High resolution quantization codebook design for multiple-antenna fading channels

This paper investigates the asymptotic structure of the channel vector quantization codebook for limited-feedback multiple-input single-output fading channels. The design criteria is to minimize the average transmission power subject to a target outage probability. First, we consider the design of scalar channel magnitude quantization codebook and prove that the asymptotically optimal quantization levels are uniformly spaced in dB scale. Such optimality does not depend on the the channel magnitude distribution, as long as some regularity conditions are satisfied. It is shown that the gradient of the objective function (the average transmission power) with respect to such quantization levels diminishes as N_p^-3/2 as the number of the levels N_p tends to infinity. We then form a product channel vector quantization codebook comprising a uniform (in dB) channel magnitude quantization codebook and a spatially uniform channel direction quantization codebook and derive the optimal bitsharing law between the two codebooks. It is shown that the asymptotically optimal number of direction quantization bits is M-1 times the number of channel magnitude quantization bits, where M is the number of base station antennas. The paper also shows that as the target outage probability decreases, more bits should be allocated to magnitude quantization.