In this letter, a precoding framework in the radio-frequency (RF) domain is developed for the downlink of a multiuser multiple-input single-output underlay cognitive radio (CR) system. Firstly, a low hardware complexity analog multiantenna architecture is proposed for the system's transmitter. The proposed analog architecture is based on a phase-shifting network driven by an variable gain amplifier and has low power consumption since it avoids the use of energy hungry components such as digital-to-analog converters (DACs). Secondly, a novel RF precoder for the design of the transmit signals is developed such that the performance of the CR system is optimized and the constraints related to both the system's architecture and the employed underlay CR paradigm are satisfied. The corresponding nonconvex and difficult optimization problem is formulated and solved via a novel algorithmic solution based on the saddle point method. The convergence of the proposed algorithmic solution is theoretically studied. The proposed approach is shown to be much more energy efficient than existing approaches based on fully digital transceivers.