  This paper considers broadcast channels with L antennas at the base station
and m single-antenna users, where L and m are typically of the same order. We
assume that only partial channel state information is available at the base
station through a finite rate feedback. Our key observation is that the optimal
number of on-users (users turned on), say s, is a function of signal-to-noise
ratio (SNR) and feedback rate. In support of this, an asymptotic analysis is
employed where L, m and the feedback rate approach infinity linearly. We derive
the asymptotic optimal feedback strategy as well as a realistic criterion to
decide which users should be turned on. The corresponding asymptotic throughput
per antenna, which we define as the spatial efficiency, turns out to be a
function of the number of on-users s, and therefore s must be chosen
appropriately. Based on the asymptotics, a scheme is developed for systems with
finite many antennas and users. Compared with other studies in which s is
presumed constant, our scheme achieves a significant gain. Furthermore, our
analysis and scheme are valid for heterogeneous systems where different users
may have different path loss coefficients and feedback rates.
