## 1 Introduction  
Nowadays, wireless powered communication networks (WPCNs) have shown significant advantages in industry and living. The major benefits of WPCNs mainly come from battery charging operations through the air without physical cable connections and recharging, and thus, replacing the battery. As such, the maintenance, servicing, and charging of many battery-powered devices deployed in networks are crucially simplified, especially for future applications and technology [1; 2; 3; 4; 5]. Nowadays, there are three primary wireless energy harvesting (EH) and transfer techniques in the two main types of wireless charging--radiative (or RF based) and non-radiative (or coupling based) are employed in practice in WPCNs--which are feasible using the following techniques. In the first method, inductive coupling based on magnetic field induction can be used for transferring electrical energy over distances ranging from a few millimeters to a few centimeters. The efficiency of this method, from around 6% to 90%, is suitable for cell phone charging, contactless smart cards, and passive RFID cards [3; 4]. Magnetic Resonant coupling is the second method, which is based on one vane scent wave coupling by making two separate coils resonate at the same frequency. Its efficiency ranges from 30% to around 90% and is suitable for plug-in hybrid electric vehicles and cell phone charging [3; 4]. The last method is RF energy transfer, which is suitable for wireless body and wireless sensor networks. From this point of view, RF energy transfer WPCNs are suitable for long-distance transfers [1; 2; 3; 4; 5]. Some papers have presented the process of EH through the RF signals in cooperative wireless networks using a MIMO relay system, and have investigated multi-user and multi-hop systems for simultaneous information and power transfer with a dual-hop channel [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. In these previous papers, the authors have focused on WPCNs using only the Rayleigh or the Rician fading channel. However, to date not many papers concentrate on using both different fading channels. Hardware impairment (HI) suffers from phase noise, I/Q imbalance, and high-power amplifier nonlinearities [19; 20; 21; 22]. HI is rarely studied in the literature on relay WPCNs. In a wireless network, the source and destination may not communicate to each other directly, because the distance between the source and destination is greater than the transmission range of them both, hence the need for an intermediate node(s) to relay. Relaying is an effective way to combat the performance degradation caused by fading, shadowing, and path loss. In relay networks, the relay nodes help to boost the information exchange between source nodes and destination nodes, by forwarding (with or without decoding) the information-bearing radio frequency signals from sources to destinations [1; 2; 3; 4; 5]. In this paper, we introduce a half-duplex (HD) energy harvesting (EH) relay network over the different fading environment with the effect of hardware impairment (HI). The model system was investigated with the amplify-and-forward (AF) and the power-splitting (PS) protocols. The system performance analysis, in term of the outage probability (OP), achievable throughput (AT), and the bit error rate (BER), was analyzed and demonstrated with the closed-form expressions. Additionally, the power splitting (PS) factor was investigated. We verified the analytical analysis using a Monte Carlo simulation with all primary parameters. The research results showed that the analytical and simulation results matched well with each other. The main contributions are summarized as follow:  
1. An HD EH relay network over the different fading environment (Rayleigh and Rician Fading Channel) with the HI effect of HI is introduced and investigated. 2. The closed form of OP, AT, and BER of the proposed system was analyzed and derived in connection with the main primary system parameters. 3.