How Many Users should be Turned On in a Multi-Antenna Broadcast Channel

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.