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Outage probability of power splitting SWIPT twoway relay networks in Nakagamim fading
EURASIP Journal on Wireless Communications and Networking volume 2018, Article number: 11 (2018)
Abstract
This paper investigates the outage probability of an energy harvesting (EH) relayaided cooperative network, where a source node transmits information to its destination node with the help of an energy harvesting cooperative node. For such a system, we derive an explicit closedform expression of outage probability over Nakagamim fading channels for both amplifyandforward (AF) and decodeandforward (DF) relay protocols, and we verify the explicit closedform expressions of outage probability with the Monte Carlo method. It is shown that the simulation results match well with the numerical ones. From the numerical analysis and simulation results, it can be observed that the system parameters have great impact on both AF and DF relay systems. For the DF system, with the increment of the power splitting ratio, the system outage probability decreases, while for the AF system, with the increment of the power splitting ratio, it first increases and then decreases. Besides, for both DF and AF systems, when the relay is placed relatively closer to the source, better outage performance will be achieved.
1 Introduction
Nowadays, Energy harvesting has appeared as a promising approach to prolong lifetime of energy constrained wireless communication system [1–4], which is usually equipped with replacing or recharging batteries. For example, in wireless sensor networks, if a sensor is depleted of energy, it will be out of work. And replacing or recharging energy may be unavailable, especially when a sensor is embedded in building structures or inside human bodies. Earlier, the energy harvesting technologies mostly relied on external and traditional energy sources such as solar, wind, and vibration. However, the application range of the traditional energy harvesting technologies is limited because of the environment uncertainty, weather dependence.
Very recently, simultaneous wireless information and power transfer (SWIPT) has been an exciting new way to provide stale energy to wireless communication where the receiver is able to harvest energy and decode information from the received signals [5–11]. In [5], the authors described the basic idea about the wireless information and power transfer from information theoretical perspective, and in [6], the authors proposed a general receiver architecture with separated information decoding and energy harvesting receiver for SWIPT for practical applications.
Following these pioneering works, plenty of works have been done for various wireless networks, including cooperative relaying network [12–16], power allocation strategies [17–19], resource scheduling [20, 21], and multipleinput multipleout (MIMO) system [22–24] or multipleinput singleoutput (MISO) [25, 26]. In [12], the authors analyzed the system maximal throughput for the time switching and power splitting protocols in AF relaying networks. The authors in [13] investigated the outage performance of the relay network over rayleigh fading channels where both AF and DF protocols were considered. In [14], the authors investigated the relay selection for SWIPT systems. In [17], the authors investigated the multiuser cooperative networks where how to distribute the harvested energy among the multiple users was studied. In [18], the authors discussed two types of power allocation policies for nonorthogonal multiple access (NOMA) system. In [20], the author proposed a greedy clustering algorithms to reduce the hardware cost of the PS scheme. In [22], a nonregenerative MIMO orthogonal frequencydivision multiplexing (OFDM) relaying system was investigated, and the maximal achievable information rates of two protocols, time swithingbased relaying and power splittingbased relaying, were explored. In [23], the authors focused on qualityofserviceconstrained energy efficient optimization in MIMO SWIPT systems via joint antenna selection and spatial switching. In [25] and [26], the secrecy performance of channel uncertainties and imperfect channel state information was studied for multipleinput and multipleoutput SWIPT system.
In this paper, we focus on a twoway relay SWIPT system over Nakagamim fading, which consists of a sourcedestination (SD) pair and a relay node R embedded power splitting (PS) (see Fig. 1). We investigate the effect of SWIPT on the outage probability and the impact of the ambient environment energy harvesting and the RF energy harvesting on the system outage probability. In detail, a closedform expression of outage probability considering AF/DF relaying schemes at node R to decode and forward the received signals to node D is derived.
The contributions are expressed as below: at first, we derive a closedform expressions of outage probability at twoway relay cooperation group for AF and DF relaying schemes with Nakagamim fading channels respectively. Secondly, we simulate the outage probability of twoway relay SWIPT systems with Monte Carlo method; at the same time, we consider the impact of power splitting fraction, the position of the relay node between the source node and destination node, the buffer energy capacity of relay node harvesting from ambient environment, etc. Finally, we give the comparison of system operation time of numerical analysis and Monte Carlo method.
The rest of the paper is organized as follows. Section 2 reports about model of the system. Section 3 presents the outage probability analysis. Section 4 presents our numerical result and validates the analytical result through Monte Carlo simulations. Finally, a conclusion will be drawn in Section 5.
2 System model
In the first section, we assumed a simplest cooperation group including a sourcedestination (SD) pair, and a relay node R. All links experience independent and identically Nakagamim fading. In the first phase, the received signals at the information receiver of R and D in downlink phase are expressed as
where P_{ i }(i∈(S,R)) is the transmit power at node i, x denotes the transmitted symbols from node S, h_{ i j }(i,j∈S,R,D) is the link channel gain between node i and j, n_{ i }(i∈D,R) denotes the independent complex Gaussian noise at the information receiver of node R and Dwith zero means and a same variance, and N_{0} and z_{ R } are the signal processing noise by the information decoder at node R followed by additional white Gaussian noise with zero means and variance σ^{2}.
So, the SNR of the received signal at information receiver of R and Dcan be expressed as
where ρ denotes the ratio of power splitter, α denotes the ratio of the distance of the relay node position departing from the source node S to the distance d between the source node S and the destination node D.
The probability density function (PDF) of h_{ s r }^{2} and h_{ s d }^{2} can be given as
where m_{ s d } and m_{ s r } denote that the Nakagamim fading parameter at the respective hop. Γ(.) stands for the Gamma function [27], and average SNR (\(\bar {\gamma _{sr}} \ and\ \bar {\gamma _{sd}}\)) of received signal at relay and destination [28, 29] can be written as
3 Outage analysis
3.1 DF scheme outage analysis
In this second phase, if R decides to forward the detected symbols, X_{ r }, to D after regenerating, the received signal at D is
where P_{ r }=(1−ρ)P_{ R F }+E_{max}, where P_{ R F } denotes the energy harvested by relay node through RF and E_{max} denotes the natural energy harvested by relay node from ambient environment (e.g., solar energy, wind energy).
Accordingly, the SNR of the received signal at D can be expressed as
The probability density function (PDF) of h_{ r d }^{2} can be given as
where the average SNR of the received signal at destination can be written as
The outage probability of the consider system for the DF scheme can be expressed as
The probability with the SNR of SR link γ_{ s r } can be expressed as
Similarly, the probability with the SNR of SD link γ_{ s d } can be expressed as
The probability with the SNR of the combined signal at D, γ_{ D }, can be expressed as
Therefore, the outage probability can be obtained by substituting (14), (15), and (16) into (13) as
3.2 AF scheme outage analysis
In this second phase, if the node R decides to forward the detected symbols, X_{ r }, to the node D after amplifying, the received signal at node D can be expressed as
where \(G=\frac {\sqrt {P_{r}}}{\sqrt {P_{s}h_{sr}^{2}+N_{0}}}\) is the amplifying factor at R. Therefore, the SNR of the received signal at D can be expressed as
where \(a=\frac {1}{\rho }\), \(b=\frac {N_{0}}{\rho N_{0}+\sigma ^{2}}\), γ_{ s r }=γ_{1}, and γ_{ r d }=γ_{2}. Let \(P_{srd}^{(\text {out})}\) denotes the outage probability of γ_{rd2}, so it can be expressed as
where u=k−l, \(v=\frac {n+l+1}{2}\), w=l−n−1, \(p=\frac {2k+nl+1}{2}\), \(q=\frac {2k+2m_{sr}nl1}{2}\).
Therefore, the outage probability of system can be obtained by substituting (14), (15), and (20) into (13) as
4 Numerical and simulation results
This section studies how the outage probability changes as a function of the system parameters in different situations under both AF and DF schemes. Unless otherwise explicitly specified, the main parameters adopted in our experiments and simulations are set as P_{ S }=P_{ R }=1, σ^{2}=0.01, γ_{ t h }=0dB, ρ=0.5, and E_{h1}=E_{h2}=E_{h3}=1.
In Fig. 2, the outage probability curves under DF schemes are presented where E_{h1}=E_{h2}=1 and ρ={0.1, 0.3, 0.5, 0.7, 0.9}. Clearly, the outage probability for a lower ρ outperforms the one for a higher ρ at the lower E_{h3}/E_{h1} and outperforms on the contrary with the increase of the value of E_{h3}/E_{h1}. This is because a lower ρ means a lower portion of the received signal power split to the ID at R, resulting in a higher received SNR at R, which leads to a higher capacity, but with the increment of E_{h3}/E_{h1}, the relay link channel will be worse, so the outage probability will become greater when the ρ increases at the same value of E_{h3}/E_{h1}. In Fig. 3, the outage probability curves under AF schemes are presented where E_{h1}=E_{h2}=1 and ρ={0.1, 0.3, 0.5, 0.7, 0.9}. We can get that the outage probability for a higher ρ outperforms the one for a lower ρ when ρ is smaller than 0.5 and on the contrary with the increase of the value of ρ. This is because a lower ρ means a lower portion of the received signal power split to the ID at R, resulting in a higher received SNR at R. Yet with the continuous increment of ρ when ρ is greater than 0.5, the outage probability will be larger than the lower ρ system at the same value of E_{h3}/E_{h1}; this is because of the transmission information becoming more and more small. In Fig. 4, the outage probability curves for the disposition of R between the S node and the D node. The best outage probability occurs at 0.3, which is the disposition of the relayaided node R departing from S node. In Fig. 5, the outage probability curves under DF and AF schemes are depicted where the value of E_{max}={0.1, 0.3, 0.5, 0.7, 0.9} and E_{h1}=E_{h3}=1. Obviously, the outage probability for a higher E_{max} outperforms that for a lower E_{max}. That is to say, when the relay node harvests the more energy from ambient environment, the better system performance will be obtained.
In Figs. 6 and 7, the outage probability curves under AF and DF schemes are depicted where E_{h1}=E_{h2} and E_{h1}={1, 2, 3, 4, 5}. We can get that the outage probability for a lower E_{h1} outperforms the one for a higher E_{h1}. Because a lower E_{h1} means a lower probability, the SNR at each receriver falls below the threshold. It can also be observed that outage probability becomes worse when the value of E_{h1}/E_{h3} increases. This is because the increasement of the value of E_{h1}/E_{h3} means the worse of the RD link, resulting in an increasing outage probability over the RD link.
In Figs. 8 and 9, the outage probability curves under DF and AF schemes are depicted where E_{h1}=E_{h3}=1 and γ_{ t h }={0, 1, 2, 3, 4}. It is clearly that the outage probability for a lower γ_{ t h } ourperforms than that for a higher γ_{ t h }. Because a lower γ_{ t h } means a lower probability, the SNR at each receiver falls below the threshold. Further, outage probability becomes worse when the value of E_{h1}/E_{h2} increases, because the increasing value of E_{h1}/E_{h2} means the SD link becoming worse too, resulting in a lower diversity gain at node D.
In Fig. 10, the outage probability curves under DF and AF schemes are depicted where E_{h2}=E_{h3}=1. It is obviously that the outage probability for a higher m outperforms the one for a lower m. It means that the greater m, the more energy the relay node can receive, so the lower the probability of system interruption.
5 Conclusions
In this paper, we presented the outage probability of power splitting SWIPT twoway relay networks in Nakagamim fading. With the help of some approximations, we got the explicit closedform expression of outage probability of cooperative system over Nakagamim fading. And the numerical results proposed by the present work were validated by the Monte Carlo method. From the numerical analysis and simulation results, we found that the system parameters have great impact on both AF and DF relay systems.
6 Method
This paper mainly studies a twoway relay SWIPT system over Nakagamim fading, which consists of a sourcedestination (SD) pair and a relay node R embedded powersplitting (PS). In this wireless network system, we consider the protocols of AF and DF and the power splitting energy receiver. In the part of experimental designment, we analyze the outage probability of the traditional energy harvesting technique, the RF energy harvesting technique, and the outage probability of this kind of relay wireless network under different parameters. At last, we verify the outage probability of the explicit closedform expressions with the Monte Carlo statistical method. From the simulation results, we can observe that the expressions obtained in this paper are correct and effective.
Abbreviations
 α :

The ratio of the distance between the relay node and the source node S to the distance d between the source node S and the destination node D
 γ _{ r d } :

The SNR of the received signal at information receiver of the node D from the node R
 γ _{ s r } :

The SNR of the received signal at information receiver of the node R from the node S
 γ _{ s d } :

The SNR of the received signal at information receiver of the node D from the node S
 γ _{ t h } :

The threshold SNR
 \(\bar {\gamma _{rd}}\) :

The average SNR of received signal at information receiver of the node D from the node R
 \(\bar {\gamma _{sr}}\) :

The average SNR of received signal at information receiver of the node R from the node S
 \(\bar {\gamma _{sd}}\) :

The average SNR of received signal at information receiver of the nodeD from the node S
 ρ :

The ratio of power splitter
 AF:

Amplifyandforward
 d :

The distance of the source node S and the destination node D
 DF:

Decodeandforward
 EH:

Energy harvesting
 E _{h1} :

E(h_{ s r }^{2}), the statistical expectation of h_{ s r }^{2}
 E _{h2} :

E(h_{ s d }^{2}), the statistical expectation of h_{ s d }^{2}
 E _{h3} :

E(h_{ r d }^{2}), the statistical expectation of h_{ r d }^{2}
 E _{max} :

The maximum natural energy harvested by relay node from ambient environment
 h _{ i j } :

The link channel gain between node i and j
 MIMO:

Multipleinput multipleout
 MISO:

Multipleinput singleoutput
 NOMA:

Nonorthogonal multiple access
 P _{ i } :

The transmit power at node i
 P _{ R F } :

The energy harvested by relay node through RF
 PS:

Power splitting
 SWIPT:

Simultaneous wireless information and power transfer
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Acknowledgements
The authors would like to thank the Editor and anonymous reviewers for their helpful comments and suggestions in improving the quality of this paper. This work is supported by National Natural Science Foundation general projects, China (nos. 61672217, 61304208), and the Foundation of the Science and technology project of Hunan Provincial Department of Education (no. 15C1414).
Funding
This paper was supported by the National Natural Science Foundation general projects, China (no. 61672217), by the National Natural Science Foundation general projects, China (no. 61304208), and also by the Foundation of the Science and technology project of Hunan Provincial Department of Education (no. 15C1414).
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SZ has fulfilled all the system modeling, analysis, and simulation and drafted the article. RL has helped revise the manuscript. HH has given critical revision of the article and has helped revise the manuscript. All authors read and approved the final manuscript.
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Zhong, S., Huang, H. & Li, R. Outage probability of power splitting SWIPT twoway relay networks in Nakagamim fading. J Wireless Com Network 2018, 11 (2018). https://doi.org/10.1186/s1363801710060
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DOI: https://doi.org/10.1186/s1363801710060
Keywords
 Energy harvesting
 Nakagamim fading channel
 Outage probability
 Relayaided cooperative networks
 Power splitting