This paper studies the structure of the channel quantization codebook for multiuser MISO systems with limited channel state information at the base-station. The problem is cast in the form of minimizing the sum power subject to the worst-case SINR constraints over spherical channel uncertainty regions. This paper adopts a zero-forcing approach for beamforming vectors design, and use a robust optimization technique via semidefinite programming (SDP) for power control as the benchmark performance measure. We then present an alternative less complex and practically feasible method for computing the power values and present sufficient conditions on the uncertainty radius so that the resulting sum power remains close to the SDP solution. The proposed conditions guarantee that the interference caused by the channel uncertainties can be effectively controlled. Based on these conditions, we study the structure of the channel quantization codebooks and show that the quantization codebook has a product form that involves spatially uniform quantization of the channel direction, and independent channel magnitude quantization which is uniform in dB scale. The structural insight obtained by our analysis also gives a bit-sharing law for dividing the quantization bits between the two codebooks. We finally show that the total number of quantization bits should increase as log(SINR$_{target}$) as the target SINR increases.
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