  We consider settings in which T multi-antenna transmitters and K
single-antenna receivers concurrently utilize the available communication
resources. Each transmitter sends useful information only to its intended
receivers and can degrade the performance of unintended systems. Here, we
assume the performance measures associated with each receiver are monotonic
with the received power gains. In general, the systems' joint operation is
desired to be Pareto optimal. However, designing Pareto optimal resource
allocation schemes is known to be difficult. In order to reduce the complexity
of achieving efficient operating points, we show that it is sufficient to
consider rank-1 transmit covariance matrices and propose a framework for
determining the efficient beamforming vectors. These beamforming vectors are
thereby also parameterized by T(K-1) real-valued parameters each between zero
and one. The framework is based on analyzing each transmitter's power
gain-region which is composed of all jointly achievable power gains at the
receivers. The efficient beamforming vectors are on a specific boundary section
of the power gain-region, and in certain scenarios it is shown that it is
necessary to perform additional power allocation on the beamforming vectors.
Two examples which include broadcast and multicast data as well as a cognitive
radio application scenario illustrate the results.
