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On the downlink of an SDMA mobile radio system, different users who share the same frequency band and time slot have to be spatially separated by beamforming. In this paper we analyze an approach to jointly calculate weights in such a way that all users receive their signal with a given signal-to-noise-and-interference ratio. The computations are based on spatial covariance matrices which describe the user-specific channels averaged over the fast fading. The presented algorithm succeeds in minimizing the array transmit power while spatially separating the users, no matter which rank their spatial covariance matrices have. But since it needs to solve a complex nonlinear constrained optimization problem, several approximations of this algorithm are presented and compared to each other on the basis of array power, complexity, and convergence.
Farsakh et al. (Thu,) studied this question.