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Throughput analysis of two-way relay networks with wireless energy harvesting capabilities
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Throughput analysis of two-way relay networks with wireless energy harvesting capabilities Syed Tariq Shah a, Kae Won Choi a, Syed Faraz Hasan b, Min Young Chung a,∗ a b
College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea School of Engineering and Advanced Technology, Massey University, Palmerston North, 4442, New Zealand
a r t i c l e
i n f o
Article history: Received 21 January 2016 Revised 23 September 2016 Accepted 28 September 2016 Available online xxx Keywords: RF energy harvesting Cooperative communication Two-way relay
a b s t r a c t Wireless energy harvesting is an efficient way to prolong the lifetime of energy constrained networks. This paper considers a two-way amplify-and-forward (AF) based relay network, where two communicating nodes concurrently transmit their information signals to a relay node. The relay node is energy constrained, and it therefore first harvests energy from the received radio frequency (RF) signals. For energy harvesting at a relay node, we have analyzed the performance of two energy harvesting protocols: the time switching based relaying protocol (TSR), and the hybrid power-time switching based relaying protocol (HPTSR). Once the energy is harvested using one of these protocols, the relay then amplifies and forwards the received information signal towards its destination. We derive analytical expressions for the outage probability and achievable throughput for the aforementioned protocols. Our numerical results verify the analytical derivation, and show the effect of different system parameters on achievable throughput. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In recent years, energy harvesting through radio frequency (RF) signals has gained significant attention from research society and industry. The idea is to prolong the wireless network lifetime through energy harvesting, instead of recharging through conventional methods, or replacing the batteries of low power nodes [1]. Other energy harvesting methods, such as solar, wind, vibration, and thermoelectric effects, can also be used to recharge these nodes [2,3]. However, these conventional techniques are unreliable since the amount of harvested energy can be highly variable [4]. The main advantage of energy harvesting through RF signals over other conventional methods lies in the fact that radio frequency signals can carry information and energy at the same time [5]. Therefore, these low power nodes simultaneously procure energy and process the received information [6–10]. This ability to harvest energy is particularly useful in powering up millions of devices in the emerging Internet of Things (IoT) era. Ever since the advent of IoT, wireless cooperative networks have gained significant research interest. As the name suggests, in a typical cooperative network, information is delivered from source to destination with the help of intermediate relay nodes. ∗
Corresponding author. Fax: +82312907684. E-mail addresses: [email protected] (S.T. Shah), [email protected] (K.W. Choi), [email protected] (S.F. Hasan), [email protected] (M.Y. Chung).
Relays improve the coverage, capacity and quality of service (QoS) of the network by dividing an imperfect communication channel (source-destination) into two appropriate communication paths (i.e. source-relay, and relay-destination) [11]. Recent state-ofthe-art advances in cooperative networks have paved the way for wireless energy cooperation between these nodes. 1.1. Background The idea to transmit both energy and information simultaneously was first proposed in [6], in which the author characterizes the fundamental trade-off for capacity-energy function under the assumption of an ideal energy harvesting receiver. Varshney in [6] first proposed the idea of simultaneously transmitting both energy and information, characterizing the fundamental trade-off for capacity-energy function under the assumption of an ideal energy harvesting receiver. Since it is impractical to design an ideal energy harvesting receiver, Zhou et al. in [8] have proposed two practical approaches. The first approach is based on time-switching (TS) technique, where the total time is divided into two intervals. The first time interval is used for energy harvesting, and the remaining time is used for information processing. The second approach is based on a power-splitting (PS) mechanism, where a PS receiver splits the received signal into two parts, based on the PS ratio. One part of the received signal is used for energy harvesting and the other part is used for information processing. Based on
http://dx.doi.org/10.1016/j.adhoc.2016.09.024 1570-8705/© 2016 Elsevier B.V. All rights reserved.
Please cite this article as: S.T. Shah et al., Throughput analysis of two-way relay networks with wireless energy harvesting capabilities, Ad Hoc Networks (2016), http://dx.doi.org/10.1016/j.adhoc.2016.09.024
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TS and PS energy harvesting receivers [8], the authors in [5] have proposed two relaying protocols namely, time switching-based relaying protocol (TSR), and power splitting-based relaying protocol (PSR). The authors in [5] have considered an amplify-and-forward (AF) relay based one-way communication network. The conclusion is that at low signal-to-noise-ratio (SNR) and high transmission rate, the TSR protocol outperforms the PSR protocol. On the other hand, at low transmission rate, the PSR protocol outperforms the TSR protocol. A combined time power switching based relaying protocol in a one-way cooperative communication network has been studied in [12]. In [13], the authors have considered a twohop communication network with energy-harvesting rechargeable nodes that exploit source-relay cooperation. According to [13], the relay assists the source node by forwarding the data to the destination; in return, the source transfers a portion of its energy to the relay. Krikidis et al. in [14], have studied the energy transfer concept in an energy harvesting based cooperative AF relay network. The performance of a greedy switching policy was investigated at relay node. According to the greedy switching policy, the relay node only transmits when its remaining energy ensures decoding at the destination. In [15], the authors have studied the power allocation strategies and outage performance under energy harvesting constraints for decode-and-forward (DF) relaying. Because of the distinct features of the two relaying protocols, the throughput analysis of AF and DF relaying networks is different under energy harvesting constraints [16]. A denoise-and-forward (DNF) based two-way relay network with non-coherent differential binary phase-shift keying modulation has been studied in [17]. An energy harvesting and information processing network based on two-way multiplicative relay using PSR protocol is studies in [18]. Their numerical results show that the proposed scheme outperforms the legacy amplify-and-forward EH relaying technique. The information and power transfer in TS based and PS based two-way AF relaying network have been studied in [19] and [20], respectively. In [19] we have only analyzed the impact of TSR protocol at high transmission rates and our results show that at high transmission rates the TSR protocol outperforms the PS based two-way AF relaying protocol proposed in [20]. This paper is an extension of [19] and in addition to TSR protocol, this article additionally studies the impact of hybrid powertime switching relay protocol (HPTSR) in two-way energy harvesting based AF relaying networks.
1.2. Paper objectives and contribution In a typical two-way relaying network, two source nodes exchange data via an energy constrained relay node. In this paper, we analyze the system performance of such a network given the energy harvesting constraints. To the best of our knowledge, this is the first effort to investigate the impact of HPTSR [12] and TSR protocols in a two-way AF relay network. In this paper, we consider a scenario in which two nodes, A and B, exchange data via the energy constrained relay node R. Secondly, we derive analytical expressions for the outage probability and achievable throughput at both the nodes for TSR and HPTSR protocols. We show that at low SNR and high transmission rate, both HPTSR- and TSR-based two-way relaying outperforms the PSR-based two-way relay network proposed in [20]. The rest of the paper is organized as follows. Section 2 presents the considered system model. Section 3 explains the energy harvesting and information processing procedures using TSR and HPTSR protocols. Section 4 derives analytical expressions for outage probability and achievable throughput. Section 5 then provides the numerical results, while Section 6 concludes the paper.
d1, g1 Node A
AF Relay R
d2, g2 Node B
Step 1: Source Nodes to Relay. Step 2: Relay to Destination Nodes. Fig. 1. System model of a two-way information processing and energy harvesting AF relay network.
2. System model 2.1. Architecture We consider a cooperative communication network that consists of two nodes A and B and a relay node R. The pair of nodes that transmit and receive data are node A and node B. We assume that there is no direct link between node A and node B, and the signal-to-noise ratio (SNR) between them is less than the minimum required threshold for effective communication. Therefore, the intermediate relay node R assists communication between the nodes [21]. Moreover, the relay node is assumed to be an energy constrained node, which first harvests the energy from received signals and then utilizes the harvested energy to amplify and forward the received signals to their destinations. Fig. 1 shows the basic architecture of the considered network, in which d1 , g1 , d2 , and g2 represent the distance and channel gain between node A and relay node R, and the distance and channel gain between node B and relay node R, respectively. The channel gains are assumed to be quasi-static block-fading channels, and the channel state is constant over a transmission block time T. It is also assumed that they are independent and identically distributed in each time block following a Rayleigh distribution. The path loss model considered in this paper is a distance dependent path-loss model such that d−a , where d is the propagation distance, and a is the path-loss exponent. 2.2. Information processing and energy harvesting The entire information transfer and energy harvesting procedure is divided into two major steps. In Step 1, node A and node B transmit their information signals to relay node R. In Step 2, after harvesting energy from the received signals, relay node R amplifies and forwards the information signal to their respective destinations. The transmit powers ps of node A and node B are assumed to be equal and constant. It is also assumed that the processing power required at the transceivers circuitry of relay node R is negligibly small, compared to its transmission power [3,8]. It is also assumed that at the beginning of transmission, the destination node can estimate the channel state information from the pilot signals sent over dual-hop link, and that the overhead due to pilot transmission is negligible. These assumptions are in line with previous research work conducted in this field [8,10,22–25]. 3. Energy harvesting and information processing In this section, we detail the procedure of energy harvesting and information processing in a two-way relay network. We also derive the SNR expressions for TSR and HPTSR protocols. 3.1. The TSR protocol According to TSR protocol the transmission time block is divided into two main parts, α T and (1 − α )T [5], as shown in Fig 2. During the time block α T (where 0 ≤ α ≤ 1), the relay node harvests energy from the received RF signals [8]. The second block
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3
Fig. 3. Transmission time-block structure for HPTSR protocol. Fig. 2. Transmission time-block structure for TSR protocol.
signal at node A becomes
√
time duration (1 − α )T is further divided into two equal halves, such that in first half (1 − α )T/2, node A and node B transmit their information signals to the relay. During the second half (1 − α )T/2, the relay node broadcasts the processed information signal. The received signal at the relay node can be expressed as:
ps g1 iA (t ) + d1a
yR (t ) =
ps g2 iB (t ) + naR (t ), d2a
yA [k] =
=
η p | g |2 s 1 d1a
+
η ps | g2 |2 d2a
γAT SR =
√ y˜A [k] =
ps g1 iA [k] + d1a
√
ps |g1 | 2 d1a
(2)
+
ps |g2 | 2 d2a
+ σR2
,
g
1 a xR [k] + naA [k] + ncA [k], d1
pr d1a d2a g1 NR [k]
d1a ξ (6)
|2
pr ps g1 g2 iB [k]
ξ
|2
d2a +
+
d1a d2a σR2.
d1a )
pr d2a g1 NR [k]
ξ
+ NA [k].
EHRT SR
(7)
in (7), the SNR (i.e.
1−α T /2
p2s | g1 ps d2a
( | g1 |
2
d2a +
| g2 |
2
d1a
(3)
(4)
where, pr is the transmit power of the relay node, which is constrained by the factor σR2 , which is the combined variance of AWGN NR [k] at the relay node. (NR [k] naR [k] + ncR [k]). The sampled signal received from relay node at node A is given by
yA [k] =
γAT SR = Signal Power/Noise Power) at node A can be expressed as
ps g2 iB [k] + naR [k] + ncR [k]. d2a
pr yR [k]
d1a g1 g2 iB [k] +
by simplifying and substituting pr =
Note that the analog signal received at the relay node is represented in terms of the time index (t) and after down conversion and analog-to-digital conversion, the received baseband signal is represented by discrete-time index [k] [26]. The relay node amplifies and transmits the received signals. The amplified and transmitted signal from the relay node can be expressed as:
xR [k] =
It can be observed that the first term in (7) is the desired signal, while the remaining two terms represent the noise. Finally,
where η is the efficiency of the energy harvesting receiver, whose value ranges between 0 to 1 (0 ≤ η ≤ 1) [8]. Then, the signal is sent to the information processing circuit for (1 − α )T /2. After down-conversion and analog-to-digital conversion (ADC) [26], the received baseband signal at the information processing circuit is given in Eq. (3), where AWGN due to RF-tobaseband conversion is denoted by ncR [k]
yR [k] =
d2a g21 iA [k] +
where ξ = ps (| g1 | g2 + Note that (6) also contains iA [k], which is already known by node A. Since this selfinterference term is already known to the destination node, it can be subtracted out using the active self-interference cancellation techniques [27,28]. The resulting signal can be expressed as:
(1)
αT ,
+ NA [k],
where a is the path loss exponent, and iA (t) and iB (t) are the information signals from node A and node B, respectively. The additive white Gaussian noise (AWGN) at the receiving antenna of the relay node is denoted by naR (t ). The received signal yR (t) is first sent to the energy harvesting circuit for time α T, and the harvested energy at the relay node can be calculated as:
EHRT SR
pr ps
(5)
where naA [k] and ncA [k] are the AWGNs at the receiving antenna and RF-to-baseband conversion at node A, respectively; and for the sake of notational simplicity, we define NA [k] naA [k] + ncA [k]. After substituting (3) in (4) and then (4) in (5) the simplified received
|2 | g2 |2 2αη (| g1 |2 d2a + | g2 |2 d1a ) ) | g1 |2 σR2 2αη + σA2 d1a (1 − α ) + d12a d22a σR2 σA2 (1 − α )
(8)
where σA2 denotes the variance of AWGN NA [k] at node A. As the second term in the denominator of (8) has a product of two noise variance terms, and its value is negligibly small, at high SNR the approximated SNR at node A can be expressed as:
γAT SR ≈
d2a
ps | g1 |2 | g2 |2 2αη . | g1 |2 2αησR2 + d1a d2a (1 − α )σA2
(9)
The same process can be repeated to derive SNR at node B, which is not covered separately here. 3.2. The HPTSR protocol The transmission time-block structure of HPTSR protocol for energy harvesting and information processing is shown in Fig 3. The HPTSR protocol is the combination of both TSR and PSR protocols [5,8,12]. Similar to TSR, the total transmission time T is divided into two parts, α T and (1 − α )T (where 0 ≤ α ≤ 1). The α T fraction of the time is used for energy harvesting and information processing from source nodes to the relay node while the remaining time (1 − α )T is used for information transmission from relay node to destination nodes. The HPTSR protocol allows energy harvesting during the α T period of the block time. For energy harvesting, the relay utilizes the power splitting based mechanism [8]. In the context of power splitting, the relay splits the power of the received signals as follows. During α T interval, the λ fraction of the received signal power P is used for energy harvesting. During the same α T interval, the remaining (1 − λ ) fraction of the power P is used for information processing. The received signal yR (t) at relay node is similar to (1). The split received signal can be expressed as:
√
λyR (t ) =
λ ps d1a
g1 iA (t ) +
λ ps d2a
g2 iB (t ) +
√
λnaR (t ).
(10)
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respective thresholds as γnT SR and γnHPT SR . In general, the outage probability pout at the destination node n is determined as:
The harvested energy at the relay node can be calculated as:
ηλ p | g |2 s 1
EHRHPT SR =
d1a
ηλ ps | g2 |2 αT . + a
(11)
d2
Using (11), the transmit power of the relay can be expressed as:
ηαλ ps | g1 |2 | g2 |2
= pr = + . (1 − α ) d1a d2a 1−α T EHRHPT SR
(12)
The received down-converted baseband signal at the relay node is given by:
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(1 − λ )yR [k] = +
( 1 − λ ) ps
d1a
g1 iA [k] +
( 1 − λ ) ps d2a
(1 − λ )naR [k] + ncR [k].
√ G (1 − λ )yR [k],
(14)
where, G is the amplification gain, which can be expressed as:
√ G=
( 1 −λ ) p s
d1a d2a
pr
| g1 |
2
d2a +
| g2 |
2
d1a
+σ
2 R
,
(15)
node (where NR [k] (1 − λ )naR [k] + ncR [k]). The sampled signal received at node A from the relay node is given by:
g
1 a xR [k] + naA [k] + ncA [k].
(16)
d1
After substituting (13) in (14) and then (14) in (16), the simplified received signal at node A becomes:
G ( 1 − λ ) ps g1 g1 iA [k]
yA [k]=
d1a
d1a
+
g2 iB [k]
d2a
+
√ Gg 1
d1a
Proposition 1. For the sake of convenience, we define j = γthr σA2 d1a d2a (1 − α ), l = ps 2αη, and m = d2a γthr σR2 2αη. Therefore, the outage probability at node A can be determined as:
pAout
m
e l g 2 ≈1− · l g 2
4 jl g2
g 1
· k1
4j l g 1 g 2
,
(22)
where, g1 , g2 , and k1 (.) denote the mean values of exponential random variables |g1 |, |g2 |, and the second type of the first-order modified Bessel function [29], respectively. Appendix A provides the detailed derivation of pAout for TSR protocol. The throughput at a receiving node is calculated as [5]:
where σR2 is the combined variance of AWGN NR [k] at the relay
yA [k] =
where γthr = − 1 and U is the constant transmission rate of the source node, which is defined as U = log2 (1 + γthr ). The following prepositions determine the outage probability of TSR and HPTSR protocols in Propositions 1 and 2, respectively.
−
(13)
(21)
2U
g2 iB [k]
The signal amplified and then transmitted from the relay node can be expressed as:
xR [k] =
pnout = p(γn < γthr ),
NR [k] + NA [k].
T hroughput T SR = U
(T − α T ) 2T
(1 − pout ).
(23)
Proposition 2. The pAout for HPTSR protocol can be analytically calculated according to (22), where j = (1 − α )(1 − λ )γthr σA2 d1a d2a , l = ηαλ(1 − λ ) ps , and m = ηαλγthr σR2 d2a . The detailed derivation of pAout for HPTSR protocol follows the same procedure as that provided in Appendix A, which, for the sake of brevity, is omitted here. Furthermore, the outage probability at node B for HPTSR protocol can also be determined in similar manner. Based on the fact that the effective communication time from relay node R to the destination node is (1 − α )T , the throughput at the destination nodes for HPTSR protocol can be estimated as:
T hroughput HPT SR = U
(T − α T ) T
(1 − pout ).
(24)
(17) 5. Numerical results
Just as we dealt with iA [k] in (6), we simplify (17) to:
y˜A [k] =
pr ( 1 − λ ) ps g1 g2 iB [k]
where ξ =
ξ d1a d2a
√ +
pr g1 NR [k]
ξ d1a
(1−λ ) ps |g1 |2 d2a +|g2 |2 d1a +d1a d2a σR2 d1a d2a
+ NA [k],
(18)
. The first term in (18) is
the desired signal, while the remaining two terms represent noise. Finally, by simplifying and substituting (12) in (18), the SNR (i.e. γAHPT SR = | Signal Power |2 /| Noise Power |2 ) at node A can be expressed as:
γAHPT SR =
ηαλ(1 − λ ) p2s | g1 |2 | g2 |2 (| g1 |2 d2a + | g2 |2 d1a ) . ps d2a (| g1 |2 d2a + | g2 |2 d1a ) ηαλσR2 | g1 |2 +(1 − α )(1 − λ )d1a σA2 + (1 − α )d12a d22a σR2 σA2
The term (1 − α )d12a d22a σR2 σA2 in (19) is a product of two noise variance terms which is negligibly small at high SNR. Therefore, the simplified SNR expression at node A is:
γAHPT SR ≈
Based on the expressions derived in the previous section, we examine the throughput of TSR and HPTSR protocols in a twoway AF relay network. It can be observed from Eqs. (9), (20), (23), and (24) that SNR and throughput at the receiving node depend on pout , U, ps , η, d1 , d2 , α , σA2 , σR2 , and σB2 . In this section, we study the impact of these parameters on the overall network performance. We also compare the results with the PSR protocol proposed in [20].
ηαλ
d2a
ηαλ(1 − λ ) ps | g1 |2 | g2 |2 . | g1 |2 σR2 + (1 − α )(1 − λ )d1a d2a σA2
(20)
4. Outage probability and throughput analysis Outage of a node occurs when the SNR of the receiving node,
γ n , gets below the minimum threshold γ thr . Since we are inter-
ested in the two different protocols TSR and HPTSR, we define their
(19)
We consider that the transmit power ps of the source nodes A and B is set to 1.5 Joules/sec while the source transmission rate is U = 3 bits/sec/Hz. The distance d1 between node A and relay R, and distance d2 between R and node B are normalized to unity. The value of the path loss exponent a is set to 2.7. The noise factors, such as the antenna noise and conversion noise, are assumed to be equal to each other at all nodes, and the value of their variances are fixed to 0.01. Also, the mean values g1 , g2 of the exponential random variables |g1 |, |g2 | are equal to 1. More detail about the parameters used in our numerical analysis is provided in Table 1. For transmission rate U = 3 bits/sec/Hz, the throughput comparison between TSR and HPTSR protocols with varying values of
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Fig. 4. Throughput comparison between TSR and HPTSR protocols with varying values of time switching factor α , when U = 3.
Fig. 5. Throughput comparison between PSR and HPTSR protocols with varying values of power splitting factor λ, when U = 3. Table 1 Numerical analysis details.
1 2 3
Parameter
Value
ps
1.5 1 1
η
d1 and d2
4 5 6
Parameter
Value
a
2.7 1 0.01
g 1 , g 2 σA2 , σR2 , σB2
time switching factor α is depicted in Fig 4. It can be seen that HPTSR protocol outperforms the TSR protocol. When the value of α rises from 0 to α = 0.23 for U = 3 (which is near to optimal), the throughput in TSR protocol increases. This is due to the fact that for values of α smaller than the optimal value, there is less time for energy harvesting at the relay node. As a result, high outage probability and low throughput are observed at the destination. The same phenomena applies to HPTSR for α = 0.35. On other hand, when U = 3 and λ = 0.65, the throughput in both TSR and HPTSR protocols starts decreasing after α = 0.23 and α = 0.35, respectively. This is because when the value of α is greater than some optimal value, the relay node consumes more time in energy harvesting, and less time remains for information transmission. Moreover, it can be also observed from Fig 4 that in both TSR and HPTSR protocols, the simulation results are very close to the analytical results. This verifies the mathematical analysis reported in Section 4. The throughput comparison between PSR and HPTSR protocols with varying values of λ is shown in Fig 5. Similar to the trend
shown in Fig 4, as the value λ increases from 0 to 0.65 (which is near to optimal), the throughput in both PSR and HPTSR protocol increases, and after that as λ increases, it starts decreasing. This is because for λ smaller than 0.65, less power is available for energy harvesting which results in low transmission power of relay (pr ); and since the throughput at the destination node highly depends on pr , its lower value results in decreased throughput. On the other hand for values of lambda larger than 0.65, more power is used for energy harvesting and less power is left for information processing which results in poor SNR at the relay and consequently on the destination node. Note that in order to maximize the throughput at the destination node, it is desirable to analytically derive the optimal vales for both α and λ; but because of the Bessel functions involved in the analytical expression of outage probability (see (22)), it seems intractable to evaluate the closed-form expressions for the optimal values of both α and λ [5]. Following an alternative path, we instead numerically evaluate the near-to-optimal values (offline optimization) for both the power splitting and time switching factors, where other system parameters are kept constant. Based on results provided in Figs 4 and 5, where the near-to-optimal values (found using offline optimization) of α and λ for both TSR and HPTSR protocols are α = 0.23, and α = 0.35, and λ = 0.65, respectively. We use these near-to-optimal values throughout the rest of the paper. Fig. 6 plots the throughput of TSR, PSR and HPTSR protocols with varying values of transmission rate U. It can be observed that for U < 4, HPTSR protocol outperforms PSR and TSR protocols. On the other hand, at transmission rates U > 4.7, TSR protocol outper-
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Fig. 6. Throughput comparison between TSR, HPTSR, and PSR protocols with varying values of transmission rate U.
Fig. 7. Throughput with varying values of energy harvesting efficiency η.
forms both PSR and HPTSR. The trend in Fig 6 also provides useful insight into the impact of U on the overall system throughput. It is obvious from the figure that the throughput in all three protocols first increases to a certain value for smaller values of U but then starts to decrease as the value of U increases. The reason for this is that the throughput in TSR and HPTSR largely depends on U (see (21) and (22)). Therefore, at low transmission rate the throughput decreases. However, at higher transmission rates, the destination node fails to successfully decode the huge amount of received data in the limited time. This results in higher outage probability and decreased throughput. Fig. 7 plots the effect of energy harvesting efficiency η on overall throughput. It is intuitive that as the energy harvesting efficiency at the relay node increases, the throughput at the destination node increases. The results in Fig 7 show that for smaller values of η, both HPTSR and PSR protocols have similar performance, and that for higher values of η, HPTSR protocol outperforms PSR. For all values of η, TSR protocol displays lower throughput than both HPTSR and PSR. For TSR, PSR and HPTSR protocols, the effect of antenna noise variance is depicted in Fig 8. In all three protocols, the achievable throughput at the destination node decreases when the antenna noise increases. The figure also clearly shows that the performance of HPTSR protocol is better than that of PSR protocol. Similarly, for smaller values of antenna noise, the performance of TSR protocol is significantly lower than those of both HPTSR and PSR. However, as the antenna noise increases, the performance gap between all three protocols decreases.
The impact of the source transmission power ps on the achievable throughput of TSR, PSR, and HPTSR protocols is depicted in Fig 9. Note from (9) and (20) that the throughput at the destination depends on the source transmission power, which can be verified from the results in Fig 9. It is clear that as the source transmission power increases, the throughput at the destination node increases. Fig. 9 also shows that at low transmission power, TSR protocol has slightly better performance than both PSR and HPTSR protocols. On other hand, at high transmission power, HPTSR and PSR protocols outperform TSR protocol 6. Conclusion and future work In this paper, we have studied the impact of TSR and HPTSR protocols on an RF energy harvesting based two-way AF relay network. Analytical expressions for achievable throughput and outage probability at the destination are derived for both TSR and HPTSR protocols. Our numerical results are verified using simulations. Interesting insights into the effects of different parameters on the achievable throughput have also been highlighted. It is shown that for the considered two-way AF relay network, at high SNR and low transmission rate, HPTSR protocol outperforms TSR and PSR. On other hand, at low SNR and high transmission rates, TSR protocol outperforms the other two protocols. In future work, we intend to extend this work to a multichannel network, where multiple source nodes will transmit their information to their respective destination nodes via an intermediate energy constrained relay node. Furthermore, with the assumption that CSI is available at the
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Fig. 8. Throughput comparison with varying antenna noise variance.
Fig. 9. Throughput comparison with varying values of source transmission power ps .
relay node, we will also propose an optimal energy harvesting and energy distribution scheme. Extending this system model to an N-way relay network, where N different source-destination pairs simultaneously communicate via an energy constrained relay node, is indeed an interesting idea. The N-way energy harvesting based relay network and its related issues can be classified into two broad categories, namely underlay mode and overlay mode. In underlay mode, multiple source nodes simultaneously transmit their information signal to an energy constrained relay via the same frequency channel. After receiving the signals, the relay first harvests the energy, and then forwards the amplified/decoded signals to their corresponding destinations. In underlay mode, the received signal at any destination node will consist of the desired information signal and N-1 interference signals. In such case, the performance of the system in terms of achievable throughput and outage probability will highly depend upon the number of source-destination pairs. In other words, as the number of source nodes increase, the harvested power at relay node will also increase; but on the other hand, at the destination node, the received signal-to-interference-plus-noise ratio (SINR) will also be affected, due to the increasing number of interfering signals. In the case of the overlay mode, N different source-destination pairs will simultaneously communicate via an energy constrained relay node using independent and orthogonal frequency resource channels. In this case, the interference at the destination node will
not be an issue; however, harvesting the right amount of power from each received signal, and then the efficient distribution of this harvested power to each corresponding relay-to-destination channel, will be challenging problems to solve. If it is assumed that the CSI of all relay-to-destination channels are available at the relay node, then one possible solution to optimize the achievable throughput at destination nodes will be to use the well known water-filling technique for power distribution at relay. Since in order to maximize the data rates at destination nodes, the waterfilling technique allocates more power to better channels [30], it may increase the outage of destination nodes. Nevertheless, more detailed research study is required to thoroughly investigate the tradeoffs associated with both modes, which is also part of our future research work. Acknowledgment This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2014R1A5A1011478). Appendix A This appendix provides the detailed derivation of pAout for TSR protocol. The pAout for HPTSR follows the same procedure as provided below, which, for the sake of brevity, is omitted here.
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The outage probability at node A for TSR protocol is given by
pAout ≈ p(γA < γthr )
(A.1)
By inserting the value of γ A in (A.1) we can simplify pAout as:
pAout ≈ p
| g1 |2 <
| g2 |2 γthr σA2 d1a d2a (1 − α ) . | g2 |4 ps 2αη− | g2 |2 d2a γthr σR2 2αη
(A.2)
For notational convenience we define j = γthr σA2 d1a d2a (1 − α ), l = ps 2αη, m = d2a γthr σR2 2αη. Thus, (A.2) can be rewritten as
pAout ≈ p
| g1 |2 <
| g2 |2 j . | g2 |4 l− | g2 |2 m
(A.3)
Note that the denominator (| g2 |4 l− | g2 |2 m) can be positive (if |g2 |2 < m/l) or negative (if |g2 |2 > m/l), if it is negative then pAout = 1. Thus the outage probability can be expressed as
pAout ≈
m/l y=0
+
| g2 |2 j dy 2 | g2 | l− | g2 | m
| g2 |2 j f | g2 |2 ( y ) p | g1 |2 > dy, | g2 |4 l− | g2 |2 m
f | g2
∞ y=m/l
|2 ( y ) p | g1 |2 <
4
(A.4) where f|g |2 (y ) and F|g |2 (y ) are the probability density function 2 1 (PDF) and cumulative distribution function (CDF) of the exponential random variable |g2 |2 and |g1 |2 , respectively, and they can be −y
−y
defined as f|g |2 (y ) = 1g e g2 and F|g |2 (y ) = p(g21 < y ) = 1 − e g1 . 2 1 2 Here g1 and g2 are the mean of exponential random variable |g1 | and |g2 |, respectively. By substituting PDF and CDF in (A.4) the outage probability at node A can be expressed as
pAout ≈ 1 −
1
∞
e
g 2
−( y + (ly−mj) g2
g1
)
dy.
(A.5)
y=m/l
By defining and substituting a new integration variable z (i.e. z = ly − m) in (A.5), the pAout can be rewritten as
pAout ≈ 1 −
1
−m
l g 2
e l g 2
∞
e
−( zj
g1
+ l z ) g2
dz.
(A.6)
z=0
The integral part can be solved according to first order modified Bessel function of second kind [29], which is
∞ 0
ν
e− 4z −τ z dz =
ν √ K ( ντ ). τ 1
(A.7)
Thus the outage probability at node A can be expressed as −
pAout
m
e l g 2 ≈1− · l g 2
4 jl g2
g 1
· k1
4j l g 1 g 2
,
(A.8)
For the sake of brevity, the detailed derivation of pBout is not included here because it follows the same procedure as given above. References [1] X. Lu, P. Wang, D. Niyato, D.I. Kim, Z. Han, Wireless networks with RF energy harvesting: a contemporary survey, IEEE Commun. Surv. Tut. 17 (2) (2015) 757–789, doi:10.1109/COMST.2014.2368999. [2] J. Xu, R. Zhang, Throughput optimal policies for energy harvesting wireless transmitters with non-ideal circuit power, IEEE J. Sel. Areas Commun. 32 (2) (2014) 322–332, doi:10.1109/JSAC.2014.141212. [3] V. Raghunathan, S. Ganeriwal, M. Srivastava, Emerging techniques for long lived wireless sensor networks, IEEE Commun. Mag. 44 (4) (2006) 108–114, doi:10.1109/MCOM.2006.1632657. [4] I. Ahmed, M.M. Butt, C. Psomas, A. Mohamed, I. Krikidis, M. Guizani, Survey on energy harvesting wireless communications: challenges and opportunities for radio resource allocation, Comput. Netw. 88 (2015) 234–248. http://dx.doi. org/10.1016/j.comnet.2015.06.009.
[5] A.A. Nasir, X. Zhou, S. Durrani, R.A. Kennedy, Relaying protocols for wireless energy harvesting and information processing, IEEE Trans. Wireless Commun. 12 (7) (2013) 3622–3636, doi:10.1109/TWC.2013.062413.122042. [6] L.R. Varshney, Transporting information and energy simultaneously, in: 2008 IEEE International Symposium on Information Theory, 2008, pp. 1612–1616, doi:10.1109/ISIT.2008.4595260. [7] P. Grover, A. Sahai, Shannon meets tesla: wireless information and power transfer, in: 2010 IEEE International Symposium on Information Theory, 2010, pp. 2363–2367, doi:10.1109/ISIT.2010.5513714. [8] X. Zhou, R. Zhang, C.K. Ho, Wireless information and power transfer: architecture design and rate-energy tradeoff, IEEE Trans. Commun. 61 (11) (2013) 4754–4767. [9] P. Popovski, A.M. Fouladgar, O. Simeone, Interactive joint transfer of energy and information, IEEE Trans. Commun. 61 (5) (2013) 2086–2097, doi:10.1109/ TCOMM.2013.031213.120723. [10] R. Zhang, C.K. Ho, MIMO broadcasting for simultaneous wireless information and power transfer, IEEE Trans. Wireless Commun. 12 (5) (2013) 1989–2001, doi:10.1109/TWC.2013.031813.120224. [11] S. Jangsher, H. Zhou, V.O.K. Li, K.C. Leung, Joint allocation of resource blocks, power, and energy-harvesting relays in cellular networks, IEEE J. Sel. Areas Commun. 33 (3) (2015) 482–495, doi:10.1109/JSAC.2015.2391916. [12] D.-T. Do, Time power switching based relaying protocol in energy harvesting mobile node: optimal throughput analysis, Mobile Inf. Syst. (2015) 8pages, doi:10.1155/2015/769286. [13] B. Gurakan, O. Ozel, J. Yang, S. Ulukus, Energy cooperation in energy harvesting wireless communications, in: IEEE International Symposium on Information Theory Proceedings (ISIT), 2012, pp. 965–969, doi:10.1109/ISIT.2012.6284706. [14] I. Krikidis, S. Timotheou, S. Sasaki, RF Energy transfer for cooperative networks: Data relaying or energy harvesting? IEEE Commun. Lett. 16 (11) (2012) 1772– 1775, doi:10.1109/LCOMM.2012.091712.121395. [15] Z. Ding, S.M. Perlaza, I. Esnaola, H.V. Poor, Power allocation strategies in energy harvesting wireless cooperative networks, IEEE Trans. Wireless Commun. 13 (2) (2014) 846–860, doi:10.1109/TWC.2013.010213.130484. [16] A.A. Nasir, X. Zhou, S. Durrani, R.A. Kennedy, Throughput and ergodic capacity of wireless energy harvesting based DF relaying network, in: 2014 IEEE International Conference on Communications (ICC), 2014, pp. 4066–4071, doi:10.1109/ICC.2014.6883957. [17] W. Xu, Z. Yang, Z. Ding, L. Wang, P. Fan, Wireless information and power transfer in two-way relaying network with non-coherent differential modulation, EURASIP J. Wireless Commun. Netw. 2015 (1) (2015) 1–10. [18] S.T. Shah, K.W. Choi, S.F. Hasan, M.Y. Chung, Energy harvesting and information processing in two-way multiplicative relay networks, Electron. Lett. 52 (9) (2016a) 751–753, doi:10.1049/el.2015.3682. [19] S.T. Shah, D. Munir, M.Y. Chung, K.W. Choi, Information processing and wireless energy harvesting in two-way amplify-and-forward relay networks, in: 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), 2016b, pp. 1–5, doi:10.1109/VTCSpring.2016.7504290. [20] Z. Chen, B. Xia, H. Liu, Wireless information and power transfer in two-way amplify-and-forward relaying channels, in: Signal and Information Processing (GlobalSIP), 2014 IEEE Global Conference on, 2014, pp. 168–172, doi:10.1109/ GlobalSIP.2014.7032100. [21] M.O. Hasna, M.S. Alouini, Performance analysis of two-hop relayed transmissions over rayleigh fading channels, in: Vehicular Technology Conference, 2002. Proceedings. VTC 2002-Fall. 2002 IEEE 56th, 4, 2002, pp. 1992– 1996 vol.4, doi:10.1109/VETECF.2002.1040567. [22] C.K. Ho, R. Zhang, Optimal energy allocation for wireless communications with energy harvesting constraints, IEEE Trans. Signal Process. 60 (9) (2012) 4808– 4818, doi:10.1109/TSP.2012.2199984. [23] S. Luo, R. Zhang, T.J. Lim, Optimal save-then-transmit protocol for energy harvesting wireless transmitters, IEEE Trans. Wireless Commun. 12 (3) (2013) 1196–1207, doi:10.1109/TWC.2013.012413.120488. [24] L. Liu, R. Zhang, K.C. Chua, Wireless information transfer with opportunistic energy harvesting, IEEE Trans. Wireless Commun. 12 (1) (2013) 288–300, doi:10.1109/TWC.2012.113012.120500. [25] B. Medepally, N.B. Mehta, Voluntary energy harvesting relays and selection in cooperative wireless networks, IEEE Trans. Wireless Commun. 9 (11) (2010) 3543–3553, doi:10.1109/TWC.2010.091510.100447. [26] S. Haykin, B. Van Veen, Signals and Systems, John Wiley & Sons, 2007. [27] E. Ahmed, A.M. Eltawil, A. Sabharwal, Self-interference cancellation with phase noise induced ici suppression for full-duplex systems, in: 2013 IEEE Global Communications Conference (GLOBECOM), 2013, pp. 3384–3388, doi:10.1109/ GLOCOM.2013.6831595. [28] E. Ahmed, A.M. Eltawil, All-digital self-interference cancellation technique for full-duplex systems, IEEE Trans. Wireless Commun. 14 (7) (2015) 3519–3532, doi:10.1109/TWC.2015.2407876. [29] I. GradshteynandI, M. ryzhik, table of integrals, series, and products, 1994. [30] P. He, L. Zhao, S. Zhou, Z. Niu, Water-filling: A geometric approach and its application to solve generalized radio resource allocation problems, IEEE Trans. Wireless Commun. 12 (7) (2013) 3637–3647, doi:10.1109/TWC.2013.061713. 130278.
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Syed Tariq Shah received his B.S. degree in telecommunication engineering from Balochistan University of Information Technology, Engineering and Management Sciences, Pakistan, in 2009. He is currently a PhD candidate in the Department of Electrical and Computer Engineering at Sungkyunkwan University. His research interests include 5G networks, LTE-Advanced networks, wireless energy harvesting and device-to-device communication.
Kae Won Choi received the B.S. degree in civil, urban, and geosystem engineering in 2001, and the M.S. and Ph.D. degrees in electrical engineering and computer science in 2003 and 2007, respectively, all from Seoul National University, Seoul, Korea. From 2008 to 2009, he was with Telecommunication Business of Samsung Electronics Co., Ltd., Korea. From 2009 to 2010, he was a Postdoctoral Researcher in the Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada. From 2010 to 2016, he was an Assistant Professor in the Department of Computer Science and Engineering, Seoul National University of Science and Technology, Korea. In 2016, he joined the faculty at Sungkyunkwan University, Korea, where he is currently an Associate Professor in the School of Electronic and Electrical Engineering. His research interests include RF energy transfer, device-to-device communication, cognitive radio, radio resource management, and wireless network optimization. He is presently an editor of IEEE Wireless Communications Letters and IEEE Communications Surveys and Tutorials.
Syed Faraz Hasan is with the School of Engineering and Advanced Technology, Massey University, New Zealand. He has previously been with Sungkyunkwan University, South Korea, and Korea Advanced Institute of Science of Technology (KAIST). He obtained his PhD degree from University of Ulster, UK, in 2011. He completed his Bachelor’s degree in Electrical Engineering from NED University of Engineering and Technology, Pakistan, in 2008. His research interests are in device-to-device communication, energy harvesting, software-defined networking and smart grids. He is a member of IEEE.
Min Young Chung received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology, Daejeon, Korea, in 1990, 1993, and 1999, respectively. From January 1999 to February 2002, he was a Senior Member of Technical Staff with the Electronics and Telecommunications Research Institute, where he was engaged in research on the development of multiprotocol label switching systems. In March 2002, he joined the Faculty of Sungkyunkwan University, Suwon, Korea, where he is currently a Professor with the College of Information and Communication Engineering. His research interests include D2D Communications, Software-Defined Networking (SDN), 5G wireless communication networks, and wireless energy harvesting. He worked as an editor on the Journal of Communications and Networks from January 2005 to February 2011, and is a member of IEEE, IEICE, KICS, KIPS and KISS.
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Ad Hoc Networks 0 0 0 (2016) 1–9
Contents lists available at ScienceDirect
Ad Hoc Networks journal homepage: www.elsevier.com/locate/adhoc
Throughput analysis of two-way relay networks with wireless energy harvesting capabilities Syed Tariq Shah a, Kae Won Choi a, Syed Faraz Hasan b, Min Young Chung a,∗ a b
College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea School of Engineering and Advanced Technology, Massey University, Palmerston North, 4442, New Zealand
a r t i c l e
i n f o
Article history: Received 21 January 2016 Revised 23 September 2016 Accepted 28 September 2016 Available online xxx Keywords: RF energy harvesting Cooperative communication Two-way relay
a b s t r a c t Wireless energy harvesting is an efficient way to prolong the lifetime of energy constrained networks. This paper considers a two-way amplify-and-forward (AF) based relay network, where two communicating nodes concurrently transmit their information signals to a relay node. The relay node is energy constrained, and it therefore first harvests energy from the received radio frequency (RF) signals. For energy harvesting at a relay node, we have analyzed the performance of two energy harvesting protocols: the time switching based relaying protocol (TSR), and the hybrid power-time switching based relaying protocol (HPTSR). Once the energy is harvested using one of these protocols, the relay then amplifies and forwards the received information signal towards its destination. We derive analytical expressions for the outage probability and achievable throughput for the aforementioned protocols. Our numerical results verify the analytical derivation, and show the effect of different system parameters on achievable throughput. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In recent years, energy harvesting through radio frequency (RF) signals has gained significant attention from research society and industry. The idea is to prolong the wireless network lifetime through energy harvesting, instead of recharging through conventional methods, or replacing the batteries of low power nodes [1]. Other energy harvesting methods, such as solar, wind, vibration, and thermoelectric effects, can also be used to recharge these nodes [2,3]. However, these conventional techniques are unreliable since the amount of harvested energy can be highly variable [4]. The main advantage of energy harvesting through RF signals over other conventional methods lies in the fact that radio frequency signals can carry information and energy at the same time [5]. Therefore, these low power nodes simultaneously procure energy and process the received information [6–10]. This ability to harvest energy is particularly useful in powering up millions of devices in the emerging Internet of Things (IoT) era. Ever since the advent of IoT, wireless cooperative networks have gained significant research interest. As the name suggests, in a typical cooperative network, information is delivered from source to destination with the help of intermediate relay nodes. ∗
Corresponding author. Fax: +82312907684. E-mail addresses: [email protected] (S.T. Shah), [email protected] (K.W. Choi), [email protected] (S.F. Hasan), [email protected] (M.Y. Chung).
Relays improve the coverage, capacity and quality of service (QoS) of the network by dividing an imperfect communication channel (source-destination) into two appropriate communication paths (i.e. source-relay, and relay-destination) [11]. Recent state-ofthe-art advances in cooperative networks have paved the way for wireless energy cooperation between these nodes. 1.1. Background The idea to transmit both energy and information simultaneously was first proposed in [6], in which the author characterizes the fundamental trade-off for capacity-energy function under the assumption of an ideal energy harvesting receiver. Varshney in [6] first proposed the idea of simultaneously transmitting both energy and information, characterizing the fundamental trade-off for capacity-energy function under the assumption of an ideal energy harvesting receiver. Since it is impractical to design an ideal energy harvesting receiver, Zhou et al. in [8] have proposed two practical approaches. The first approach is based on time-switching (TS) technique, where the total time is divided into two intervals. The first time interval is used for energy harvesting, and the remaining time is used for information processing. The second approach is based on a power-splitting (PS) mechanism, where a PS receiver splits the received signal into two parts, based on the PS ratio. One part of the received signal is used for energy harvesting and the other part is used for information processing. Based on
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TS and PS energy harvesting receivers [8], the authors in [5] have proposed two relaying protocols namely, time switching-based relaying protocol (TSR), and power splitting-based relaying protocol (PSR). The authors in [5] have considered an amplify-and-forward (AF) relay based one-way communication network. The conclusion is that at low signal-to-noise-ratio (SNR) and high transmission rate, the TSR protocol outperforms the PSR protocol. On the other hand, at low transmission rate, the PSR protocol outperforms the TSR protocol. A combined time power switching based relaying protocol in a one-way cooperative communication network has been studied in [12]. In [13], the authors have considered a twohop communication network with energy-harvesting rechargeable nodes that exploit source-relay cooperation. According to [13], the relay assists the source node by forwarding the data to the destination; in return, the source transfers a portion of its energy to the relay. Krikidis et al. in [14], have studied the energy transfer concept in an energy harvesting based cooperative AF relay network. The performance of a greedy switching policy was investigated at relay node. According to the greedy switching policy, the relay node only transmits when its remaining energy ensures decoding at the destination. In [15], the authors have studied the power allocation strategies and outage performance under energy harvesting constraints for decode-and-forward (DF) relaying. Because of the distinct features of the two relaying protocols, the throughput analysis of AF and DF relaying networks is different under energy harvesting constraints [16]. A denoise-and-forward (DNF) based two-way relay network with non-coherent differential binary phase-shift keying modulation has been studied in [17]. An energy harvesting and information processing network based on two-way multiplicative relay using PSR protocol is studies in [18]. Their numerical results show that the proposed scheme outperforms the legacy amplify-and-forward EH relaying technique. The information and power transfer in TS based and PS based two-way AF relaying network have been studied in [19] and [20], respectively. In [19] we have only analyzed the impact of TSR protocol at high transmission rates and our results show that at high transmission rates the TSR protocol outperforms the PS based two-way AF relaying protocol proposed in [20]. This paper is an extension of [19] and in addition to TSR protocol, this article additionally studies the impact of hybrid powertime switching relay protocol (HPTSR) in two-way energy harvesting based AF relaying networks.
1.2. Paper objectives and contribution In a typical two-way relaying network, two source nodes exchange data via an energy constrained relay node. In this paper, we analyze the system performance of such a network given the energy harvesting constraints. To the best of our knowledge, this is the first effort to investigate the impact of HPTSR [12] and TSR protocols in a two-way AF relay network. In this paper, we consider a scenario in which two nodes, A and B, exchange data via the energy constrained relay node R. Secondly, we derive analytical expressions for the outage probability and achievable throughput at both the nodes for TSR and HPTSR protocols. We show that at low SNR and high transmission rate, both HPTSR- and TSR-based two-way relaying outperforms the PSR-based two-way relay network proposed in [20]. The rest of the paper is organized as follows. Section 2 presents the considered system model. Section 3 explains the energy harvesting and information processing procedures using TSR and HPTSR protocols. Section 4 derives analytical expressions for outage probability and achievable throughput. Section 5 then provides the numerical results, while Section 6 concludes the paper.
d1, g1 Node A
AF Relay R
d2, g2 Node B
Step 1: Source Nodes to Relay. Step 2: Relay to Destination Nodes. Fig. 1. System model of a two-way information processing and energy harvesting AF relay network.
2. System model 2.1. Architecture We consider a cooperative communication network that consists of two nodes A and B and a relay node R. The pair of nodes that transmit and receive data are node A and node B. We assume that there is no direct link between node A and node B, and the signal-to-noise ratio (SNR) between them is less than the minimum required threshold for effective communication. Therefore, the intermediate relay node R assists communication between the nodes [21]. Moreover, the relay node is assumed to be an energy constrained node, which first harvests the energy from received signals and then utilizes the harvested energy to amplify and forward the received signals to their destinations. Fig. 1 shows the basic architecture of the considered network, in which d1 , g1 , d2 , and g2 represent the distance and channel gain between node A and relay node R, and the distance and channel gain between node B and relay node R, respectively. The channel gains are assumed to be quasi-static block-fading channels, and the channel state is constant over a transmission block time T. It is also assumed that they are independent and identically distributed in each time block following a Rayleigh distribution. The path loss model considered in this paper is a distance dependent path-loss model such that d−a , where d is the propagation distance, and a is the path-loss exponent. 2.2. Information processing and energy harvesting The entire information transfer and energy harvesting procedure is divided into two major steps. In Step 1, node A and node B transmit their information signals to relay node R. In Step 2, after harvesting energy from the received signals, relay node R amplifies and forwards the information signal to their respective destinations. The transmit powers ps of node A and node B are assumed to be equal and constant. It is also assumed that the processing power required at the transceivers circuitry of relay node R is negligibly small, compared to its transmission power [3,8]. It is also assumed that at the beginning of transmission, the destination node can estimate the channel state information from the pilot signals sent over dual-hop link, and that the overhead due to pilot transmission is negligible. These assumptions are in line with previous research work conducted in this field [8,10,22–25]. 3. Energy harvesting and information processing In this section, we detail the procedure of energy harvesting and information processing in a two-way relay network. We also derive the SNR expressions for TSR and HPTSR protocols. 3.1. The TSR protocol According to TSR protocol the transmission time block is divided into two main parts, α T and (1 − α )T [5], as shown in Fig 2. During the time block α T (where 0 ≤ α ≤ 1), the relay node harvests energy from the received RF signals [8]. The second block
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3
Fig. 3. Transmission time-block structure for HPTSR protocol. Fig. 2. Transmission time-block structure for TSR protocol.
signal at node A becomes
√
time duration (1 − α )T is further divided into two equal halves, such that in first half (1 − α )T/2, node A and node B transmit their information signals to the relay. During the second half (1 − α )T/2, the relay node broadcasts the processed information signal. The received signal at the relay node can be expressed as:
ps g1 iA (t ) + d1a
yR (t ) =
ps g2 iB (t ) + naR (t ), d2a
yA [k] =
=
η p | g |2 s 1 d1a
+
η ps | g2 |2 d2a
γAT SR =
√ y˜A [k] =
ps g1 iA [k] + d1a
√
ps |g1 | 2 d1a
(2)
+
ps |g2 | 2 d2a
+ σR2
,
g
1 a xR [k] + naA [k] + ncA [k], d1
pr d1a d2a g1 NR [k]
d1a ξ (6)
|2
pr ps g1 g2 iB [k]
ξ
|2
d2a +
+
d1a d2a σR2.
d1a )
pr d2a g1 NR [k]
ξ
+ NA [k].
EHRT SR
(7)
in (7), the SNR (i.e.
1−α T /2
p2s | g1 ps d2a
( | g1 |
2
d2a +
| g2 |
2
d1a
(3)
(4)
where, pr is the transmit power of the relay node, which is constrained by the factor σR2 , which is the combined variance of AWGN NR [k] at the relay node. (NR [k] naR [k] + ncR [k]). The sampled signal received from relay node at node A is given by
yA [k] =
γAT SR = Signal Power/Noise Power) at node A can be expressed as
ps g2 iB [k] + naR [k] + ncR [k]. d2a
pr yR [k]
d1a g1 g2 iB [k] +
by simplifying and substituting pr =
Note that the analog signal received at the relay node is represented in terms of the time index (t) and after down conversion and analog-to-digital conversion, the received baseband signal is represented by discrete-time index [k] [26]. The relay node amplifies and transmits the received signals. The amplified and transmitted signal from the relay node can be expressed as:
xR [k] =
It can be observed that the first term in (7) is the desired signal, while the remaining two terms represent the noise. Finally,
where η is the efficiency of the energy harvesting receiver, whose value ranges between 0 to 1 (0 ≤ η ≤ 1) [8]. Then, the signal is sent to the information processing circuit for (1 − α )T /2. After down-conversion and analog-to-digital conversion (ADC) [26], the received baseband signal at the information processing circuit is given in Eq. (3), where AWGN due to RF-tobaseband conversion is denoted by ncR [k]
yR [k] =
d2a g21 iA [k] +
where ξ = ps (| g1 | g2 + Note that (6) also contains iA [k], which is already known by node A. Since this selfinterference term is already known to the destination node, it can be subtracted out using the active self-interference cancellation techniques [27,28]. The resulting signal can be expressed as:
(1)
αT ,
+ NA [k],
where a is the path loss exponent, and iA (t) and iB (t) are the information signals from node A and node B, respectively. The additive white Gaussian noise (AWGN) at the receiving antenna of the relay node is denoted by naR (t ). The received signal yR (t) is first sent to the energy harvesting circuit for time α T, and the harvested energy at the relay node can be calculated as:
EHRT SR
pr ps
(5)
where naA [k] and ncA [k] are the AWGNs at the receiving antenna and RF-to-baseband conversion at node A, respectively; and for the sake of notational simplicity, we define NA [k] naA [k] + ncA [k]. After substituting (3) in (4) and then (4) in (5) the simplified received
|2 | g2 |2 2αη (| g1 |2 d2a + | g2 |2 d1a ) ) | g1 |2 σR2 2αη + σA2 d1a (1 − α ) + d12a d22a σR2 σA2 (1 − α )
(8)
where σA2 denotes the variance of AWGN NA [k] at node A. As the second term in the denominator of (8) has a product of two noise variance terms, and its value is negligibly small, at high SNR the approximated SNR at node A can be expressed as:
γAT SR ≈
d2a
ps | g1 |2 | g2 |2 2αη . | g1 |2 2αησR2 + d1a d2a (1 − α )σA2
(9)
The same process can be repeated to derive SNR at node B, which is not covered separately here. 3.2. The HPTSR protocol The transmission time-block structure of HPTSR protocol for energy harvesting and information processing is shown in Fig 3. The HPTSR protocol is the combination of both TSR and PSR protocols [5,8,12]. Similar to TSR, the total transmission time T is divided into two parts, α T and (1 − α )T (where 0 ≤ α ≤ 1). The α T fraction of the time is used for energy harvesting and information processing from source nodes to the relay node while the remaining time (1 − α )T is used for information transmission from relay node to destination nodes. The HPTSR protocol allows energy harvesting during the α T period of the block time. For energy harvesting, the relay utilizes the power splitting based mechanism [8]. In the context of power splitting, the relay splits the power of the received signals as follows. During α T interval, the λ fraction of the received signal power P is used for energy harvesting. During the same α T interval, the remaining (1 − λ ) fraction of the power P is used for information processing. The received signal yR (t) at relay node is similar to (1). The split received signal can be expressed as:
√
λyR (t ) =
λ ps d1a
g1 iA (t ) +
λ ps d2a
g2 iB (t ) +
√
λnaR (t ).
(10)
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respective thresholds as γnT SR and γnHPT SR . In general, the outage probability pout at the destination node n is determined as:
The harvested energy at the relay node can be calculated as:
ηλ p | g |2 s 1
EHRHPT SR =
d1a
ηλ ps | g2 |2 αT . + a
(11)
d2
Using (11), the transmit power of the relay can be expressed as:
ηαλ ps | g1 |2 | g2 |2
= pr = + . (1 − α ) d1a d2a 1−α T EHRHPT SR
(12)
The received down-converted baseband signal at the relay node is given by:
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(1 − λ )yR [k] = +
( 1 − λ ) ps
d1a
g1 iA [k] +
( 1 − λ ) ps d2a
(1 − λ )naR [k] + ncR [k].
√ G (1 − λ )yR [k],
(14)
where, G is the amplification gain, which can be expressed as:
√ G=
( 1 −λ ) p s
d1a d2a
pr
| g1 |
2
d2a +
| g2 |
2
d1a
+σ
2 R
,
(15)
node (where NR [k] (1 − λ )naR [k] + ncR [k]). The sampled signal received at node A from the relay node is given by:
g
1 a xR [k] + naA [k] + ncA [k].
(16)
d1
After substituting (13) in (14) and then (14) in (16), the simplified received signal at node A becomes:
G ( 1 − λ ) ps g1 g1 iA [k]
yA [k]=
d1a
d1a
+
g2 iB [k]
d2a
+
√ Gg 1
d1a
Proposition 1. For the sake of convenience, we define j = γthr σA2 d1a d2a (1 − α ), l = ps 2αη, and m = d2a γthr σR2 2αη. Therefore, the outage probability at node A can be determined as:
pAout
m
e l g 2 ≈1− · l g 2
4 jl g2
g 1
· k1
4j l g 1 g 2
,
(22)
where, g1 , g2 , and k1 (.) denote the mean values of exponential random variables |g1 |, |g2 |, and the second type of the first-order modified Bessel function [29], respectively. Appendix A provides the detailed derivation of pAout for TSR protocol. The throughput at a receiving node is calculated as [5]:
where σR2 is the combined variance of AWGN NR [k] at the relay
yA [k] =
where γthr = − 1 and U is the constant transmission rate of the source node, which is defined as U = log2 (1 + γthr ). The following prepositions determine the outage probability of TSR and HPTSR protocols in Propositions 1 and 2, respectively.
−
(13)
(21)
2U
g2 iB [k]
The signal amplified and then transmitted from the relay node can be expressed as:
xR [k] =
pnout = p(γn < γthr ),
NR [k] + NA [k].
T hroughput T SR = U
(T − α T ) 2T
(1 − pout ).
(23)
Proposition 2. The pAout for HPTSR protocol can be analytically calculated according to (22), where j = (1 − α )(1 − λ )γthr σA2 d1a d2a , l = ηαλ(1 − λ ) ps , and m = ηαλγthr σR2 d2a . The detailed derivation of pAout for HPTSR protocol follows the same procedure as that provided in Appendix A, which, for the sake of brevity, is omitted here. Furthermore, the outage probability at node B for HPTSR protocol can also be determined in similar manner. Based on the fact that the effective communication time from relay node R to the destination node is (1 − α )T , the throughput at the destination nodes for HPTSR protocol can be estimated as:
T hroughput HPT SR = U
(T − α T ) T
(1 − pout ).
(24)
(17) 5. Numerical results
Just as we dealt with iA [k] in (6), we simplify (17) to:
y˜A [k] =
pr ( 1 − λ ) ps g1 g2 iB [k]
where ξ =
ξ d1a d2a
√ +
pr g1 NR [k]
ξ d1a
(1−λ ) ps |g1 |2 d2a +|g2 |2 d1a +d1a d2a σR2 d1a d2a
+ NA [k],
(18)
. The first term in (18) is
the desired signal, while the remaining two terms represent noise. Finally, by simplifying and substituting (12) in (18), the SNR (i.e. γAHPT SR = | Signal Power |2 /| Noise Power |2 ) at node A can be expressed as:
γAHPT SR =
ηαλ(1 − λ ) p2s | g1 |2 | g2 |2 (| g1 |2 d2a + | g2 |2 d1a ) . ps d2a (| g1 |2 d2a + | g2 |2 d1a ) ηαλσR2 | g1 |2 +(1 − α )(1 − λ )d1a σA2 + (1 − α )d12a d22a σR2 σA2
The term (1 − α )d12a d22a σR2 σA2 in (19) is a product of two noise variance terms which is negligibly small at high SNR. Therefore, the simplified SNR expression at node A is:
γAHPT SR ≈
Based on the expressions derived in the previous section, we examine the throughput of TSR and HPTSR protocols in a twoway AF relay network. It can be observed from Eqs. (9), (20), (23), and (24) that SNR and throughput at the receiving node depend on pout , U, ps , η, d1 , d2 , α , σA2 , σR2 , and σB2 . In this section, we study the impact of these parameters on the overall network performance. We also compare the results with the PSR protocol proposed in [20].
ηαλ
d2a
ηαλ(1 − λ ) ps | g1 |2 | g2 |2 . | g1 |2 σR2 + (1 − α )(1 − λ )d1a d2a σA2
(20)
4. Outage probability and throughput analysis Outage of a node occurs when the SNR of the receiving node,
γ n , gets below the minimum threshold γ thr . Since we are inter-
ested in the two different protocols TSR and HPTSR, we define their
(19)
We consider that the transmit power ps of the source nodes A and B is set to 1.5 Joules/sec while the source transmission rate is U = 3 bits/sec/Hz. The distance d1 between node A and relay R, and distance d2 between R and node B are normalized to unity. The value of the path loss exponent a is set to 2.7. The noise factors, such as the antenna noise and conversion noise, are assumed to be equal to each other at all nodes, and the value of their variances are fixed to 0.01. Also, the mean values g1 , g2 of the exponential random variables |g1 |, |g2 | are equal to 1. More detail about the parameters used in our numerical analysis is provided in Table 1. For transmission rate U = 3 bits/sec/Hz, the throughput comparison between TSR and HPTSR protocols with varying values of
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5
Fig. 4. Throughput comparison between TSR and HPTSR protocols with varying values of time switching factor α , when U = 3.
Fig. 5. Throughput comparison between PSR and HPTSR protocols with varying values of power splitting factor λ, when U = 3. Table 1 Numerical analysis details.
1 2 3
Parameter
Value
ps
1.5 1 1
η
d1 and d2
4 5 6
Parameter
Value
a
2.7 1 0.01
g 1 , g 2 σA2 , σR2 , σB2
time switching factor α is depicted in Fig 4. It can be seen that HPTSR protocol outperforms the TSR protocol. When the value of α rises from 0 to α = 0.23 for U = 3 (which is near to optimal), the throughput in TSR protocol increases. This is due to the fact that for values of α smaller than the optimal value, there is less time for energy harvesting at the relay node. As a result, high outage probability and low throughput are observed at the destination. The same phenomena applies to HPTSR for α = 0.35. On other hand, when U = 3 and λ = 0.65, the throughput in both TSR and HPTSR protocols starts decreasing after α = 0.23 and α = 0.35, respectively. This is because when the value of α is greater than some optimal value, the relay node consumes more time in energy harvesting, and less time remains for information transmission. Moreover, it can be also observed from Fig 4 that in both TSR and HPTSR protocols, the simulation results are very close to the analytical results. This verifies the mathematical analysis reported in Section 4. The throughput comparison between PSR and HPTSR protocols with varying values of λ is shown in Fig 5. Similar to the trend
shown in Fig 4, as the value λ increases from 0 to 0.65 (which is near to optimal), the throughput in both PSR and HPTSR protocol increases, and after that as λ increases, it starts decreasing. This is because for λ smaller than 0.65, less power is available for energy harvesting which results in low transmission power of relay (pr ); and since the throughput at the destination node highly depends on pr , its lower value results in decreased throughput. On the other hand for values of lambda larger than 0.65, more power is used for energy harvesting and less power is left for information processing which results in poor SNR at the relay and consequently on the destination node. Note that in order to maximize the throughput at the destination node, it is desirable to analytically derive the optimal vales for both α and λ; but because of the Bessel functions involved in the analytical expression of outage probability (see (22)), it seems intractable to evaluate the closed-form expressions for the optimal values of both α and λ [5]. Following an alternative path, we instead numerically evaluate the near-to-optimal values (offline optimization) for both the power splitting and time switching factors, where other system parameters are kept constant. Based on results provided in Figs 4 and 5, where the near-to-optimal values (found using offline optimization) of α and λ for both TSR and HPTSR protocols are α = 0.23, and α = 0.35, and λ = 0.65, respectively. We use these near-to-optimal values throughout the rest of the paper. Fig. 6 plots the throughput of TSR, PSR and HPTSR protocols with varying values of transmission rate U. It can be observed that for U < 4, HPTSR protocol outperforms PSR and TSR protocols. On the other hand, at transmission rates U > 4.7, TSR protocol outper-
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Fig. 6. Throughput comparison between TSR, HPTSR, and PSR protocols with varying values of transmission rate U.
Fig. 7. Throughput with varying values of energy harvesting efficiency η.
forms both PSR and HPTSR. The trend in Fig 6 also provides useful insight into the impact of U on the overall system throughput. It is obvious from the figure that the throughput in all three protocols first increases to a certain value for smaller values of U but then starts to decrease as the value of U increases. The reason for this is that the throughput in TSR and HPTSR largely depends on U (see (21) and (22)). Therefore, at low transmission rate the throughput decreases. However, at higher transmission rates, the destination node fails to successfully decode the huge amount of received data in the limited time. This results in higher outage probability and decreased throughput. Fig. 7 plots the effect of energy harvesting efficiency η on overall throughput. It is intuitive that as the energy harvesting efficiency at the relay node increases, the throughput at the destination node increases. The results in Fig 7 show that for smaller values of η, both HPTSR and PSR protocols have similar performance, and that for higher values of η, HPTSR protocol outperforms PSR. For all values of η, TSR protocol displays lower throughput than both HPTSR and PSR. For TSR, PSR and HPTSR protocols, the effect of antenna noise variance is depicted in Fig 8. In all three protocols, the achievable throughput at the destination node decreases when the antenna noise increases. The figure also clearly shows that the performance of HPTSR protocol is better than that of PSR protocol. Similarly, for smaller values of antenna noise, the performance of TSR protocol is significantly lower than those of both HPTSR and PSR. However, as the antenna noise increases, the performance gap between all three protocols decreases.
The impact of the source transmission power ps on the achievable throughput of TSR, PSR, and HPTSR protocols is depicted in Fig 9. Note from (9) and (20) that the throughput at the destination depends on the source transmission power, which can be verified from the results in Fig 9. It is clear that as the source transmission power increases, the throughput at the destination node increases. Fig. 9 also shows that at low transmission power, TSR protocol has slightly better performance than both PSR and HPTSR protocols. On other hand, at high transmission power, HPTSR and PSR protocols outperform TSR protocol 6. Conclusion and future work In this paper, we have studied the impact of TSR and HPTSR protocols on an RF energy harvesting based two-way AF relay network. Analytical expressions for achievable throughput and outage probability at the destination are derived for both TSR and HPTSR protocols. Our numerical results are verified using simulations. Interesting insights into the effects of different parameters on the achievable throughput have also been highlighted. It is shown that for the considered two-way AF relay network, at high SNR and low transmission rate, HPTSR protocol outperforms TSR and PSR. On other hand, at low SNR and high transmission rates, TSR protocol outperforms the other two protocols. In future work, we intend to extend this work to a multichannel network, where multiple source nodes will transmit their information to their respective destination nodes via an intermediate energy constrained relay node. Furthermore, with the assumption that CSI is available at the
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Fig. 8. Throughput comparison with varying antenna noise variance.
Fig. 9. Throughput comparison with varying values of source transmission power ps .
relay node, we will also propose an optimal energy harvesting and energy distribution scheme. Extending this system model to an N-way relay network, where N different source-destination pairs simultaneously communicate via an energy constrained relay node, is indeed an interesting idea. The N-way energy harvesting based relay network and its related issues can be classified into two broad categories, namely underlay mode and overlay mode. In underlay mode, multiple source nodes simultaneously transmit their information signal to an energy constrained relay via the same frequency channel. After receiving the signals, the relay first harvests the energy, and then forwards the amplified/decoded signals to their corresponding destinations. In underlay mode, the received signal at any destination node will consist of the desired information signal and N-1 interference signals. In such case, the performance of the system in terms of achievable throughput and outage probability will highly depend upon the number of source-destination pairs. In other words, as the number of source nodes increase, the harvested power at relay node will also increase; but on the other hand, at the destination node, the received signal-to-interference-plus-noise ratio (SINR) will also be affected, due to the increasing number of interfering signals. In the case of the overlay mode, N different source-destination pairs will simultaneously communicate via an energy constrained relay node using independent and orthogonal frequency resource channels. In this case, the interference at the destination node will
not be an issue; however, harvesting the right amount of power from each received signal, and then the efficient distribution of this harvested power to each corresponding relay-to-destination channel, will be challenging problems to solve. If it is assumed that the CSI of all relay-to-destination channels are available at the relay node, then one possible solution to optimize the achievable throughput at destination nodes will be to use the well known water-filling technique for power distribution at relay. Since in order to maximize the data rates at destination nodes, the waterfilling technique allocates more power to better channels [30], it may increase the outage of destination nodes. Nevertheless, more detailed research study is required to thoroughly investigate the tradeoffs associated with both modes, which is also part of our future research work. Acknowledgment This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2014R1A5A1011478). Appendix A This appendix provides the detailed derivation of pAout for TSR protocol. The pAout for HPTSR follows the same procedure as provided below, which, for the sake of brevity, is omitted here.
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The outage probability at node A for TSR protocol is given by
pAout ≈ p(γA < γthr )
(A.1)
By inserting the value of γ A in (A.1) we can simplify pAout as:
pAout ≈ p
| g1 |2 <
| g2 |2 γthr σA2 d1a d2a (1 − α ) . | g2 |4 ps 2αη− | g2 |2 d2a γthr σR2 2αη
(A.2)
For notational convenience we define j = γthr σA2 d1a d2a (1 − α ), l = ps 2αη, m = d2a γthr σR2 2αη. Thus, (A.2) can be rewritten as
pAout ≈ p
| g1 |2 <
| g2 |2 j . | g2 |4 l− | g2 |2 m
(A.3)
Note that the denominator (| g2 |4 l− | g2 |2 m) can be positive (if |g2 |2 < m/l) or negative (if |g2 |2 > m/l), if it is negative then pAout = 1. Thus the outage probability can be expressed as
pAout ≈
m/l y=0
+
| g2 |2 j dy 2 | g2 | l− | g2 | m
| g2 |2 j f | g2 |2 ( y ) p | g1 |2 > dy, | g2 |4 l− | g2 |2 m
f | g2
∞ y=m/l
|2 ( y ) p | g1 |2 <
4
(A.4) where f|g |2 (y ) and F|g |2 (y ) are the probability density function 2 1 (PDF) and cumulative distribution function (CDF) of the exponential random variable |g2 |2 and |g1 |2 , respectively, and they can be −y
−y
defined as f|g |2 (y ) = 1g e g2 and F|g |2 (y ) = p(g21 < y ) = 1 − e g1 . 2 1 2 Here g1 and g2 are the mean of exponential random variable |g1 | and |g2 |, respectively. By substituting PDF and CDF in (A.4) the outage probability at node A can be expressed as
pAout ≈ 1 −
1
∞
e
g 2
−( y + (ly−mj) g2
g1
)
dy.
(A.5)
y=m/l
By defining and substituting a new integration variable z (i.e. z = ly − m) in (A.5), the pAout can be rewritten as
pAout ≈ 1 −
1
−m
l g 2
e l g 2
∞
e
−( zj
g1
+ l z ) g2
dz.
(A.6)
z=0
The integral part can be solved according to first order modified Bessel function of second kind [29], which is
∞ 0
ν
e− 4z −τ z dz =
ν √ K ( ντ ). τ 1
(A.7)
Thus the outage probability at node A can be expressed as −
pAout
m
e l g 2 ≈1− · l g 2
4 jl g2
g 1
· k1
4j l g 1 g 2
,
(A.8)
For the sake of brevity, the detailed derivation of pBout is not included here because it follows the same procedure as given above. References [1] X. Lu, P. Wang, D. Niyato, D.I. Kim, Z. Han, Wireless networks with RF energy harvesting: a contemporary survey, IEEE Commun. Surv. Tut. 17 (2) (2015) 757–789, doi:10.1109/COMST.2014.2368999. [2] J. Xu, R. Zhang, Throughput optimal policies for energy harvesting wireless transmitters with non-ideal circuit power, IEEE J. Sel. Areas Commun. 32 (2) (2014) 322–332, doi:10.1109/JSAC.2014.141212. [3] V. Raghunathan, S. Ganeriwal, M. Srivastava, Emerging techniques for long lived wireless sensor networks, IEEE Commun. Mag. 44 (4) (2006) 108–114, doi:10.1109/MCOM.2006.1632657. [4] I. Ahmed, M.M. Butt, C. Psomas, A. Mohamed, I. Krikidis, M. Guizani, Survey on energy harvesting wireless communications: challenges and opportunities for radio resource allocation, Comput. Netw. 88 (2015) 234–248. http://dx.doi. org/10.1016/j.comnet.2015.06.009.
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Please cite this article as: S.T. Shah et al., Throughput analysis of two-way relay networks with wireless energy harvesting capabilities, Ad Hoc Networks (2016), http://dx.doi.org/10.1016/j.adhoc.2016.09.024
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Syed Tariq Shah received his B.S. degree in telecommunication engineering from Balochistan University of Information Technology, Engineering and Management Sciences, Pakistan, in 2009. He is currently a PhD candidate in the Department of Electrical and Computer Engineering at Sungkyunkwan University. His research interests include 5G networks, LTE-Advanced networks, wireless energy harvesting and device-to-device communication.
Kae Won Choi received the B.S. degree in civil, urban, and geosystem engineering in 2001, and the M.S. and Ph.D. degrees in electrical engineering and computer science in 2003 and 2007, respectively, all from Seoul National University, Seoul, Korea. From 2008 to 2009, he was with Telecommunication Business of Samsung Electronics Co., Ltd., Korea. From 2009 to 2010, he was a Postdoctoral Researcher in the Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada. From 2010 to 2016, he was an Assistant Professor in the Department of Computer Science and Engineering, Seoul National University of Science and Technology, Korea. In 2016, he joined the faculty at Sungkyunkwan University, Korea, where he is currently an Associate Professor in the School of Electronic and Electrical Engineering. His research interests include RF energy transfer, device-to-device communication, cognitive radio, radio resource management, and wireless network optimization. He is presently an editor of IEEE Wireless Communications Letters and IEEE Communications Surveys and Tutorials.
Syed Faraz Hasan is with the School of Engineering and Advanced Technology, Massey University, New Zealand. He has previously been with Sungkyunkwan University, South Korea, and Korea Advanced Institute of Science of Technology (KAIST). He obtained his PhD degree from University of Ulster, UK, in 2011. He completed his Bachelor’s degree in Electrical Engineering from NED University of Engineering and Technology, Pakistan, in 2008. His research interests are in device-to-device communication, energy harvesting, software-defined networking and smart grids. He is a member of IEEE.
Min Young Chung received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology, Daejeon, Korea, in 1990, 1993, and 1999, respectively. From January 1999 to February 2002, he was a Senior Member of Technical Staff with the Electronics and Telecommunications Research Institute, where he was engaged in research on the development of multiprotocol label switching systems. In March 2002, he joined the Faculty of Sungkyunkwan University, Suwon, Korea, where he is currently a Professor with the College of Information and Communication Engineering. His research interests include D2D Communications, Software-Defined Networking (SDN), 5G wireless communication networks, and wireless energy harvesting. He worked as an editor on the Journal of Communications and Networks from January 2005 to February 2011, and is a member of IEEE, IEICE, KICS, KIPS and KISS.
Please cite this article as: S.T. Shah et al., Throughput analysis of two-way relay networks with wireless energy harvesting capabilities, Ad Hoc Networks (2016), http://dx.doi.org/10.1016/j.adhoc.2016.09.024