Limited Feedback Multi-Antenna Quantization Codebook Design-Part I: Single-User Channels

In this two-part paper, we study the design and optimization of limited feedback single-user and multiuser systems with a multiple-antenna base station and single-antenna users. The design problem is cast in form of minimizing the average transmission power at the base station subject to the outage probability constraints at the users’ side. The optimization is over the users’ channel quantization codebooks and the transmission power control function at the base station. Our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem. The first part of the paper addresses the single-user system and the second part studies the multiuser case. For the single-user case, we start by showing that uniformly quantizing the channel magnitude in dB scale is asymptotically optimal, regardless of the magnitude distribution function. We derive the optimal uniform (in dB) channel magnitude codebook and combine it with a spatially uniform channel direction codebook to achieve a product channel quantization codebook. We then optimize such a product structure in the asymptotic regime of B → ∞, where B is the total number of quantization feedback bits. The paper shows that for channels in the real space, the asymptotically optimal number of direction quantization bits should be (M−1)/2 times the number of magnitude quantization bits, where M is the number of base station antennas. We also show that the designed system approaches the performance of the perfect channel state information system as 2− 2B M+1 .