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Considering the spectrum sharing system (SSS) coexisting with multipleprimary networks, we have employed a well-designed reconfigurable intelligentsurface (RIS) to control the radio environments of wireless channels andrelieve the scarcity of the spectrum resource in this work. Specifically, theenhancement of the spectral efficiency of the secondary user in the consideredSSS is decomposed into two subproblems which are a second-order coneprogramming (SOCP) and a fractional programming of the convex quadratic form(CQFP), respectively, to optimize alternatively the beamforming vector at thesecondary access point (S-AP) and the reflecting coefficients at the RIS. TheSOCP subproblem is shown as a concave problem, which can be solved optimallyusing standard convex optimization tools. The CQFP subproblem can be solved bya low-complexity method of gradient-based linearization with domain (GLD),providing a sub-optimal solution for fast deployment. Taking the discrete phasecontrol at the RIS into account, a nearest point searching with penalty (NPSP)method is also developed, realizing the discretization of the phase shifts ofthe RIS in practice. The simulation results indicate that both GLD and NPSP canachieve an excellent performance.

Reconfigurable Intelligent Surface-Aided Spectrum Sharing Coexisting with Multiple Primary Networks