A Limited-Feedback Scheduling and Beamforming Scheme for Multi-User Multi-Antenna Systems

This paper proposes an efficient two-stage limited-feedback beamforming and scheduling scheme for multiple-antenna cellular communication systems. The system model includes a base-station with $M$ antennas and a large pool of users with a total feedback rate of $B$ bits per fading block. The feedback process is divided into two stages. In the first stage, the users measure their channel gains from each antenna and feedback the index of the antenna with the highest channel gain along with the gain itself. Based on this information, the base-station schedules $M$ users with the highest channel gains from its $M$ antennas and polls those users for explicit quantization of their vector channels in the second stage. Based on these quantized channels, the base-station then forms zero-forcing beamforming vectors for downlink transmission. This paper presents an approximate analysis for the proposed scheme which is used to optimize the bit allocation between the two feedback stages. It is shown that for a total number of feedback bits $B$, the number of feedback bits assigned to the second stage, $B_2$, should scale as $M(M{-}1)\log(\SNR\times B)$. In particular, the fraction $B_2/B$ behaves as ${\log B}/{B}$ in the asymptotic regime where $B \rightarrow \infty$. Further, the approximate downlink sum rate is shown to scale as $M\log\SNR + M\log\log B$, suggesting that both multiuser multiplexing and multiuser diversity gains are realized. As the numerical results verify, the proposed feedback scheme, in spite of its low complexity, performs very close to the more complicated beamforming and scheduling schemes in the literature and in fact outperforms such schemes in the high-SNR regime.