# Energy Harvesting over Rician Fading Channel:
## 1 Introduction
In fact, not only the papers we mentioned about SWIPT for WSN, but most of the other results on outage performance up to now ([PERSON] et al., 2018; [PERSON] et al., 2018) also focus on Rayleigh fading channels, where we can exploit the fact that the square of channel gain magnitude is exponentially distributed. As a general comment, it is noted that very few publications about energy harvesting for Rician fading channel exist in the open technical literature. In fact, together with Rayleigh channel, Rician channel should be also considered as one of the small-scale fading models for WSNs, especially for the cases of relatively short range power transfer distance and with existence of a strong line-of-sight (LOS) path ([PERSON] et al., 2018). Recently, [PERSON] et al. [PERSON] et al. (2018) have derived the capacity expressions for wireless powered communication systems over a Rician fading channel. However, there is no relay in this study. The source directly harvests the energy from the power beacon. In [PERSON] et al. (2018), the authors provided the throughput analysis of relay networks with two energy harvesting protocols (continuous and discrete) over a Rician fading channel, but were only limited in the case of perfect hardware. Furthermore, the paper only provided the integral form of the throughput for the continuous case, so it is not a computationally friendly result. [PERSON] et al. [PERSON] et al. (2018) did provide impressive results on joint optimization of power allocation, power splitting for EH, and relay placement for SWIPT over a Rician channel. Nevertheless, they only use an approximation expression of outage probability to formulate the optimization problem, and did not consider the hardware impairment at the nodes. In practice, the transceiver hardware is imperfect due to phase noise, I/Q (In-phase/Quadrature) imbalance and amplifier nonlinearities ([PERSON] et al., 2018). The modeling of hardware impairment in system performance analysis has been presented in many works, for instance, in [PERSON] et al. (2018), where the authors analyzed the performance of dual-hop relaying systems in hardware impairment condition, in terms of the capacity, throughput and symbol error rate (SER). We also proposed and evaluated an energy harvesting-based spectrum access model in cognitive radio network with hardware impairment ([PERSON] et al., 2018). Again, these works about hardware impairment considered the Rayleigh channels only. In our current work, we tackle the problem of investigating the performance analysis of SWIPT for WSN over a Rician fading channel, which takes into account the hardware impairment at source and relay nodes. Specifically, we consider an AF two-way half-duplex energy harvesting relay network model suffering from hardware impairments at all nodes over the Rician fading channels. The exact analytical expressions of the achievable throughput, outage probability, and the exact-form expression for the PDF of SNR at each destination node of a half-duplex AF bidirectional wireless sensor networks over a Rician fading channel are derived rigorously. The main contributions of this paper can be described in more details as follows:  
* The exact form expression of outage probability and achievable throughput at each destination node with imperfect hardware and in Rician fading environment are derived mathematically. * We derive the exact-form cumulative distribution function (CDF) of the SNR at each destination node, and use this result to derive the integral exact-form of the SER at destination nodes. * We also conduct the asymptotic analysis and provide the approximation of all performance factors mentioned above at high \(P/N_{0}\) regime. * The analytical results are all confirmed by Monte Carlo simulations. Using the simulation results, the effect of various system parameters on the system performance is carefully studied. The rest of this paper is organized as follows. Section 2 describes the system model and the EH protocol that is used in this paper.