# Multihop Capability Analysis in Wireless Information and Power Transfer Multirelay Cooperative Networks

Authors: Qilin Wu; Xianzhong Zhou; Qian Cao; Huan Fang
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

We study simultaneous wireless information and power transfer (SWIPT) in multihop wireless cooperative networks, where the multihop capability that denotes the largest number of transmission hops is investigated. By utilizing the broadcast nature of multihop wireless networks, we first propose a cooperative forwarding power (CFP) scheme. In CFP scheme, the multiple relays and receiver have distinctly different tasks. Specifically, multiple relays close to the transmitter harvest power from the transmitter first and then cooperatively forward the power (not the information) towards the receiver. The receiver receives the information (not the power) from the transmitter first, and then it harvests the power from the relays and is taken as the transmitter of the next hop. Furthermore, for performance comparison, we suggest two schemes: cooperative forwarding information and power (CFIP) and direct receiving information and power (DFIP). Also, we construct an analysis model to investigate the multihop capabilities of CFP, CFIP, and DFIP schemes under the given targeted throughput requirement. Finally, simulation results validate the analysis model and show that the multihop capability of CFP is better than CFIP and DFIP, and for improving the multihop capabilities, it is best effective to increase the average number of relay nodes in cooperative set.


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## Body

## 1. Introduction

Among several wireless energy harvesting techniques, simultaneous wireless information and power transfer (SWIPT) has drawn great attention [1–3]. SWIPT was first proposed in [1, 2], where the transmitter sends one wireless signal, and the receiver harvests energy and decodes information from the signal at the same time. Owing to practical constraint, SWIPT cannot be performed on one circuit. Therefore, two practical architectures, called time switching and power splitting, have been proposed by permitting the receiver to have two circuits to carry out energy harvesting and information decoding separately [3].On the other hand, cooperative communication has been shown to be a promising method to mitigate the wireless channel impairments by applying either amplify-and-forward (AF) or decode-and-forward (DF) relaying protocol [4] in relay nodes. However, a relay node needs to expend its energy for accomplishing the information forwarding, which can make the relay node reluctant to participate in the cooperation. Fortunately, by using energy harvesting node as relay, the cooperative excitement of relay node can be ignited and the network performance can be significantly improved.The performance of SWIPT in cooperative relay networks has been analyzed in various studies (see Section2), but these studies assume that they have at most two hops from source to destination with the signal forwarding by relays. For multihop (more than two hops) networks, because the energy harvesting efficiency cannot reach 100% (the range of 10%–80% is normal) [5], the difficulty is how to transmit energy and information simultaneously from source to destination, that is, solving the SWIPT issue in the multihop case. To solve this problem, we consider using cooperative multiple relays by fully utilizing the broadcast nature of multihop wireless networks. Unlike previous studies, Chen et al. [6] considered multihop scenarios and identified the largest number of transmission hops. However, the work in [6] did not consider multiple cooperative relays and failed to provide insights into the impact factors that affected the largest number of transmission hops.Although the use of cooperative relays can reduce the loss of energy, it is not guaranteed that the information is transmitted to the destination with enough power. Then, what is the largest number of transmission hops under the given targeted throughput requirement? This problem is closely related to the initial energy of source node, the number of relay nodes, communication distance, and other parameters, which sparks our research motivation. In this paper, we first propose a cooperative forwarding power (CFP) scheme, and then, for performance comparison, we suggest two schemes: cooperative forwarding information and power (CFIP) and direct receiving information and power (DFIP). Furthermore, we construct analysis model to investigate the multihop capabilities of CFP, CFIP, and DFIP schemes under the given targeted throughput requirement from application layer. Finally, simulation results validate the analysis model and show that the multihop capability of CFP is better than CFIP and DFIP, and for improving the multihop capabilities, it is best effective to increase the average number of relay nodes in a cooperative set. Therefore, through our study in this paper, the appropriate values of related parameters can be set to achieve the given transmission hops from source to destination.The remainder of this paper is organized as follows. First, the related works are described in Section2. Next, system models and network scenario are given in Section 3, and in Section 4, we present CFP, CFIP, and DFIP schemes. Afterwards, Section 5 presents analytical models for evaluating the performance of the three schemes, and simulation results are given to validate the analytical model and obtain some important insights in Section 6. Finally, conclusions are given in Section 7.


## 2. Related Works

According to the difference in information transmission ways, communication systems adopted by existing literature can be categorized into point-to-point SWIPT systems and cooperative relay SWIPT systems. In the following, we present an overview of existing literature in the above two SWIPT systems.(A) Point-to-Point SWIPT Systems.After the pioneering works of Varshney [1] and Grover and Sahai [2], the performance of practical SWIPT systems is investigated in several studies. Zhang and Ho [3] considered two scenarios, where the information receiver and energy receiver are separated or colocated. More importantly, the work in [3] used rate-energy region to characterize the tradeoff between information rate and energy transfer and proposed two practical receiver designs, namely, time switching and power splitting, for colocated receivers. Later in [7–9], sophisticated architectures for improving the rate-energy region were further proposed. Moreover, multiuser scheduling in SWIPT system was studied for achieving the maximum sum throughput in [10] and tradeoff between the average per user harvested energy and ergodic achievable rate in [11]. Unlike the above works, Zhong et al. [12] considered a novel network architecture, where the source is powered by a dedicated power beacon (PB), and gave the average throughput analysis for two different transmission modes, namely, delay tolerant and delay intolerant. Recently, for reutilizing interferences to avoid a great waste of energy, Zhao et al. [13, 14] proposed a novel SWIPT scheme based on opportunistic communications in interference alignment (IA) networks and analyzed the performance of SWIPT in IA networks, respectively.(B) Cooperative Relay SWIPT Systems.Considering that there is no direct point-to-point link between the source and destination, it is necessary to make use of relay for forwarding information to destination, where the relay node is energy-constrained and needs to harvest energy from the source. Nasir et al. [15] proposed time switching-based relaying (TSR) and power splitting-based relaying (PSR) protocols and derived the throughput for both TSR and PSR under delay-limited and delay-tolerant transmission modes. Afterwards, Do [16] considered that both relay and destination are mobile node and analyzed the optimal throughput performance for the proposed time power switching-based relaying (TPSR) protocol. Unlike the previous studies, Zhang and Chen [17] considered that the relay can harvest energy from source, destination, or joint source and destination and investigated the maximal throughputs of three wireless power transfer (WPT) schemes, respectively. Furthermore, to overcome the loss of spectral efficiency induced by one-way relaying and half-duplex relaying, two-way relaying [18–20] and full-duplex relaying [21–23] were introduced into SWIPT system, respectively. Instead of considering one relay-assisted SWIPT cooperative system in the aforementioned works, the works of [24–26] investigated multirelay-assisted case and analyzed the outage probability and end-to-end rate, respectively. Unlike the existing prominent works, we investigate SWIPT in a multihop scenario and analyze the multihop capability of SWIPT system with multirelay-assisted cooperative transmission.


## 3. System Model

We consider a network scenario shown in Figure1, where the source node (S) wants to transmit data packets to the destination node (D). We assume that a path RS,p1,p2,…,pi,…,pk,D has been selected by virtue of a routing algorithm and all nodes are equipped with a single omnidirectional antenna and work in half-duplex mode. For cooperative transmission, we also assume that each node in a routing path R is surrounded by a number of relays. In addition, for facilitating the analysis, we suggest the relay and channel models as follows.Figure 1
Network scenario.(A) Relay Model.We assume that S is considered as an energy-unconstrained node with a maximum transmit power Ps, while other relay nodes are energy-constrained and have not energy to complete the forwarding operation, but they can harvest energy from the received signal by power splitting. More specifically, each relay i splits a portion of the received signal energy αi for information decoding and the remaining part 1-αi for energy harvesting. Since the processing power consumed by the receive circuitry at the relay nodes is assumed to be negligible as compared to the power used for signal forwarding [15], we assume that all nodes have the energy to receive signal. In this paper, all relays form a cooperative set and simultaneously forward the signals to the receiver by using distributed space-time codes (DSTC) [27].(B) Channel Model.We assume that the additive white Gaussian noises (AWGN) at all nodes are independent circular symmetric complex Gaussian random variables with zero mean and unit variance. The channel fading is modeled by large-scale path loss and statistically independent small-scale Rayleigh fading. It is also assumed that the fading channel gains are assumed to be constant during one block time Tt,v in which the information is transmitted from the transmitter to receiver, and independent and identical distribution (i.i.d.) is used from one transmission to the next. Also, we assume that perfect channel state information (CSI) is available at the receiver side through channel estimation and hi,j denotes the channel gain between node i and node j, which are circular symmetric complex Gaussian random variables with zero mean and unit variance [5, 15, 18].


## 4. Proposed Scheme

To investigate the multihop capability in SWIPT multihop cooperative networks, we give the following three transmission schemes. We first proposecooperative forwarding power (CFP) scheme. In CFP scheme, the relays and receiver have distinctly different tasks. Specifically, multiple relays close to the transmitter harvest power from the transmitter first and then cooperatively forward the power (not the information) towards the receiver. The receiver receives the information (not the power) from the transmitter first, and then it harvests the power from the relays and is taken as the transmitter of the next hop. Furthermore, we use the following two schemes as comparison.(A) Cooperative Forwarding Information and Power (CFIP) Scheme.In this scheme, it is assumed that there is no direct link between the transmitter and receiver of a path (this assumption is adopted by most of the previous studies [5, 15–26]), such as pi and pi+1 in Figure 1. Multiple relays harvest power and decode the information from the transmitter first and then cooperatively forward the information and power to the receiver. Then, the receiver harvests the power and decodes the information from the relays and is taken as the transmitter of the next hop to transmit the information and power. Note that, at present, CFIP is often used in at most two-hop scenarios by most of the previous works to analyze system performance. So, we extend this scheme to multihop scenario for comparing and analyzing the multihop capability in SWIPT cooperative networks.(B) Direct Receiving Information and Power (DFIP) Scheme.This scheme does not consider cooperative transmission, which means that the receiver harvests power and decodes the information from the transmitter directly (this assumption is adopted by most of the previous studies [3, 7–14]). Then, the receiver is taken as the transmitter of the next hop to transmit the information and power. The purpose of proposing this scheme is to investigate whether cooperative transmission can bring more performance improvement than direct transmission in SWIPT networks.It should be pointed out that our schemes are independent of the specific routing protocol and only require an existing path from source to destination. In fact, the analysis results of multihop capability can be used to design a new routing protocol in SWIPT networks. Also, our schemes are indifferent to the specific method of relay selection, because the analysis results of multihop capability are related to the number of relays instead of which node becomes a relay.


## 5. Analytical Model

### 5.1. For CFP Scheme

In CFP scheme, one transmission is divided into two phases. In the first phase, the transmitter (source orpi) transmits the signal to the receiver (pi or destination), and thus, the relays overhear the signal and harvest the power from the signal, and at the same time, the receiver decodes the information from the signal. In the second phase, the relays form a cooperative set according to the DSTC to forward the harvested power by transmitting the special signal to the receiver cooperatively, and then the receiver harvests the power from the special signal and is taken as the transmitter in the next hop with the harvested power. Note here that the special signal is different from the signal from the transmitter to receiver and does not include the useful information that needs to be decoded by the receiver. Therefore, for the special signal, we let the relays transmit a PTS (power ready to send) frame cooperatively in which the frame format is extended to the RTS and CTS control frames in IEEE 802.11 protocol [28].First of all, let us consider that the signal is transmitted from the source to receiver nodep1 in Figure 1. Let yr,i denote the received signal at relay i around the source node in the first phase; we can derive (1)yr,i=1ds,imPshs,ixs+nr,i,where hs,i is the source to relay i channel gain, ds,i is the distance from S to relay i, m is the path loss exponent, nr,i is the additive white Gaussian noise at relay i with zero mean and σn,r2 variance, and xs is the normalized information signal from the source. Because the relays do not decode the signal from the transmitter to receiver, we can let αi=0. According to (1), the harvested energy Er,i at relay i during energy harvesting time Tt,v is given by(2)Er,i=ηPshs,i2Tt,vds,im,where η is the energy harvesting efficiency coefficient and Tt,v is the transmission time for the signal. Note that we do not consider multirate network scenarios, which means that Tt,v is equal for any one hop in the routing path. In (2), we ignore the impact of noise since the noise power is normally very small and below the sensitivity of the energy receiver [29].In the second phase, each relayi uses the transmission power Pr,i=Er,i/Tc,v and forms a cooperative set with other relays to transmit the PTS frame towards the receiver p1, simultaneously. Consequently, p1 does not decode the PTS frame but only harvests the energy that can be expressed by Ep,1 as (3)Ep,1=η∑i=1NrPr,ihi,p12di,p1mTc,v=η2PsTt,v∑i=1Nrhs,i2hi,p12ds,imdi,p1m,where hi,p1 is channel gain from the relay i to receiver p1, Tc,v is the transmission time for the PTS, Nr is the average number of relay nodes in cooperative set, and di,p1 is the distance from the relay i to receiver p1. So, we can derive the transmission power Pp,1 from p1 to receiver node p2 in the second hop as follows:(4)Pp,1=Ep,1Tt,v=η2Ps∑i=1Nrhs,i2hi,p12ds,imdi,p1m.According to the abovementioned analysis, letPp,j-1 denote jth (j≥2) hop transmission power, where the signal is transmitted from pj-1 to pj node (p0 is the source node); we can obtain(5)Pp,j-1=η2j-1Ps∏k=2j∑i=1Nrhpk-2,i2hi,pk-12dpk-2,imdi,pk-1m,where hpk-2,i, hi,pk-1 denote the channel gains from pk-2 to its relay i and from its relay i to pk-1, respectively, and dpk-2,im,di,pk-1m denote the distance from pk-2 to its relay i and from its relay i to pk-1, respectively. So, we can obtain the signal-to-noise ratio (SNR) γj at the receiver node pj as follows: γj=Pp,j-1hpj-1,pj2/σpj-1,pj2dpj-1,pjm, where σpj-1,pj2 denotes the variance of additive white Gaussian noise at receiver pj. Given a targeted throughput R0, if we find the maximum value of l for that log2⁡(1+γl)≥R0 holds, we can derive that the value of l is the largest number of hops supported by the CFP scheme. Therefore, we can derive(6)2l-1log2⁡η+∑k=2llog2⁡∑i=1Nrhpk-2,i2hi,pk-12dpk-2,imdi,pk-1m⁡+log2⁡hpl-1,pl2dpl-1,plmσpl-1,pl2≥log2⁡2R0-1Ps.In formula (6), for calculability, we replace the exponential random variables hpk-2,i2, hi,pk-12, and hpl-1,pl2with their mean values λr, λf, and λd, respectively. Since we have assumed that the channel gain is circular symmetric complex Gaussian random variables with zero mean and unit variance, we get λr=λf=λd=1. Furthermore, we assume that dpk-2,idi,pk-1 is constant and equal to dc. Also, dpl-1,pl, which is the distance from pl-1 to pl, is set to be constant value dd. Consequently, we can obtain (7)l-1log2⁡η2Nrdcm≥log2⁡2R0-1Psddmσ2,where we letσpl-1,pl2 be equal to constant value σ2. In formula (7), if 2R0-1ddmσ2>Ps, that is, log2⁡Ps/ddmσ2+1<R0, the signal cannot be transmitted from the source node to the next hop for satisfying the targeted throughput R0. Therefore, for multihop transmission, it is required that 2R0-1ddmσ2<Ps. Furthermore, we consider that, in a routing path (such as in Figure 1), the transmission power of node pi+1 is lower than that of node pi because the transmission power of node pi+1 is charged from the node pi. So, it is also required that η2Nr/dcm<1. Note that we do not consider the case of η2Nr/dcm≥1 because, in this case, the transmission power of node pi+1 is greater than that of node pi so that the information can be transmitted all the time. Accordingly, we can derive the largest number of hops Lmaxcfp supported by the CFP scheme as follows:(8)Lmaxcfp=1+log2⁡2R0-1/Psddmσ2log2⁡η2Nr/dcm,where . denotes the round down function. From formula (8), we can find that the largest number of hops is affected by the parameters Ps, η, α, Nr, and dc. In simulation, we will give the detailed analysis for these parameters.


### 5.2. For CFIP Scheme

Unlike CFP scheme, in CFIP scheme, a relayi not only harvests the power, but also decodes the information from the transmitter. So, we have αi≠0. If we consider that the transmitter is the source node, a relay i harvests the power Er,i′ as follows:(9)Er,i′=η1-αPshs,i2Tt,vds,im.Note here that, for ease of analysis, we let αi be constant and equal to α. Let Pp,j-1′ denotejth (j≥2) hop transmission power, where the signal is transmitted from pj-1 to pj through multiple relays; we can obtain(10)Pp,j-1′=η1-α2j-1Ps×∏k=2j∑i=1Nr′hpk-2,i2hi,pk-12dpk-2,imdi,pk-1m,where Nr′ is the average number of relay nodes in cooperative set. Note that, because only the relay, which can decode the information successfully, becomes one member of the cooperative set in CFIP scheme, we have Nr′≤Nr. Let γj′ denote SNR at the receiver node pj; we can derive(11)γj′=η1-α∑i=1Nr′Pp,j-1′hpj-1,i2hi,pj2dpj-1,imdi,pjmσi,pj2,where σi,pj2 is the variance of additive white Gaussian noise at receiver pj. Similarly to the above analysis for CFP, while requiring log2⁡1+γl′≥R0, we can obtain(12)l-1log2⁡η1-α2Nr′dcm≥log2⁡2R0-1dcmσ2η1-αNr′Ps,where we let σi,pj2 be equal to constant value σ2. In formula (12), we have η1-α2Nr′/dcm<1 because the transmission power of node pi+1 is lower than that of node pi. Furthermore, for multihop transmission, we have 2R0-1dcmσ2/η1-αNr′Ps<1; that is, log2⁡η1-αPsNr′/dcmσ2+1>R0. Otherwise, the information cannot be transmitted from the source to p1. Consequently, the largest number of hops Lmaxcfip supported by the CFIP scheme can be given as follows:(13)Lmaxcfip=1+log2⁡2R0-1dcmσ2/η1-αNr′Pslog2⁡η21-α2Nr′/dcm.


### 5.3. For DFIP Scheme

Unlike CFP and CFIP schemes, in DFIP scheme, the receiver harvests the power and decodes the information from the transmitter directly without relay cooperation. Therefore, if we consider that the transmitter is the source node, the receiverp1 harvests the power Ed,1 as follows:(14)Ed,1=η1-αPshs,12Tt,vds,1m,where hs,1 is channel gain from the source node to receiver p1 and ds,1 is the distance from the source to p1. Then, the node p1 transmits the information to the next hop node p2 using the power Pd,1=Ed,1/Tt,v. Let Pd,j-1 denote jth (j≥2) hop transmission power, where the signal is transmitted from pj-1 to pj; we can obtain (15)Pd,j-1=η1-αj-1Ps∏k=2jhpk-2,k-12dpk-2,k-1m.So, we can obtain SNR γjd at receiver pj as γjd=Pd,j-1hpj-1,pj2/σpj-1,pj2dpj-1,pjm. Similarly to the above analysis for CFP and CFIP, while requiring log2⁡(1+γld)≥R0, we can obtain (16)l-1log2⁡η1-αddm≥log2⁡2R0-1Psddmσ2.Accordingly, we can derive the largest number of hops Lmaxdfip supported by the DFIP scheme as follows:(17)Lmaxdfip=1+log2⁡2R0-1/Psddmσ2log2⁡η1-α/ddm.In formula (17), we have η1-α/ddm<1 because the transmission power of node pi+1 is lower than that of node pi. For multihop transmission, it is required that 2R0-1ddmσ2<Ps. Otherwise, the information cannot be transmitted from the source to p1.


## 5.1. For CFP Scheme

In CFP scheme, one transmission is divided into two phases. In the first phase, the transmitter (source orpi) transmits the signal to the receiver (pi or destination), and thus, the relays overhear the signal and harvest the power from the signal, and at the same time, the receiver decodes the information from the signal. In the second phase, the relays form a cooperative set according to the DSTC to forward the harvested power by transmitting the special signal to the receiver cooperatively, and then the receiver harvests the power from the special signal and is taken as the transmitter in the next hop with the harvested power. Note here that the special signal is different from the signal from the transmitter to receiver and does not include the useful information that needs to be decoded by the receiver. Therefore, for the special signal, we let the relays transmit a PTS (power ready to send) frame cooperatively in which the frame format is extended to the RTS and CTS control frames in IEEE 802.11 protocol [28].First of all, let us consider that the signal is transmitted from the source to receiver nodep1 in Figure 1. Let yr,i denote the received signal at relay i around the source node in the first phase; we can derive (1)yr,i=1ds,imPshs,ixs+nr,i,where hs,i is the source to relay i channel gain, ds,i is the distance from S to relay i, m is the path loss exponent, nr,i is the additive white Gaussian noise at relay i with zero mean and σn,r2 variance, and xs is the normalized information signal from the source. Because the relays do not decode the signal from the transmitter to receiver, we can let αi=0. According to (1), the harvested energy Er,i at relay i during energy harvesting time Tt,v is given by(2)Er,i=ηPshs,i2Tt,vds,im,where η is the energy harvesting efficiency coefficient and Tt,v is the transmission time for the signal. Note that we do not consider multirate network scenarios, which means that Tt,v is equal for any one hop in the routing path. In (2), we ignore the impact of noise since the noise power is normally very small and below the sensitivity of the energy receiver [29].In the second phase, each relayi uses the transmission power Pr,i=Er,i/Tc,v and forms a cooperative set with other relays to transmit the PTS frame towards the receiver p1, simultaneously. Consequently, p1 does not decode the PTS frame but only harvests the energy that can be expressed by Ep,1 as (3)Ep,1=η∑i=1NrPr,ihi,p12di,p1mTc,v=η2PsTt,v∑i=1Nrhs,i2hi,p12ds,imdi,p1m,where hi,p1 is channel gain from the relay i to receiver p1, Tc,v is the transmission time for the PTS, Nr is the average number of relay nodes in cooperative set, and di,p1 is the distance from the relay i to receiver p1. So, we can derive the transmission power Pp,1 from p1 to receiver node p2 in the second hop as follows:(4)Pp,1=Ep,1Tt,v=η2Ps∑i=1Nrhs,i2hi,p12ds,imdi,p1m.According to the abovementioned analysis, letPp,j-1 denote jth (j≥2) hop transmission power, where the signal is transmitted from pj-1 to pj node (p0 is the source node); we can obtain(5)Pp,j-1=η2j-1Ps∏k=2j∑i=1Nrhpk-2,i2hi,pk-12dpk-2,imdi,pk-1m,where hpk-2,i, hi,pk-1 denote the channel gains from pk-2 to its relay i and from its relay i to pk-1, respectively, and dpk-2,im,di,pk-1m denote the distance from pk-2 to its relay i and from its relay i to pk-1, respectively. So, we can obtain the signal-to-noise ratio (SNR) γj at the receiver node pj as follows: γj=Pp,j-1hpj-1,pj2/σpj-1,pj2dpj-1,pjm, where σpj-1,pj2 denotes the variance of additive white Gaussian noise at receiver pj. Given a targeted throughput R0, if we find the maximum value of l for that log2⁡(1+γl)≥R0 holds, we can derive that the value of l is the largest number of hops supported by the CFP scheme. Therefore, we can derive(6)2l-1log2⁡η+∑k=2llog2⁡∑i=1Nrhpk-2,i2hi,pk-12dpk-2,imdi,pk-1m⁡+log2⁡hpl-1,pl2dpl-1,plmσpl-1,pl2≥log2⁡2R0-1Ps.In formula (6), for calculability, we replace the exponential random variables hpk-2,i2, hi,pk-12, and hpl-1,pl2with their mean values λr, λf, and λd, respectively. Since we have assumed that the channel gain is circular symmetric complex Gaussian random variables with zero mean and unit variance, we get λr=λf=λd=1. Furthermore, we assume that dpk-2,idi,pk-1 is constant and equal to dc. Also, dpl-1,pl, which is the distance from pl-1 to pl, is set to be constant value dd. Consequently, we can obtain (7)l-1log2⁡η2Nrdcm≥log2⁡2R0-1Psddmσ2,where we letσpl-1,pl2 be equal to constant value σ2. In formula (7), if 2R0-1ddmσ2>Ps, that is, log2⁡Ps/ddmσ2+1<R0, the signal cannot be transmitted from the source node to the next hop for satisfying the targeted throughput R0. Therefore, for multihop transmission, it is required that 2R0-1ddmσ2<Ps. Furthermore, we consider that, in a routing path (such as in Figure 1), the transmission power of node pi+1 is lower than that of node pi because the transmission power of node pi+1 is charged from the node pi. So, it is also required that η2Nr/dcm<1. Note that we do not consider the case of η2Nr/dcm≥1 because, in this case, the transmission power of node pi+1 is greater than that of node pi so that the information can be transmitted all the time. Accordingly, we can derive the largest number of hops Lmaxcfp supported by the CFP scheme as follows:(8)Lmaxcfp=1+log2⁡2R0-1/Psddmσ2log2⁡η2Nr/dcm,where . denotes the round down function. From formula (8), we can find that the largest number of hops is affected by the parameters Ps, η, α, Nr, and dc. In simulation, we will give the detailed analysis for these parameters.


## 5.2. For CFIP Scheme

Unlike CFP scheme, in CFIP scheme, a relayi not only harvests the power, but also decodes the information from the transmitter. So, we have αi≠0. If we consider that the transmitter is the source node, a relay i harvests the power Er,i′ as follows:(9)Er,i′=η1-αPshs,i2Tt,vds,im.Note here that, for ease of analysis, we let αi be constant and equal to α. Let Pp,j-1′ denotejth (j≥2) hop transmission power, where the signal is transmitted from pj-1 to pj through multiple relays; we can obtain(10)Pp,j-1′=η1-α2j-1Ps×∏k=2j∑i=1Nr′hpk-2,i2hi,pk-12dpk-2,imdi,pk-1m,where Nr′ is the average number of relay nodes in cooperative set. Note that, because only the relay, which can decode the information successfully, becomes one member of the cooperative set in CFIP scheme, we have Nr′≤Nr. Let γj′ denote SNR at the receiver node pj; we can derive(11)γj′=η1-α∑i=1Nr′Pp,j-1′hpj-1,i2hi,pj2dpj-1,imdi,pjmσi,pj2,where σi,pj2 is the variance of additive white Gaussian noise at receiver pj. Similarly to the above analysis for CFP, while requiring log2⁡1+γl′≥R0, we can obtain(12)l-1log2⁡η1-α2Nr′dcm≥log2⁡2R0-1dcmσ2η1-αNr′Ps,where we let σi,pj2 be equal to constant value σ2. In formula (12), we have η1-α2Nr′/dcm<1 because the transmission power of node pi+1 is lower than that of node pi. Furthermore, for multihop transmission, we have 2R0-1dcmσ2/η1-αNr′Ps<1; that is, log2⁡η1-αPsNr′/dcmσ2+1>R0. Otherwise, the information cannot be transmitted from the source to p1. Consequently, the largest number of hops Lmaxcfip supported by the CFIP scheme can be given as follows:(13)Lmaxcfip=1+log2⁡2R0-1dcmσ2/η1-αNr′Pslog2⁡η21-α2Nr′/dcm.


## 5.3. For DFIP Scheme

Unlike CFP and CFIP schemes, in DFIP scheme, the receiver harvests the power and decodes the information from the transmitter directly without relay cooperation. Therefore, if we consider that the transmitter is the source node, the receiverp1 harvests the power Ed,1 as follows:(14)Ed,1=η1-αPshs,12Tt,vds,1m,where hs,1 is channel gain from the source node to receiver p1 and ds,1 is the distance from the source to p1. Then, the node p1 transmits the information to the next hop node p2 using the power Pd,1=Ed,1/Tt,v. Let Pd,j-1 denote jth (j≥2) hop transmission power, where the signal is transmitted from pj-1 to pj; we can obtain (15)Pd,j-1=η1-αj-1Ps∏k=2jhpk-2,k-12dpk-2,k-1m.So, we can obtain SNR γjd at receiver pj as γjd=Pd,j-1hpj-1,pj2/σpj-1,pj2dpj-1,pjm. Similarly to the above analysis for CFP and CFIP, while requiring log2⁡(1+γld)≥R0, we can obtain (16)l-1log2⁡η1-αddm≥log2⁡2R0-1Psddmσ2.Accordingly, we can derive the largest number of hops Lmaxdfip supported by the DFIP scheme as follows:(17)Lmaxdfip=1+log2⁡2R0-1/Psddmσ2log2⁡η1-α/ddm.In formula (17), we have η1-α/ddm<1 because the transmission power of node pi+1 is lower than that of node pi. For multihop transmission, it is required that 2R0-1ddmσ2<Ps. Otherwise, the information cannot be transmitted from the source to p1.


## 6. Numerical Results and Analysis

In this section, we perform computer simulations to validate our theory analysis and gain insights into the multihop capabilities of the proposed CFP, CFIP, and DFIP schemes. Also, we need to observe whether the values ofLmaxcfp scheme are larger than the values of Lmaxcfip and Lmaxdfip with the given targeted throughput R0 under the effect of different network parameters. In the following simulations, we set σ2=-70 dB, R0=2 bits/sec/Hz, and m=2.7 (which corresponds to an urban cellular network environment [5]) and give the numerical results considering the effect of parameters Ps, η, α, Nr, and dc. For simplicity, we assume that dd=dc and Nr′=Nr.First, we observe the numerical results about the values ofLmaxcfp, Lmaxcfip, and Lmaxdfip affected by the values of cooperative transmission distance (CTD) dc that denotes the product of two distances from sender to relay and from relay to receiver, which are shown in Figure 2. From Figure 2, we can find that the analytical results are practically consistent with the simulation results, which verifies the effectiveness of our theory analytical model. Note that, for CFIP scheme, the simulation results are not in full agreement with the analysis results because Nr′ is smaller than Nr in practice. Besides, we can also observe the following:(1)
The CTD has an important impact on the largest number of transmission hops; it is because, with the increase ofdc, both the harvested energy and received signal strength at sender node of the next hop decrease due to the larger path loss. Consequently, the achievable number of transmission hops is reduced with no sufficient energy, especially for the larger values of dc.(2)
The multihop capability of CFP is better than CFIP and DFIP; it is because, in CFP scheme, multiple relays forward only the power (not the information) towards the receiver cooperatively so that the sender node of the next hop can obtain more energy to support the larger transmission hops, especially for the smaller values ofdc.(3)
The multihop capability of CFP and CFIP is better than DFIP since they use multiple relays to harvest energy. It can be observed in (8) and (13) that the values of Lmaxcfp and Lmaxcfip increase with the increase of Nr and Nr′. Furthermore, if we consider the fact that the value of Nr is larger than Nr′, this can further the multihop capability of CFP compared to CFIP.Figure 2
Analytical versus simulation results with different CTD, wherePs=2W, η=0.6, α=0.5, and Nr=10.As the analytical results agree well with the simulation results, for the purpose of conciseness, in the following, we will plot the simulation results for different parametersη, α, Nr, and Ps when dc=3m. But for dc=8m and dc=15m, we only give analytical results. Next, we investigate the impacts of two parameters η and α on the largest number of transmission hops, respectively, with considering the effect of CTD dc. From Figures 3 and 4, we can obtain the following:(1)
For the small values ofdc, by increasing the value of η or reducing the value of α, the largest number of transmission hops can be improved. But if increasing the value of dc, the largest number of transmission hops cannot obtain obvious improvement through changing the values of η or α. In (8), (13), and (17), because η and α have a limited range of values (∈0,1), while dc has a larger value, the values of Lmaxcfp, Lmaxcfip, and Lmaxdfip cannot be affected obviously by changing the values of η or α.(2)
The multihop capability of CFP is better than CFIP and DFIP, especially for the smaller values ofdc, which is because multiple relays forward only the power cooperatively. For example, from Figure 3, we can observe the impact of parameter η on results and obtain that when dc=3m, the average largest number of hops of CFP, CFIP, and DFIP is 18, 8, and 4.9, respectively; when dc=8m, the average values are 4.5, 3.8, and 2.9, respectively; when dc=15m, the average values are 3.1, 2.8, and 2, respectively.Figure 3
Numerical results for the impact of parameterη on the multihop capability with different values of CTD: (a) dc=3m, (b) dc=8m, and (c) dc=15m, where Ps=2W, α=0.5, and Nr=20.
(a)
(b)
(c)Figure 4
Numerical results for the impact of parameterα on the multihop capability with different values of CTD: (a) dc=3m, (b) dc=8m (c), and dc=15m, where Ps=2W, η=0.6, and Nr=20.
(a)
(b)
(c)Finally, let us study the impacts of two parametersNr and Ps on the multihop capability, respectively. In Figure 5, we give the simulation results for the effect of parameter Nr with considering the effect of dc. Considering that X<1 of fractional denominator log2⁡X in (8) and (13), we consider a larger range of values of Nr and vary the values of Nr for different values of dc (i.e., let the maximum value of Nr be equal to dc2.7). In order to facilitate drawing, a numerical value x on the x-axis of Figure 5 only denotes an exponential quantity, and in fact, the corresponding value of Nr is equal to dcx. From Figure 5, we can see the following:(1)
With the increase ofNr, the multihop capabilities of three schemes are improved correspondingly, and the multihop capability of CFP is better than CFIP and DFIP. Specifically, when dc=3m, the average largest number of hops of CFP, CFIP, and DFIP is 10.3, 6.3, and 5, respectively; when dc=8m, the average values are 7.5, 5.1, and 3, respectively; when dc=15m, the average values are 6, 4.6, and 2, respectively.(2)
Although, with the increase ofdc, the multihop capabilities of three schemes are weakened correspondingly, the degree of weakening is depressed compared with the case of considering the effect of parameters η or α. For example, considering that the value of dc changes from 3m to 15m in CFP scheme, the degree of weakening is 10.3-6/10.3×100%=27.18% when considering the effect of parameter Nr, but the value is 18-3.1/18×100%=82.78% when considering the effect of parameter η. Therefore, increasing the number Nr of relay nodes can improve the multihop capabilities effectively when the CTD dc increases; it is because Nr has a larger range value and can affect the values of Lmaxcfp, Lmaxcfip, and Lmaxdfip in (8), (13), and (17), obviously.Figure 5
Numerical results for the impact of parameterNr on the multihop capability with different values of CTD: (a) dc=3m, (b) dc=8m, and (c) dc=15m, where Ps=2W, η=0.6, and α=0.5.
(a)
(b)
(c)In Figure6, we investigate the impact of parameter Ps on the numerical results with considering the effect of dc. In order to compare the results with parameter Nr in a larger range of values, we also let a numerical value x on the x-axis of Figure 6 only denote an exponential quantity, where the corresponding value of Ps is equal to dcx. From Figure 6, we can observe the following:(1)
With the increase ofPs, the multihop capabilities of the three schemes are improved correspondingly, and the multihop capability of CFP is better than CFIP and DFIP. However, with the increase of dc, the multihop capabilities of the three schemes are weakened correspondingly. Specifically, when dc=3m, the average largest number of hops of CFP, CFIP, and DFIP is 21.4, 9.9, and 5.5, respectively; when dc=8m, the average values are 5.9, 4.8, and 3.4, respectively; when dc=15m, the average values are 4.1, 3.6, and 2.8, respectively.(2)
Compared with the case of considering the effect of parameterNr, the degree of weakening is much worse. For example, considering that the value of dc changes from 3 m to 15 m in CFP scheme, the degree of weakening is 21.4-4.1/21.4×100%=80.8% when considering the effect of parameter Ps, but the value of the degree of weakening is 10.3-6/10.3×100%=27.18% when considering the effect of parameter Nr. Therefore, for improving the multihop capabilities, increasing the value of parameter Nr is more effective.Figure 6
Numerical results for the impact of parameterPs on the multihop capability with different values of CTD: (a) dc=3m, (b) dc=8m, and (c) dc=15m, where η=0.6, α=0.5, and Nr=20.
(a)
(b)
(c)According to the abovementioned results and analysis, we can obtain the important conclusions as follows: (1) the multihop capability of CFP is better than CFIP and DFIP, (2) all of the parametersPs, η, α, Nr, and dc can affect the multihop capability of the three schemes, where the parameter dc can produce an important effect, and (3) for improving the multihop capability, it is best effective to increase the value of parameter Nr. Of course, we can further improve the multihop capability by simultaneously adjusting the values of parameters Ps, η, and α.


## 7. Conclusions

In this paper, we study SWIPT in multihop wireless cooperative networks, where the multihop capabilities of CFP, CFIP, and DFIP schemes, are analyzed. For this purpose, we construct analysis model to investigate the multihop capabilities of CFP, CFIP, and DFIP schemes, respectively. Finally, numerical results show that the multihop capability of CFP is better than CFIP and DFIP, and for improving the multihop capabilities, it is best effective to increase the average number of relay nodes in cooperative set.Through the analysis model proposed in this paper, the appropriate values of related parameters, that is, initial energy of source node, the number of relay nodes, the energy harvesting efficiency coefficient, and power splitting coefficient, can be set to achieve the given transmission hops from source to destination.



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*Source: 1857015-2018-01-17.xml*