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We propose and study photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser. By injecting a slave laser with two detuned master lasers at the stable locking states, microwave signals with frequencies corresponding to the frequency spacing of the master lasers can be generated. Without the need for a microwave reference source, the dual-beam optical injection scheme has the advantages of low cost and less system complexity. Moreover, without the limitations of period-doubling bifurcation and Hopf bifurcation, by utilizing the period-one oscillation state with a single-beam injection scheme, the microwave signals generated with the proposed scheme have a much broader tuning range. In this paper, optical and power spectra of the microwave signals generated with the dual-beam optical injection scheme are compared with those generated with the optical mixing, the single-beam injection, and the unlocked dual-beam injection schemes. Generation of tunable microwave signals up to 120 GHz is demonstrated, which is currently limited by the locking range of the slave laser determined by the frequency difference between the Hopf (higher frequency) and the saddle node (lower frequency) bifurcation curves.