Amplitude-Dependent Phase-Gradient Directional Beamforming for IRS: A Scalable Optimization Framework

Intelligent reflecting surface (IRS) usually consists of a large number of passive elements, for which the element-grouping strategies can be adopted to group adjacent elements into a sub-surface for lower computational complexity. For the grouped elements of a sub-surface, the linear gradient phase shift configuration can achieve directional IRS reflect beam towards the intended receiver. In this paper, we propose a practical scalable optimization framework for element-grouping IRS by adopting the amplitude-dependent phase-gradient directional beamforming, which induces a new amplitude-phase coupling to the reflected signal. Specifically, by deriving the phase-gradient condition from Fermat’s principle, we propose a practical phase-gradient IRS reflection model. Under this practical model, the amplitude-phase coupling becomes complicated, which brings technical challenges to the IRS beamforming optimization. We study a joint transmit and reflect beamforming optimization problem to minimize the transmit power. By designing a trigonometric transformation to deal with the complicated amplitude-phase coupling, we propose a penalty-based phase control strategy under given element grouping. Subsequently, to solve the element-grouping combinatorial problem with performance guarantee, we propose a low-complexity IRS reflect beamforming algorithm based on Markov approximation. Simulation results demonstrate that the proposed algorithm achieves substantial performance gains compared to conventional schemes.