Limited Feedback Multi-Antenna Quantization Codebook Design-Part II: Multiuser Channels

This is the second part of a two-part paper on optimal design of limited feedback single-user and multius er spatial multiplexing systems. The first part of the paper studies the single-user system and this part addresses the multiuse r case. The 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 power control function at the base station as well as the users’ channel quantization codebooks. The base statio n has M antennas and servesM single-antenna users, which share a common feedback link with a total rate ofB bits per fading block. We first fix the quantization codebooks and study the optimal power control problem which leads to an upper bound for the average transmission sum power. The upper bound solution is then used to optimize the quantization codebooks and to deri ve the optimal bit allocation laws in the asymptotic regime of B → ∞. The paper shows that for channels in the real space, the optimal number of channel direction quantization bits should be M − 1 times the number of channel magnitude quantization bits. It is shown that the users with higher requested QoS (lower target outage probabilities) and higher requested downlink rates (higher target SINR’s) should receive larger shares o f the feedback rate. The paper further shows that, for the target QoS parameters to be feasible, the total feedback bandwidth sho uld scale logarithmically with γ̄, the geometric mean of the target SINR values, and1/q̄, the geometric mean of the inverse target outage probabilities. Moreover, the minimum required feedback rate increases if the users’ target parameters deviate fromthe average parameters̄γ and q̄. Finally, we show that, asB increases, the multiuser system performance approaches the performan ce of the perfect channel state information system as1/q̄ · 2− B M2 .