  Multibeam technology enables the use of two or more subbeams for joint
communication and radio sensing, to meet different requirements of beamwidth
and pointing directions. Generating and optimizing multibeam subject to the
requirements is critical and challenging, particularly for systems using analog
arrays. This paper develops optimal solutions to a range of multibeam design
problems, where both communication and sensing are considered. We first study
the optimal combination of two pre-generated subbeams, and their beamforming
vectors, using a combining phase coefficient. Closed-form optimal solutions are
derived to the constrained optimization problems, where the received signal
powers for communication and the beamforming waveforms are alternatively used
as the objective and constraint functions. We also develop global optimization
methods which directly find optimal solutions for a single beamforming vector.
By converting the original intractable complex NP-hard global optimization
problems to real quadratically constrained quadratic programs, near-optimal
solutions are obtained using semidefinite relaxation techniques. Extensive
simulations validate the effectiveness of the proposed constrained multibeam
generation and optimization methods.
