A Simple Channel-Covariance Based SINR Union Bound for the Multi-users in Downlink Beamforming

In downlink beam forming, an exist feasible region is of great importance before we search the optimum object value and the correspond beam former. However, there does not always exist a feasible region among the constraints. In this paper, all the users' target signal-to-interference plus noise (SINR) are investigated based on channel covariance matrices. An crucial and simple conclusion on the constrains of users' balance SINR bound is drawn using the Rayleigh-Ritz Theorem. Another two corollaries are derived to present the trade off relationship among the users' maximum target SINR and the reason why increasing the transmit power could not raise the users' maximum target SINR infinitely. Simulation shows that our conclusions fit the model very well.