High resolution channel quantization rules for multiuser spatial multiplexing systems

This paper addresses the optimal channel quantization codebook design for limited feedback multiple-antenna multiuser channels. The base station is equipped with M antennas and serves M single-antenna users, which share a total feedback rate B. We assume real space channels for convenience; the extension of the analysis to complex space is straightforward. The codebook optimization problem is cast in form of minimizing the average downlink transmission power subject to the users' outage probability constraints. This paper adopts a product codebook structure for channel quantization comprising a uniform (in dB) channel magnitude quantization codebook and a spatially uniform channel direction quantization codebook. We first formulate a robust power control problem that minimizes the sum power subject to the worst-case SINR constraints over the channel quantization regions. By using an upper bound solution to this problem, we then optimize the quantization codebooks given the target outage probabilities and the target SINR's. In the asymptotic regime of B → ∞, the optimal number of channel direction quantization bits is shown to be M-1 times the number of channel magnitude quantization bits. It is further 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 of the feedback rate. The paper also shows that, for the target parameters to be feasible, the total feedback bandwidth should scale logarithmically with γ̄, the geometric mean of the target SINR values, and 1/q̄, the geometric mean of the inverse target outage probabilities. Moreover, the minimum required feedback rate increases if the users' target parameters deviate from the average parameters γ̄ and q̄. Finally, we show that, as B increases, the multiuser system performance approaches the performance of the perfect channel state information system as 1 over q̄ times 2 raise to minus B over M raise to 2.