Abstract: To compensate for the severe pathloss in satellite broadcasting system, the phased array with a half wavelength aperture is the conventional scheme. However, it is difficult to further scale up the phased array to provide high data rate communication. The reconfigurable holographic surface (RHS) with continuous or quasi-continuous aperture is a promising alternative to phased array for satellite communications. Unlike the amplitude ratio controlled RHS, the amplitude-controlled RHS is firstly modelled in the satellite broadcasting system. To reduce the computational complexity of the RHS sum rate maximization problem, the unrolled gradient projection (GP) method is proposed. The simulation results show that the RHS scheme has larger sum rate than the phased array method, and the unrolled GP method for RHS is faster than the phased array method.