In this study we seek to maximize the capacity of an intelligent reflecting surface (IRS)-Assisted wireless system by simultaneously optimizing the transmit beamforming at the base station and the reflecting beamforming at the IRS. However, unlike traditional regular IRS-Assisted wireless systems, in this study only a limited number of IRS elements are selected from an enlarged regular IRS structure to improve the capacity while reducing IRS power consumption. The original reflecting beamforming design problem thus requires the joint optimization of the IRS element selection and the coefficients of the selected IRS elements, which is non-convex. A known solution suffers from high time and computational complexities. We address these issues first by reformulating the joint IRS element selection and the reflecting beamforming design problem as a new equivalent reflecting beamforming design problem, where the IRS element selection mechanism is embedded into the coefficient of each IRS element. We then propose a probability-learning algorithm to solve the proposed equivalent reflecting beamforming design problem. Simulation results reveal that the proposed algorithm outperforms state-of-The-Art algorithms at significantly lower complexity.
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