Deploying active reflecting elements at the intelligent reflecting surface (IRS) increases signal amplification capability but incurs higher power consumption. Therefore, it remains a challenging and open problem to determine the optimal number of active/passive elements for maximizing energy efficiency (EE). To answer this question, we consider a hybrid active-passive IRS (H-IRS) assisted wireless communication system, where the H-IRS consists of both active and passive reflecting elements.Specifically, we study the optimization of the number of active/passive elements at the H-IRS to maximize EE. To this end, we first derive the closed-form expression for a near-optimal solution under the line-of-sight (LoS) channel case and obtain its optimal solution under the Rayleigh fading channel case. Then, an efficient algorithm is employed to obtain a high-quality sub-optimal solution for the EE maximization under the general Rician channel case. Simulation results demonstrate the effectiveness of the H-IRS for maximizing EE under different Rician factors and IRS locations.

翻译：在智能反射面（IRS）上部署有源反射元件可增强信号放大能力，但会导致更高的功耗。因此，如何确定有源/无源元件的最优数量以最大化能量效率（EE）仍是一个具有挑战性的开放问题。为解答该问题，我们考虑一种由有源和无源反射元件共同构成的混合有源-无源IRS（H-IRS）辅助无线通信系统。具体而言，我们研究了H-IRS中有源/无源元件数量的优化问题以最大化能量效率。为此，我们首先推导了视距（LoS）信道场景下近优解的闭式表达式，并获得了瑞利衰落信道场景下的最优解。随后，采用一种高效算法针对一般莱斯信道场景下的EE最大化问题获取高质量次优解。仿真结果验证了H-IRS在不同莱斯因子和IRS位置下实现EE最大化的有效性。