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We theoretically and experimentally demonstrate a novel broadband phase-to-intensity modulation conversion technique for microwave photonics processing system. The technique is based on optical carrier phase shift of a phase modulated signal using stimulated Brillouin scattering. More than 360 ° carrier phase shift can be achieved. By simply adjusting the carrier phase shift while preserving its amplitude unchanged, the phase modulation can be fully or partially converted to intensity modulation. The main advantage of the proposed method lies in its broadband nature since the SBS is only imparted on the optical carrier and the phase modulated sidebands are not affected as long as the modulating frequency is higher than the Brillouin bandwidth. In addition, as a microwave photonics processing application, we demonstrate the dispersion induced power penalty control in radio-over-fiber systems using the proposed technique. Experimental results match well with the theoretical prediction.