  In this paper, we propose a multi-input multi-output beamforming transmit
optimization model for joint radar sensing and multi-user communications, where
the design of the beamformers is formulated as an optimization problem whose
objective is a weighted combination of the sum rate and the Cram\'{e}r-Rao
bound, subject to the transmit power budget constraint. Obtaining a global
solution for the formulated problem is a challenging task, because the sum rate
maximization problem itself (even without considering the sensing metric) is
known to be NP-hard. In this paper, we propose an efficient global
branch-and-bound algorithm for solving the formulated problem based on the
McCormick envelope relaxation and the semidefinite relaxation technique. The
proposed algorithm is guaranteed to find the global solution for the considered
problem, and thus serves as an important benchmark for performance evaluation
of the existing local or suboptimal algorithms for solving the same problem.
