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)中部署有源反射单元可增强信号放大能力，但会带来更高的功耗。因此，确定有源/无源单元的最优数量以实现能效(EE)最大化仍是具有挑战性的开放问题。为回答该问题，本文考虑了一种由有源和无源反射单元共同构成的混合有源-无源智能反射面(H-IRS)辅助无线通信系统。具体而言，我们研究了H-IRS中有源/无源单元数量的优化以实现能效最大化。为此，我们首先在视距(LoS)信道场景下推导出近优解的闭式表达式，并在瑞利衰落信道场景下获得其最优解。随后，针对一般莱斯信道场景下的能效最大化问题，采用高效算法获得高质量次优解。仿真结果验证了H-IRS在不同莱斯因子及IRS位置下实现能效最大化的有效性。