# Hybrid Active-Passive Reconfigurable Intelligent Surface for Cooperative Transmission Systems
## 1 Introduction
Moreover, these passive REs are still limited by the power budget, which hinders the existing capability of passive RIS [21]. To mitigate the \"multiplicative fading\" effect, in [19], the notion of active RIS (A-RIS) is put forward, whereby it not only adjusts the phase of the incident signal, but also amplifies the incident signal to normal levels, as opposed to passive RIS. Additionally, active RIS still benefits from passive RIS's advantages without the requirement for complicated and power-hungry RF chain components. When the total number of REs was low, the author of [7] observed that active RIS performed better than passive RIS when comparing the two under an identical power limitation. Ref. [20] revealed that in MIMO systems, comparatively speaking, active RIS could reach up to 67% sum-rate gain compared with passive RIS, while passive RIS was capable of only a meager 3% sum-rate gain, which was almost negligible. Ref. [22] studied the position of active RIS in wireless systems, and revealed that moving active RIS closer to the receiver was a good idea. The security performance of the active RIS-assisted wireless communication system was discussed in [23], where the authors found that the dependability of the signal transmission and the secrecy outage probability (SOP) could both be considerably increased by using active RIS. Notwithstanding the fact that active RIS performs better than passive RIS in particular, every active RE enhances the incident signal through a power amplifier, resulting in greater power consumption. Based on existing research, we are aware that improving the system's performance will result from adding more REs to RIS, but when there are too many active RIS elements, it will lead to a high power consumption, which is contrary to our original intention of using RIS. In [24], the concept of an active RIS sub-connected architecture was proposed, where multiple REs control the phase shifts independently, but share the same power amplifier. Although this architecture is more energy efficient compared with controlling each RE with a single amplifier, each sub-connected architecture still requires 256 REs to achieve optimal energy efficiency (EE). Recently, a decode-and-forward-scheme-based hybrid RIS was investigated in [25], which greatly increased the complexity of the RIS system. With the aim of making active RIS require a small amount of REs to reach the desired SNR at the receiver, a new model of wireless communication system, the hybrid active-passive RIS (HAPR) collaborative transmission system, is proposed in this paper. It is envisioned that each RE of the RIS are, at the same time, supported by a passive load impedance (positive resistor) and an active load impedance (negative resistor), which are independent of each other and have their own switches to control the operation. Depending on the wireless communication environment, each RE chooses whether to operate with active load impedance support or with passive load impedance support. HAPR combines the advantages of A-RIS and P-RIS to significantly reduce the number of REs while meeting established communication requirements. The information that follows is a list of this paper's main contributions:  
* Firstly, we introduce HAPR into a wireless communication system to assist the transmission. In this model, we identify the value of the amplification factor that maximizes the SNR of the receiver. * Secondly, we study the OP of HAPR and obtain the close-form approximation expression by utilizing the compound Simpson formula. In addition, the expressions of active RIS and passive RIS are calculated and compared with the above expressions. * Finally, we verify the correctness of our derived formulations by Monte Carlo simulation and further analyze the simulation results. Numerical results reveal that our proposed HAPR system outperforms the conventional passive and active RIS systems mentioned above and requires fewer REs to achieve the target OP than the two conventional schemes. Notations: Lowercase letters indicate scalar quantities.