# Wireless Energy Harvesting with Cooperative Relaying under the Best Relay Selection Scheme
## 1 Introduction
In contrast, EE has not been recognized by researchers and was not taken into consideration by 3 GPP to indicate its performance until recent times. The continuous promotion of green energy has drawn more attention to energy-efficient transmission. Hence, the trade-off between SE and EE demands a critical study to achieve a balance between the two performance metrics in future wireless systems [13]. Based on the literature review, choosing the EH relay that minimizes the total energy consumption (EC) and then illustrating the SE-EE metric for EH relay in this scenario has not been investigated yet. Therefore, we study SE and EE design in N-EH relay networks. A direct link and the outage probability (OP) are taken into consideration. In this work, an efficient algorithm is derived to achieve individual constraints and minimize the total EC, depending on the objective function. The EE is formulated as an optimization problem with a specific objective function to minimize the total EC under maximum energy constraint and a threshold constraint for SNR. The novelty and technical contribution in this study can be summarized as follows:  
1. Analysis of the outage probability (OP) for AF-EH relaying under best relay selection (BRS) scheme with SWIPT technique, by computing the OP for the direct path and the OP for the best relay path. The EH relay can be more valuable over small areas. Consequently, the proposed system is considered in which the source, relays and destination are located in a small territory. In this case, outage probability will be beneficial due to the restrictions decreed on the relays by the energy constraints. 2. Investigation of the performance of total consumed energy for AF wireless energy harvesting (WEH) relaying under BRS scheme, by minimizing the total EC to improve EE for EH relaying over conventional relaying. 3. Derivation of the energy efficiency (EE) for AF-EH relaying, taking into account the outage probability factor and compare the results with conventional cooperative relaying with a different number of relays. Also, the effect of the power-splitting ratio on the EE is applied and the steady-state convergence is shown for different values of the power-splitting ratio. 4. The SE-EE trade-off is analysed for both conventional and EH relays, with the aim of optimizing the total energy consumption, by illustrating the design of the wireless networks that consider only SE and the design of the wireless networks that consider only EE. The SE-EE metric is useful in the design of required wireless EH networks to quantify the desired SE and EE. The rest of this paper is organized as follows. Section 2 discusses recent previous studies. Section 3 describes the system model in this study. In Section 4, performance analysis for energy harvesting (EH) relaying is presented. Numerical results are presented in Section 5 and conclusions are made in Section 6. Following notations is used in this manuscript: \(\gamma_{m}\) is the SNR thresholds for link adaptation, \(\gamma_{si}\) is instantaneous SNR between \(S\) and \(R_{i}\), \(\gamma_{id}\) is the instantaneous SNR between \(R_{i}\) and \(D\), \(\gamma_{sd}\) is the SNR of the direct path between \(S\) and \(D\), \(\gamma_{bs}\) is the SNR of the best relay selection, \(\gamma_{T}\) is the combined SNR at the \(D\), \(\Gamma^{th}\) is the SNR threshold.