Nonlinear energy‐harvesting relaying with beamforming and hardware impairments in κ−μ shadowed fading environment

Abstract

In this paper, the energy harvesting in a decode‐and‐forward (DF) relaying system with beamforming and hardware impairments that is based on a realistic nonlinear model is studied under κ−μ shadowed fading environments. This study was undertaken in consideration of a source and a destination that are equipped with multiple antennas and communication that occurs through a single‐antenna energy‐constrained DF relay. At the relay node, a nonlinear energy harvester is assumed, which limits the level of the harvested power with a saturation threshold. Here, a power‐splitting‐based relaying protocol is considered, whereby new and exact analytical expressions are derived for the outage probability and throughput under κ−μ shadowed fading, accounting for hardware impairments at all nodes. The κ−μ shadowed fading model is capable of modeling the different kinds of empirical wireless channels that undergo either shadowing or fading and fading and shadowing simultaneously, including the particular cases of the κ−μ, Rician shadowed, Rician, Nakagami‐ truem^, and Rayleigh fading channels. The authors analyze the system performance for different system parameters such as the power splitting ratio, number of antennas, hardware impairments, saturation threshold power, and fading and shadowing parameters. These results are then generalized and can easily be reduced for an ideal hardware and linear energy‐harvesting relaying, and for a number of particular cases including the Rayleigh/Rayleigh, Nakagami‐ truem^/Nakagami‐ truem^, Rician/Rician, Rician shadowed/Rician shadowed, and mixed κ−μ shadowed, κ−μ, Rician shadowed, Rician, Nakagami‐ truem^, and Rayleigh fading channels. The results of this study are helpful in terms of the analysis of the performance of the energy‐harvesting DF relay network under a variety of environments for which the fading and the shadowing arise jointly and separately.

Non-Linear Energy Harvesting Dual-hop DF Relaying System over n-µ Fading Channels

“…where w 1 = h1 ||h1|| [7], and P s and x are the source transmit power and the normalized source information signal, respectively. Further, at the relay antenna, n a,r ∼ CN (0, σ 2 a,r ) is the additive white Gaussian noise (AWGN).…”

“…Integrating a dual-hop relaying system with wireless energy harvesting techniques can enhance the coverage capacity and network life-time [2], [3]. In a dual-hop wireless energy harvesting relaying network, the relay is an energy constrained device which harvests the energy through RF signals [4].…”

“…One of the well-known relaying methods is a decode-andforward (DF) relaying, in which relay decodes and sends the information to the destination [2]- [4]. Several authors have investigated the wireless energy harvesting in a DF relaying system [2]- [5], [7]- [13] (and references therein).…”

“…In the works [2]- [4] (and their references), for the dualhop energy harvesting DF relaying networks, a linear energy harvesting receiver was assumed. But, in reality, an energy harvesting circuit is non-linear owing to the non-linearity of the electronic components, i.e., inductors, capacitors, and diodes [7]. Therefore, a non-linear energy harvesting receiver is not a practical node and restrict the level of the harvested power.…”

“…Therefore, a non-linear energy harvesting receiver is not a practical node and restrict the level of the harvested power. The performance of DF energy harvesting relaying systems with a non-linear energy harvesting receiver was studied over conventional fading channels [7]- [13] and general κ − µ shadowed fading channels [7].…”