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This paper addresses the optimal design of limited-feedback downlinkmulti-user spatial multiplexing systems. A multiple-antenna base-station isassumed to serve multiple single-antenna users, who quantize and feed backtheir channel state information (CSI) through a shared rate-limited feedbackchannel. The optimization problem is cast in the form of minimizing the averagetransmission power at the base-station subject to users' targetsignal-to-interference-plus-noise ratios (SINR) and outage probabilityconstraints. The goal is to derive the feedback bit allocations among the usersand the corresponding channel magnitude and direction quantization codebooks ina high-resolution quantization regime. Toward this end, this paper develops anoptimization framework using approximate analytical closed-form solutions, theaccuracy of which is then verified by numerical results. The results show that,for channels in the real space, the number of channel direction quantizationbits should be $(M-1)$ times the number of channel magnitude quantization bits,where $M$ is the number of base-station antennas. Moreover, users with higherrequested quality-of-service (QoS), i.e. lower target outage probabilities, andhigher requested downlink rates, i.e. higher target SINR's, should use largershares of the feedback rate. It is also shown that, for the target QoSparameters to be feasible, the total feedback bandwidth should scalelogarithmically with the geometric mean of the target SINR values and thegeometric mean of the inverse target outage probabilities. In particular, theminimum required feedback rate is shown to increase if the users' targetparameters deviate from the corresponding geometric means. Finally, the papershows that, as the total number of feedback bits $B$ increases, the performanceof the limited-feedback system approaches the perfect-CSI system as${2^{-{B}/{M^2}}}$.

Bit Allocation Laws for Multi-Antenna Channel Feedback Quantization: Multi-User Case