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Transmit beamforming is a powerful means of increasing capacity in systems in which the transmitter is equipped with an antenna array, especially in systems in which receive beamforming is not available, as is typical in the base-to-mobile downlink in a cellular communication system. In this paper, the problem of transmit beamforming is formulated as one of minimizing the power radiated by the base station, subject to satisfying quality of service requirements at the mobiles. For a single cell system, a global minimum is shown to exist, and an iterative algorithm that converges to it is provided. The solution extends to accommodate receive beamforming at the mobiles. It also extends to provide a mechanism for space-time transmit filtering, which exploits the differences between the temporal as well as the spatial channels between the base station and different mobiles. Finally, a system with multiple source-destination pairs (e.g., in an ad hoc network) is considered. An iterative algorithm that outputs a convergent sequence of feasible points with monotonically decreasing costs is provided for this case.
Visotsky et al. (Mon,) studied this question.