How Many Bits of Feedback is Multiuser Diversity Worth in MIMO Downlink?

The impact of multiuser diversity on MIMO downlink is generally measured in terms of two asymptotic quantities derived from the sum-rate, namely the scaling law of the sum-rate versus the number of users n (for a fixed signal-to-noise ratio, SNR) and the multiplexing gain (i.e., asymptotic growth of the sum-rate versus SNR). Designing optimal strategies with respect to these two criteria requires the availability of channel state information (CSI) at the transmitter, which in turn demands feedback of information from receivers to the transmitter. An open question is: how many bits of feedback are really necessary to achieve optimality of these criteria, i.e., to fully exploit multiuser diversity? In this paper, the optimal scaling law of the sum-rate with respect to n, for fixed SNR, fixed number of transmit antennas M and any number of receiving antennas N (i.e., M log log nN), is proved to be achievable with a deterministic feedback of only one bit per user. The impact of adding feedback bits is also investigated. Furthermore, it is shown that the optimal multiplexing gain of M is guaranteed if the total feedback per cell is proportional to the SNR (in dB). The proofs build on opportunistic beamforming and binary quantization of the signal-to-noise-plus-interference ratio