This paper deals with the problem of phase-only transmit beamforming in spectrum sharing microwave systems. In contrast to sub-6 GHz schemes, general microwave systems require a large number of antennas due to its huge path loss. As a consequence, digital beamforming needs a large number of computational resources compared to analog beamforming, which only needs a single radio-frequency chain, results the less computational demanding solution. Analog schemes are usually composed by a phase shifter network whose elements transmit at a certain fixed power so that the system designer shall compute the phase values for each element given a set of directions. This approach leads to non-convex quadratic problems where the traditional semidefinite relaxation fails to deliver satisfactory outcomes. In order to solve this, we propose a nonsmooth method that behaves well in several scenarios. Numerical evaluations in different spectrum sharing scenarios, which show the performance of our method, are provided.
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