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.
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