Multiuser diversity for the multiple antenna broadcast channel with linear receivers: asymptotic analysis

Opportunistic scheduling based on channel state information at the transmitter can provide significant performance gains for transmission over broadcast channels by exploiting the independence of fading realizations across the user population. For a multiple antenna broadcast channel this opportunism (commonly termed multiuser diversity) takes the form of selecting either a single "best" user (opportunistic time-sharing) or a collection of users whose channels jointly maximize the sum of allocated rates during every transmission (multiuser multiplexing). In this paper, we analytically characterize the capacity gain achieved by opportunistic schedulers with both single-user and multiuser multiplexing. We characterize capacity gain with both optimal receivers and the more practical linear receivers. We investigate the effect of multiuser diversity on the performance of linear receivers. Asymptotically in size of the user population, we prove that (i) capacity with the suboptimal linear receiver scales identically compared with optimal signaling, (ii) capacity with multiuser linear receivers scales identically compared with the capacity of the multiple antenna broadcast channel achieved by "dirty-paper" coding. Both these capacity scaling laws in (i) and (ii) exhibit a log log N dependence on size of the user population, N.