Asymptotic analysis of reduced-feedback strategies for MIMO Gaussian broadcast channels

Achieving the sum-capacity of a multiple-input-multiple- output (MIMO) Gaussian broadcast channel is known to require full channel state information (CSI) at the base station, which implies the need of a large amount of feedback information from the users. Different asymptotics of the sum-capacity, such as its scaling law with respect to the number of users n or the multiplexing gain, are conventionally used to assess the performance of suboptimal schemes with reduced feedback, or equivalently with partial channel state information at the transmitter. In this correspondence, the optimal scaling law of the sum-rate with respect to n, for fixed signal-to-noise ratio (SNR), fixed number of transmit antennas M and any number of receiving antennas N (i.e., M log log n N), is proved to be achievable with a deterministic feedback of only one bit per user. Moreover, the amount of feedback is shown to be further reduced with no asymptotic optimality loss by applying the selective feedback principle, leading to an average feedback rate that scales as log n. Finally, the asymptotic performance with respect to SNR is studied, by assessing how fast the number of users needs to increase with the SNR in order to guarantee a noninterference limited behavior.