In this paper, we report the theoretical and experimental implementation of a photonic mixer for Radio-Over-Fiber (RoF) transmission systems, which incorporates an all-optical 10.87 GHz microwave frequency signal generator based on beating laser frequency with its first order Stimulated Brillouin Scattering (SBS) frequency shift. A 13GHz Radio Frequency (RF) is down-converted to 2.13 GHz Intermediate Frequency (IF) signal. The proposed system configuration represents a cost-effective photonic mixer that can be deployed for up and down conversion around 11 GHz in RoF transmission systems. The optically generated microwave signal of 10.87 GHz has a phase noise of -109 dBc/Hz at 15- MHz offset. The proposed photonic mixer exhibits a Spurious-Free Dynamic Range (SFDR) of 93dB.Hz 2/3. This RoF transmission system configuration deploys dual parallel Gallium Arsenide (GaAs) Mach Zehnder Modulator as a photonic mixer, and a single laser source as a Brillouin pump and as an optical carrier at the same time. To the best of our knowledge, this type of photonic mixers has not been reported in the literature.