On the Solution to a Class of Multi-Functional Beamforming Problems

Many emerging wireless applications require the simultaneous execution of multiple functions, such as information transmission and reception, or communication and sensing. This has driven the study of different means to optimize performance tradeoffs. Among these, the design of multi-functional beamformers often involves nonconvex quadratically constrained quadratic programs (QCQPs), which are commonly approached via semidefinite relaxation (SDR). Two well-known issues affecting the SDR approach are its tightness and the ability to extract a QCQP-feasible solution from the SDR solution. In this context, we identify a sufficient condition for strong duality of a class of nonconvex QCQPs, in which case the exact optimal solution can be readily obtained. The applicability of the proposed framework to the design of multi-functional beamformers is illustrated.