  This paper considers broadcast channels with L antennas at the base station
and m single-antenna users, where each user has perfect channel knowledge and
the base station obtains channel information through a finite rate feedback.
The key observation of this paper is that the optimal number of on-users (users
turned on), say s, is a function of signal-to-noise ratio (SNR) and other
system parameters. Towards this observation, we use asymptotic analysis to
guide the design of feedback and transmission strategies. As L, m and the
feedback rates approach infinity linearly, we derive the asymptotic optimal
feedback strategy and a realistic criterion to decide which users should be
turned on. Define the corresponding asymptotic throughput per antenna as the
spatial efficiency. It is a function of the number of on-users s, and
therefore, s should be appropriately chosen. Based on the above asymptotic
results, we also develop a scheme for a system with finite many antennas and
users. Compared with other works where s is presumed constant, our scheme
achieves a significant gain by choosing the appropriate s. Furthermore, our
analysis and scheme is valid for heterogeneous systems where different users
may have different path loss coefficients and feedback rates.
