. We then focus our attention on the application of the proposed general framework to
providing capacity analysis of a feedback-based MISO system over spatially correlated fading channels.
In particular, with capacity loss as an objective function, upper and lower bounds on the average distortion
of MISO systems with transformed codebooks are provided and compared to that of the optimal channel
quantizers. The expressions are examined to provide interesting insights in the high and low SNR regime.
Numerical and simulation results are presented which confirm the tightness of the distortion bounds.
