# An Energy-Efficient Scheme for Multirelay Cooperative Networks with Energy Harvesting

Authors: Dingcheng Yang; Chuanqi Zhu; Lin Xiao; Xiaomei Shen; Tiankui Zhang
Journal: Mobile Information Systems
 (2016)

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## Abstract

This study investigates an energy-efficient scheme in multirelay cooperative networks with energy harvesting where multiple sessions need to communicate with each other via the relay node. A two-step optimal method is proposed which maximizes the system energy efficiency, while taking into account the receiver circuit energy consumption. Firstly, the optimal power allocation for relay nodes is determined to maximize the system throughput; this is based on directional water-filling algorithm. Secondly, using quantum particle swarm optimization (QPSO), a joint relay node selection and session grouping optimization is proposed. With this algorithm, sessions can be classified into multiple groups that are assisted by the specific relay node with the maximum energy efficiency. This approach leads to a better global optimization in searching ability and efficiency. Simulation results show that the proposed scheme can improve the energy efficiency effectively compared with direct transmission and opportunistic relay-selected cooperative transmission.


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## Body

## 1. Introduction

With the rapid growth of wireless communications, it is important to consider the costs in energy usage. This is especially true in cooperative networks where nodes are powered by batteries with finite capacities, as energy efficiency is critical because it affects the operation time of the network [1]. Hence, improving the energy efficiency for cooperative networks is essential to mitigate the limited energy available in nodes. Therefore, this gives us a good motivation to investigate the energy efficiency in cooperative networks.Network-coded cooperation schemes are considered as a promising technology to improve energy efficiency and network throughput [2]. Network coding nodes combine multiple input data into one output stream to reduce the number of transmission time slots. However, the receiver circuit power consumption when network coding is used has not been rigorously considered before, an omission that is addressed in this paper.Moreover, energy harvesting is a promising technique that can be used in relay nodes to increase flexibility and reduce the energy charge; it can bring more energy efficiency for wireless networks [3]. Most of the existing studies focus on power allocation schemes for relay nodes in a scenario with multiple unicast sessions. However, when using network coding, the network coding noise and receiver circuit power consumption increase as the size of session groups increases. Hence, there is a need to study how to perform relay node selection and session grouping for energy-efficient multirelay cooperative networks and that is the topic of this paper.


### 1.1. Related Work

Research about network-coded cooperative networks to improve network throughput is considered in [4–8]. In [3], the concept of network coding noise which hinders the performance of the overall network was first introduced. In [5], the authors analyzed the origin of the noise by studying signal aggregation at relay nodes and signal extraction at destination nodes. In [6], two novel closed-form power allocation scheme was proposed to reduce network coding noise in two-unicast wireless systems. Based on [6], a joint group assignment and power allocation algorithm were studied in [7]; this aims to reduce network coding noise in a multiunicast cooperative network. Furthermore, the relay selection and session grouping problem was investigated in [8], as session grouping can effectively reduce network coding noise. However, in all of these works, the circuit energy consumption with network coding was not considered.To achieve better tradeoff between network throughput and power consumption, the metric energy efficiency is used in [9–11]. In [9], the authors studied the energy-efficient relay selection and power allocation problem for a two-way relay channel based on network coding. Paper [10] presented an opportunistic listening scheme to promote energy efficiency for network-coded cooperative networks in two-unicast sessions. Paper [11] proposed an energy-efficient multicast scheme with network coding.Moreover, energy harvesting technologies for cooperative networks have been investigated in [12–17] and these represent a promising approach for powering nodes. In [12], an opportunistic wireless information and energy transfer relaying scheme was proposed by Lagrangian optimality. Reference [13] used the directional water-filling algorithm to maximize the sum-rate.In cooperative relay networks with energy harvesting, the relay nodes selected and the choice of power allocation scheme have a great impact on the system performance. In [14], finite energy storage was considered in relay nodes and a relay selection scheme was proposed based on finite-state Markov chain. In [15, 16], the source nodes and relay nodes were considered as energy harvesting nodes, and then the system throughput was maximized by optimizing both relay selection and power allocation.Another line of work on joint wireless energy and information transmission in relay networks is simultaneous wireless information and power transfer (SWIPT). Researchers have focused on improving energy efficiency and a particularly relevant piece of work is [17]. To maximize the total energy efficiency, the authors proposed a joint relay selection and resource allocation scheme for SWIPT relay networks with multiple source nodes and destination nodes pairs and energy harvesting relay nodes.Improving the energy efficiency in relay networks is of critical importance for resolving the energy shortage of nodes. In the literature [14–17], the energy arrival time and the amount of harvested energy are known prior to transmission. However, in real systems, the amount of the harvested energy is affected by many factors, such as weather and channel conditions, so it is necessary to consider a transmission scheme that can efficiently use the harvested energy from random energy sources.


### 1.2. Contributions and Organization

In this paper, we focus on a multirelay cooperative network, where relay nodes are powered by random energy sources. Unlike previous works, our study considers network coding, finite energy storage, and energy harvesting. The aim of this paper is to optimize energy efficiency in multirelay cooperative networks with energy harvesting. In [18], we have proposed an energy-efficient session grouping scheme in a single relay network-coded cooperative network. In this work, we extend our previous work to a multirelay cooperative network and consider the energy harvesting technology.Our contributions are concluded in three aspects:(i)
The receiver circuit power consumption with network coding is analyzed.(ii)
An optimal power allocation for relay nodes is proposed based on the directional water-filling algorithm.(iii)
An energy-efficient relay selection and session grouping scheme is proposed based on the quantum particle swarm optimization (QPSO).The rest of this paper is organized as follows. Section2 presents the network model including the throughput model and power consuming model. Section 3 studies the optimal power allocation scheme and jointly optimizing multirelay selection and session grouping scheme. Section 4 shows the numerical results and analysis for the proposed scheme. Section 5 is the conclusion of this paper.


## 1.1. Related Work

Research about network-coded cooperative networks to improve network throughput is considered in [4–8]. In [3], the concept of network coding noise which hinders the performance of the overall network was first introduced. In [5], the authors analyzed the origin of the noise by studying signal aggregation at relay nodes and signal extraction at destination nodes. In [6], two novel closed-form power allocation scheme was proposed to reduce network coding noise in two-unicast wireless systems. Based on [6], a joint group assignment and power allocation algorithm were studied in [7]; this aims to reduce network coding noise in a multiunicast cooperative network. Furthermore, the relay selection and session grouping problem was investigated in [8], as session grouping can effectively reduce network coding noise. However, in all of these works, the circuit energy consumption with network coding was not considered.To achieve better tradeoff between network throughput and power consumption, the metric energy efficiency is used in [9–11]. In [9], the authors studied the energy-efficient relay selection and power allocation problem for a two-way relay channel based on network coding. Paper [10] presented an opportunistic listening scheme to promote energy efficiency for network-coded cooperative networks in two-unicast sessions. Paper [11] proposed an energy-efficient multicast scheme with network coding.Moreover, energy harvesting technologies for cooperative networks have been investigated in [12–17] and these represent a promising approach for powering nodes. In [12], an opportunistic wireless information and energy transfer relaying scheme was proposed by Lagrangian optimality. Reference [13] used the directional water-filling algorithm to maximize the sum-rate.In cooperative relay networks with energy harvesting, the relay nodes selected and the choice of power allocation scheme have a great impact on the system performance. In [14], finite energy storage was considered in relay nodes and a relay selection scheme was proposed based on finite-state Markov chain. In [15, 16], the source nodes and relay nodes were considered as energy harvesting nodes, and then the system throughput was maximized by optimizing both relay selection and power allocation.Another line of work on joint wireless energy and information transmission in relay networks is simultaneous wireless information and power transfer (SWIPT). Researchers have focused on improving energy efficiency and a particularly relevant piece of work is [17]. To maximize the total energy efficiency, the authors proposed a joint relay selection and resource allocation scheme for SWIPT relay networks with multiple source nodes and destination nodes pairs and energy harvesting relay nodes.Improving the energy efficiency in relay networks is of critical importance for resolving the energy shortage of nodes. In the literature [14–17], the energy arrival time and the amount of harvested energy are known prior to transmission. However, in real systems, the amount of the harvested energy is affected by many factors, such as weather and channel conditions, so it is necessary to consider a transmission scheme that can efficiently use the harvested energy from random energy sources.


## 1.2. Contributions and Organization

In this paper, we focus on a multirelay cooperative network, where relay nodes are powered by random energy sources. Unlike previous works, our study considers network coding, finite energy storage, and energy harvesting. The aim of this paper is to optimize energy efficiency in multirelay cooperative networks with energy harvesting. In [18], we have proposed an energy-efficient session grouping scheme in a single relay network-coded cooperative network. In this work, we extend our previous work to a multirelay cooperative network and consider the energy harvesting technology.Our contributions are concluded in three aspects:(i)
The receiver circuit power consumption with network coding is analyzed.(ii)
An optimal power allocation for relay nodes is proposed based on the directional water-filling algorithm.(iii)
An energy-efficient relay selection and session grouping scheme is proposed based on the quantum particle swarm optimization (QPSO).The rest of this paper is organized as follows. Section2 presents the network model including the throughput model and power consuming model. Section 3 studies the optimal power allocation scheme and jointly optimizing multirelay selection and session grouping scheme. Section 4 shows the numerical results and analysis for the proposed scheme. Section 5 is the conclusion of this paper.


## 2. Network Model

As is depicted in Figure1, we consider a network-coded cooperative network which consists of N sessions and K relay nodes in a square with dimensions D×D. In this model, we assume that the relay nodes operate in amplify-and-forward (AF) mode and use orthogonal channels. Sessions that select the same node share one channel and transmit data under time division multiple access (TDMA). Moreover, the relay nodes can harvest energy from random energy sources, such as wind energy and solar energy.Figure 1
Multirelay cooperative network model.


### 2.1. Total Throughput

In cooperative relaying networks, there are three transmission schemes: (i) direct transmission, (ii) opportunistic relay-selected cooperative transmission, and (iii) network-coded cooperative transmission. The transmitting power of relay nodes is not constant since the random energy arrivals in the relay nodes.In network-coded cooperative networks, sessions in a group are assumed to be relayed in equal power.Prkm is defined as the transmit power of relay node rk for group m. The amplification factor αrkm for rk is expressed as(1)αrkm2=PrkmGmrkσrk2+∑sl∈GmrkPslhslrk2,where Gmrk denotes the set of sessions in group m for rk, Gmrk is the cardinality of Gmrk, and Psl captures the transmit power of source node sl.Under network-coded cooperative networks, there exits network coding noise (NC noise) at each destination node, when extracting desired data from the combined data. We assume that a sessionsn,dn is in a group Gmrk, so the NC noise zdnNC at dn is expressed as(2)zdnNC=zdn+∑sl∈Gmrksl≠snαrkhrkdnzrk-∑sl∈Gmrksl≠snαrkhrkdnhslrkhsldnzdn,where zdn and zrk are the Gaussian noise at dn and rk, respectively, and huv denotes the channel gain between node u and node v.Suppose that the channel between all nodes follows a simplified channel model that combines the distance-dependent signal attenuation and long term shadowing with loss exponentα>2. Thus, huv can be expressed as huv=u-v-α, where u-v represents the distance between node u and node v and α is the channel loss exponent. From (2), the variance of the NC noise at dn is shown as (3)σdnNC2=σdn2+Gmrk-1αrkmhrkdn2σrk2+σdn2∑sl∈Gmrksl≠snαrkmhslrkhrkdnhsldn2.A session has the option to select a relay node from different available relay nodes in our network. In addition, each session may use at most one relay node. We assume thatN sessions are sorted into M groups, each session belongs to only one group. For notational simplicity, G0rk is defined as the direct transmission group by using the channel of rk. We consider data transmission for each group (Gmrk sessions) in a time frame T, which is equally divided into Gmrk+1 time slots. For the first Gmrk time slots, source nodes transmit data one by one, while the relay node and each destination node keep receiving data from all source nodes. At the last time slot, rk transmits the combined data, which is received by each destination node to extract desired data. tn is defined as the time duration of each session; then, we have(4)tn=T∑m=0MGmrk·GmrkGmrk+1.Thus, the throughput for a session sn,dn is shown as(5)RNCsn,rk,Gmrk=tn·W·INCsn,rk,GmrkT=W∑m=0MGmrk×GmrkGmrk+1×INCsn,rk,Gmrk,where sn,dn∈Gmrk and W is the bandwidth of each relay node. INCsn,rk,Gmrk is the mutual information for a session sn,dn; it is expressed as (6)INCsn,rk,Gmrk=log2⁡1+γsndn+γsnrkγrkdnGmrkσdnNC2/σdn2+γrkdn+σdnNC2/σdn2∑sl∈Gmrkγslrk,where γsndn=Psn/σdn2hsndn2, γsnrk=Psn/σrk2hsnrk2, and γrkdn=Prk/σdn2hrkdn2. From (5) and (6), the throughput for a session sn,dn under network-coded cooperative transmission scheme is (7)RNCsn,rk,dn=W∑m=0MGmrk×GmrkGmrk+1×log2⁡1+γsndn+γsnrkγrkdnGmrkσdnNC2/σdn2+γrkdn+σdnNC2/σdn2∑sl∈Gmrkγslrk.Similar to our previous work, for opportunistic cooperative communication scheme and network-coded cooperative communication without grouping scheme, throughput (7) is also appropriate when Gmrk=1 and Gmrk=N, respectively [18]. Under direct transmission scheme, the throughput for sn,dn is(8)RDsn,rk,dn=W∑m=0MGmrk×log⁡1+sndn.


### 2.2. Power Consumption

In this part, we derive the expression of total power consumption in network-coded cooperative networks.We denote the transmission power for source nodes asPs. Assuming that the transmitting circuit power Pct and the receiver circuit power Pcr are the same, for a group in network-coded cooperative networks with grouping scheme, the destination nodes keep receiving data, while the relay node keeps receiving data except for the last slot. The receiving time for each destination node in a group Gmrk is(9)td-cr=T∑m=0MGmrk·Gmrk.Thus, in a time frameT, the total receiver circuit energy consumption at destination nodes is (10)Ed_crGmrk=td_crPcrGmrk.Let tr-cr denote the receiving time of relay node rk for Gmrk; then, we have(11)tr-cr=T∑m=0MGmrk·Gmrk2Gmrk+1.We assume that the transmission time tsend of source nodes and relay nodes for Gmrk are the same; it is shown as(12)tsend=T∑m=0MGmrk·GmrkGmrk+1.Thus, the total energy consumption for the source nodes and relay nodes can be written as follows, respectively:(13)EstGmrk=Ps+Pct·tsend·Gmrk,ErksumGmrk=Prkm+Pct·tsend+Pcr·trcr.Until now, the total power consumption for transmitting Gmrk is (14)PGmrk=Ed_crGmrk+Es_tGmrk+Erk_sumGmrkT,m≥1.From (14), the total power consumption consists of three main components: source nodes, relay nodes, and destination nodes. From (11)–(13), P(Gmrk) can be rewritten as follows:(15)PGmrk=1∑m=0MGmrk·Gmrk2Gmrk+1·Ps+1+1GmrkPct+2+GmrkPcr+PrkmGmrk.For opportunistic cooperative communication scheme and network-coded cooperative communication without grouping scheme, the total receiver circuit power consumption for a groupGmrk is obtained by substituting Gmrk=1 and Gmrk=N into (15). For the direct transmission group, each destination node keeps receiving data for its time slot. Hence, the power consumption of direct transmission group can be expressed as(16)PG0rk=G0rk∑m=0MGmrk·Pcr+Ps+Pct.Combining (15) and (16), the expression of total power consumption in network-coded cooperative networks is(17)Ptotal=∑k=1K∑m=0M-1PGmrk.


## 2.1. Total Throughput

In cooperative relaying networks, there are three transmission schemes: (i) direct transmission, (ii) opportunistic relay-selected cooperative transmission, and (iii) network-coded cooperative transmission. The transmitting power of relay nodes is not constant since the random energy arrivals in the relay nodes.In network-coded cooperative networks, sessions in a group are assumed to be relayed in equal power.Prkm is defined as the transmit power of relay node rk for group m. The amplification factor αrkm for rk is expressed as(1)αrkm2=PrkmGmrkσrk2+∑sl∈GmrkPslhslrk2,where Gmrk denotes the set of sessions in group m for rk, Gmrk is the cardinality of Gmrk, and Psl captures the transmit power of source node sl.Under network-coded cooperative networks, there exits network coding noise (NC noise) at each destination node, when extracting desired data from the combined data. We assume that a sessionsn,dn is in a group Gmrk, so the NC noise zdnNC at dn is expressed as(2)zdnNC=zdn+∑sl∈Gmrksl≠snαrkhrkdnzrk-∑sl∈Gmrksl≠snαrkhrkdnhslrkhsldnzdn,where zdn and zrk are the Gaussian noise at dn and rk, respectively, and huv denotes the channel gain between node u and node v.Suppose that the channel between all nodes follows a simplified channel model that combines the distance-dependent signal attenuation and long term shadowing with loss exponentα>2. Thus, huv can be expressed as huv=u-v-α, where u-v represents the distance between node u and node v and α is the channel loss exponent. From (2), the variance of the NC noise at dn is shown as (3)σdnNC2=σdn2+Gmrk-1αrkmhrkdn2σrk2+σdn2∑sl∈Gmrksl≠snαrkmhslrkhrkdnhsldn2.A session has the option to select a relay node from different available relay nodes in our network. In addition, each session may use at most one relay node. We assume thatN sessions are sorted into M groups, each session belongs to only one group. For notational simplicity, G0rk is defined as the direct transmission group by using the channel of rk. We consider data transmission for each group (Gmrk sessions) in a time frame T, which is equally divided into Gmrk+1 time slots. For the first Gmrk time slots, source nodes transmit data one by one, while the relay node and each destination node keep receiving data from all source nodes. At the last time slot, rk transmits the combined data, which is received by each destination node to extract desired data. tn is defined as the time duration of each session; then, we have(4)tn=T∑m=0MGmrk·GmrkGmrk+1.Thus, the throughput for a session sn,dn is shown as(5)RNCsn,rk,Gmrk=tn·W·INCsn,rk,GmrkT=W∑m=0MGmrk×GmrkGmrk+1×INCsn,rk,Gmrk,where sn,dn∈Gmrk and W is the bandwidth of each relay node. INCsn,rk,Gmrk is the mutual information for a session sn,dn; it is expressed as (6)INCsn,rk,Gmrk=log2⁡1+γsndn+γsnrkγrkdnGmrkσdnNC2/σdn2+γrkdn+σdnNC2/σdn2∑sl∈Gmrkγslrk,where γsndn=Psn/σdn2hsndn2, γsnrk=Psn/σrk2hsnrk2, and γrkdn=Prk/σdn2hrkdn2. From (5) and (6), the throughput for a session sn,dn under network-coded cooperative transmission scheme is (7)RNCsn,rk,dn=W∑m=0MGmrk×GmrkGmrk+1×log2⁡1+γsndn+γsnrkγrkdnGmrkσdnNC2/σdn2+γrkdn+σdnNC2/σdn2∑sl∈Gmrkγslrk.Similar to our previous work, for opportunistic cooperative communication scheme and network-coded cooperative communication without grouping scheme, throughput (7) is also appropriate when Gmrk=1 and Gmrk=N, respectively [18]. Under direct transmission scheme, the throughput for sn,dn is(8)RDsn,rk,dn=W∑m=0MGmrk×log⁡1+sndn.


## 2.2. Power Consumption

In this part, we derive the expression of total power consumption in network-coded cooperative networks.We denote the transmission power for source nodes asPs. Assuming that the transmitting circuit power Pct and the receiver circuit power Pcr are the same, for a group in network-coded cooperative networks with grouping scheme, the destination nodes keep receiving data, while the relay node keeps receiving data except for the last slot. The receiving time for each destination node in a group Gmrk is(9)td-cr=T∑m=0MGmrk·Gmrk.Thus, in a time frameT, the total receiver circuit energy consumption at destination nodes is (10)Ed_crGmrk=td_crPcrGmrk.Let tr-cr denote the receiving time of relay node rk for Gmrk; then, we have(11)tr-cr=T∑m=0MGmrk·Gmrk2Gmrk+1.We assume that the transmission time tsend of source nodes and relay nodes for Gmrk are the same; it is shown as(12)tsend=T∑m=0MGmrk·GmrkGmrk+1.Thus, the total energy consumption for the source nodes and relay nodes can be written as follows, respectively:(13)EstGmrk=Ps+Pct·tsend·Gmrk,ErksumGmrk=Prkm+Pct·tsend+Pcr·trcr.Until now, the total power consumption for transmitting Gmrk is (14)PGmrk=Ed_crGmrk+Es_tGmrk+Erk_sumGmrkT,m≥1.From (14), the total power consumption consists of three main components: source nodes, relay nodes, and destination nodes. From (11)–(13), P(Gmrk) can be rewritten as follows:(15)PGmrk=1∑m=0MGmrk·Gmrk2Gmrk+1·Ps+1+1GmrkPct+2+GmrkPcr+PrkmGmrk.For opportunistic cooperative communication scheme and network-coded cooperative communication without grouping scheme, the total receiver circuit power consumption for a groupGmrk is obtained by substituting Gmrk=1 and Gmrk=N into (15). For the direct transmission group, each destination node keeps receiving data for its time slot. Hence, the power consumption of direct transmission group can be expressed as(16)PG0rk=G0rk∑m=0MGmrk·Pcr+Ps+Pct.Combining (15) and (16), the expression of total power consumption in network-coded cooperative networks is(17)Ptotal=∑k=1K∑m=0M-1PGmrk.


## 3. Joint Optimization of Relay Selection and Session Grouping

In this section, we divide the energy efficiency problem into two subproblems: the power allocation problem and the energy-efficient transmission optimization problem. For the first problem, an energy allocation scheme is proposed based on directional water-filling structure. For the second problem, we use quantum particle swarm optimization (QPSO) and propose a new algorithm which jointly considers relay selection problem and session grouping based on the solution of the first problem.


### 3.1. Optimal Power Allocation

The conventional water-filling algorithm is a useful technique in wireless communication for allocating power between different channels. It implies allocating more power to the channel with the higher SNR. In [19], a directional water-filling algorithm was introduced which considers the causality constraints on the energy usage. In this paper, we solve the optimal power allocation problem based on directional water-filling.The relay nodes harvest energy from unpredictable energy sources, such as solar energy and wind energy which greatly depend on the conditions of the environment.We assume energy arrivalsE1,E2,…,EN occur in the time instants t1,t2,…,tN by a deadline T; the duration of each slot is Ln=tn-tn-1. Let t0=0 for simplicity. The transmission rates are affected by the incoming energy. The objective is to maximize the throughput by optimizing power allocation for relay nodes.It is assumed that the transmit power of each relay is constant within each slot. Each relay node is equipped with an energy receiver. The harvested energy is stored in a rechargeable battery. Thus, the energy causality constraints are obtained as follows:(18)∑n=1nLnPn≤∑n=0n-1Ei,n=1,2,…,N+1,(19)∑n=0nEn-∑n=1nLnPn≤Emax,n=1,…,N,where Pn denotes the transmit power of relay nodes during slot Ln and Emax is the storage capacity of the battery at relay nodes. It is also assumed that E0 is the initial battery energy and E0>0. Then, the optimization problem can be formulated as(20)maxPn≥0∑n=1N+1WLn2log⁡1+Pns.t.∑n=1nLnPn≤∑n=0n-1En,n=1,2,…,N+1∑n=0nEn-∑n=1nLnPn≤Emax,n=1,…,N.Since the objective function in (20) is not convex, constraint (18) and constraint (19) are linear in Pn, which are convex functions. Hence, the above optimization problem is a convex optimization problem. We define the Lagrangian function as follows:(21)ς=∑n=1N+1WLn2log⁡1+Pn-∑n=1N+1τn∑n=1nLnPn-∑n=0n-1En,where τn is the Lagrangian multipliers and τn>0. Additional complimentary slackness conditions can be expressed as follows:(22)τn∑n=1nLnPn-∑n=0n-1En=0,n=1,2,…,N,(23)ηn∑n=0nEn-∑n=1nLnPn-Emax=0,n=1,2,…,N.Since the constraint is satisfied with equality, increasing Pn will increase the objective function. Then, the optimal transmit power during each slot can be obtained by applying the KKT optimality conditions:(24)Pn∗=1∑j=nN+1τn-∑j=nNηn-1,n=1,…,Nand PN+1∗=1/τN+1-1. Pn∗ is unique which satisfies ∑n=1nLnPn=∑n=0n-1En.WhenEmax=∞, since constraints in (19) and slackness conditions in (23) are satisfied, from (24), the optimal power Pn∗ is monotonically increasing: Pn+1∗≥Pn∗. The results indicate that energy can be spread to the future for operating optimally. When the constraint in (18) is not satisfied with equality (∑n=1lLnPn<∑n=0l-1En), then τl=0; thus, Pl∗=Pl+1∗. It shows that the energy is utilized for relay nodes not only in the current slot but also in future slots. When Pn∗<Pn+1∗, it means that the total energy is used for current slot and no energy is used in the future.As proven before, the harvested energy can only be used in the future, which means our algorithm allows energy to only flow to the right. To solve this problem, we propose an optimal power allocation based on directional water-filling.It is assumed that the optimal energy at time instantst1,t2,…,tN is denoted by Et1,Et2,…,EtN and is obtained before the power allocation process. The process of the algorithm is then as follows.Step 1.
Initialize the power allocation flag to 0, and let the algorithm pointer point to the last slottN.Step 2.
Compare the energy level intN with the energy level in tN-1.Step 3.
No power allocation is performed when the energy level in the current slot exceeds the previous slot.Step 4.
If the energy level in the current slot is lower than the previous slot, allocate energy equally to bothtN and tN-1. Set the power allocation flag to 1, mark these two slots as tN-1, and then the algorithm pointer points to tN-1.Step 5.
Point the algorithm pointer to the previous slot.Step 6.
If the pointer reachest1 and the power allocation flag is 1, go to Step 2; if the point reaches t1 and the flag is 0, stop and output Pn∗ as the optimal power allocation; otherwise, go to Step 3.


### 3.2. Multirelay Selection and Session Grouping

Energy efficiency is defined as the ratio of network throughput to total power consumption. Note that (7), (8), and (17) are the functions of Gmrk. It is essential to consider how to put sessions into different groups and select a relay for each group. We define the session grouping results as Θ∈CK×N×M. Θnrk,m indicates whether a session belongs to Gmrk.(25)Θnrk,m=1,sn,dn∈Gmrk,0,otherwise.A session sn,dn can be in at most one group; thus,(26)∑k=1,m=0k=K,m=M-1Θnrk,m=1.The optimization target of session grouping is to maximize the energy efficiency in our network model. We combine (7), (8), and (17) and formulate the optimization problem as(27)maxEE=∑n=1N∑k=1KΘnrk,0RDsn,dn+∑n=1N∑k=1K∑m=1M-1Θnrk,mRNCsn,rk,Gmrk∑k=1K∑m=0M-1PGmrks.t.Gmrk=sn,dn,∀n,Θnrk,m=1∑m=0M-1Θnrk,m=1,∀n,sn∈GmrkΘnrk,m∈0,1,1≤n≤N,0≤m≤M.Obviously, the optimization problem in (27) is a general “0-1” programming problem. However, this is a nonlinear problem that can be solved only by exhaustive search. Since each source node is expected to transmit data to its destination node from K available channels, either with or without the assistance of a relay node, the complexity of exhaustive search is (28)Cexhaustive=2MKN.From (28), the complexity increases exponential with the number of sessions, which is intolerable when the number of sessions is large. To solve this problem, a joint relay selection and session grouping scheme is proposed based on QPSO.QPSO is a novel multiagent optimization system modified by PSO that is inspired by the social behavior of agents. Each agent, called quantum particle, files in a 2N-dimensional space according to the historical experiences of itself and of colleagues. 2N represents the dimension of the optimization problem [20, 21].We define the position of thejth quantum particle as (29)Lj=U⃑V⃑=μj1μj2⋯μjNεj1εj2⋯εjN,where μjn represents the relay number of session sn,dn and εjn represents the group number of session sn,dn. In QPSO algorithm, μjn and εjn are mapped into quantum particle’s bit position which can be expressed as(30)xjn=kmin+μjnkmax-kmin,yjn=mmin+εjnmmax-mmin,where kmax and kmin are the upper bound and lower bound of the relay node number, respectively. Similarly, mmax and mmin express the upper bound and lower bound of the group number.From (30), the quantum particle’s bit position is in the space of 1,K×0,M. Therefore, (29) can be simplified as (31)X⃑Y⃑=xj1xj2⋯xjNyj1yj2⋯yjN.We use the integral functionround(·) to find the optimal Θnrk,m. Thus, the expression of Θnrk,m is shown as(32)Θnrk,m=1,ifroundxjn=k,roundyjn=m,0,otherwise.We set the objective function in (27) as the fitness function. The local optimal bit position of the jth quantum particle is (33)P⃑Q⃑=pj1pj2pj3pj4⋯pjNqj1qj2qj3qj4⋯qjN.The global optimal bit position of the whole quantum particle population is(34)Pg⃑Qg⃑=pg1pg2pg3pg4⋯pgNqg1qg2qg3qg4⋯qgN.In this proposed algorithm, we consider the generation in two dimensions. The quantum rotation angles are calculated by (35)θjni+1=e1pjni-μjni+e2pgni-μjni,φjni+1=e4qjni-εjni+e5qgni-εjni,where e1 and e2 express the relative important degree of P⃑ and Pg⃑, and the updating process of the quantum particle can be expressed as(36)μjni+1=1-μjni2,ifpjni=μjni=pgni,e3<c1,μjnicos⁡θjni-1-μjni2sin⁡θjni,others,εjni+1=1-εjni2,ifqjni=εjni=qgni,e6<c2,εjnicos⁡φjni-1-εjni2sin⁡φjni,others,where e3 and e6 are uniform random number between 0 and 1 and c1 and c2 are mutation probabilities between 0 and 1/N.Assumption 1.
The power allocation process has finished.Assumption 2.
All the channel state information (CSI) is a priori known.Therefore, the process of QPSO algorithm is given in the following steps.Step 1.
Initialize quantum particle population, including the quantum particles’ bit positionsLj and the local optimal bit positions. Calculate the fitness of each quantum particle, and record the global optimal bit position from (27).Step 2.
Update the rotation angle for each quantum particle from (35). Update the bit positions for each quantum particle from (36).Step 3.
Calculate the fitness of all quantum particles based on updated positions.Step 4.
Update the local optimal quantum position for each quantum particle and the global optimal quantum position.Step 5.
If it reaches the predefined value of the maximum generation, stop the process, output the global optimal quantum position, and map it into the final transmission strategy by (30), (31), and (32); if not, go to Step 3.


## 3.1. Optimal Power Allocation

The conventional water-filling algorithm is a useful technique in wireless communication for allocating power between different channels. It implies allocating more power to the channel with the higher SNR. In [19], a directional water-filling algorithm was introduced which considers the causality constraints on the energy usage. In this paper, we solve the optimal power allocation problem based on directional water-filling.The relay nodes harvest energy from unpredictable energy sources, such as solar energy and wind energy which greatly depend on the conditions of the environment.We assume energy arrivalsE1,E2,…,EN occur in the time instants t1,t2,…,tN by a deadline T; the duration of each slot is Ln=tn-tn-1. Let t0=0 for simplicity. The transmission rates are affected by the incoming energy. The objective is to maximize the throughput by optimizing power allocation for relay nodes.It is assumed that the transmit power of each relay is constant within each slot. Each relay node is equipped with an energy receiver. The harvested energy is stored in a rechargeable battery. Thus, the energy causality constraints are obtained as follows:(18)∑n=1nLnPn≤∑n=0n-1Ei,n=1,2,…,N+1,(19)∑n=0nEn-∑n=1nLnPn≤Emax,n=1,…,N,where Pn denotes the transmit power of relay nodes during slot Ln and Emax is the storage capacity of the battery at relay nodes. It is also assumed that E0 is the initial battery energy and E0>0. Then, the optimization problem can be formulated as(20)maxPn≥0∑n=1N+1WLn2log⁡1+Pns.t.∑n=1nLnPn≤∑n=0n-1En,n=1,2,…,N+1∑n=0nEn-∑n=1nLnPn≤Emax,n=1,…,N.Since the objective function in (20) is not convex, constraint (18) and constraint (19) are linear in Pn, which are convex functions. Hence, the above optimization problem is a convex optimization problem. We define the Lagrangian function as follows:(21)ς=∑n=1N+1WLn2log⁡1+Pn-∑n=1N+1τn∑n=1nLnPn-∑n=0n-1En,where τn is the Lagrangian multipliers and τn>0. Additional complimentary slackness conditions can be expressed as follows:(22)τn∑n=1nLnPn-∑n=0n-1En=0,n=1,2,…,N,(23)ηn∑n=0nEn-∑n=1nLnPn-Emax=0,n=1,2,…,N.Since the constraint is satisfied with equality, increasing Pn will increase the objective function. Then, the optimal transmit power during each slot can be obtained by applying the KKT optimality conditions:(24)Pn∗=1∑j=nN+1τn-∑j=nNηn-1,n=1,…,Nand PN+1∗=1/τN+1-1. Pn∗ is unique which satisfies ∑n=1nLnPn=∑n=0n-1En.WhenEmax=∞, since constraints in (19) and slackness conditions in (23) are satisfied, from (24), the optimal power Pn∗ is monotonically increasing: Pn+1∗≥Pn∗. The results indicate that energy can be spread to the future for operating optimally. When the constraint in (18) is not satisfied with equality (∑n=1lLnPn<∑n=0l-1En), then τl=0; thus, Pl∗=Pl+1∗. It shows that the energy is utilized for relay nodes not only in the current slot but also in future slots. When Pn∗<Pn+1∗, it means that the total energy is used for current slot and no energy is used in the future.As proven before, the harvested energy can only be used in the future, which means our algorithm allows energy to only flow to the right. To solve this problem, we propose an optimal power allocation based on directional water-filling.It is assumed that the optimal energy at time instantst1,t2,…,tN is denoted by Et1,Et2,…,EtN and is obtained before the power allocation process. The process of the algorithm is then as follows.Step 1.
Initialize the power allocation flag to 0, and let the algorithm pointer point to the last slottN.Step 2.
Compare the energy level intN with the energy level in tN-1.Step 3.
No power allocation is performed when the energy level in the current slot exceeds the previous slot.Step 4.
If the energy level in the current slot is lower than the previous slot, allocate energy equally to bothtN and tN-1. Set the power allocation flag to 1, mark these two slots as tN-1, and then the algorithm pointer points to tN-1.Step 5.
Point the algorithm pointer to the previous slot.Step 6.
If the pointer reachest1 and the power allocation flag is 1, go to Step 2; if the point reaches t1 and the flag is 0, stop and output Pn∗ as the optimal power allocation; otherwise, go to Step 3.


## 3.2. Multirelay Selection and Session Grouping

Energy efficiency is defined as the ratio of network throughput to total power consumption. Note that (7), (8), and (17) are the functions of Gmrk. It is essential to consider how to put sessions into different groups and select a relay for each group. We define the session grouping results as Θ∈CK×N×M. Θnrk,m indicates whether a session belongs to Gmrk.(25)Θnrk,m=1,sn,dn∈Gmrk,0,otherwise.A session sn,dn can be in at most one group; thus,(26)∑k=1,m=0k=K,m=M-1Θnrk,m=1.The optimization target of session grouping is to maximize the energy efficiency in our network model. We combine (7), (8), and (17) and formulate the optimization problem as(27)maxEE=∑n=1N∑k=1KΘnrk,0RDsn,dn+∑n=1N∑k=1K∑m=1M-1Θnrk,mRNCsn,rk,Gmrk∑k=1K∑m=0M-1PGmrks.t.Gmrk=sn,dn,∀n,Θnrk,m=1∑m=0M-1Θnrk,m=1,∀n,sn∈GmrkΘnrk,m∈0,1,1≤n≤N,0≤m≤M.Obviously, the optimization problem in (27) is a general “0-1” programming problem. However, this is a nonlinear problem that can be solved only by exhaustive search. Since each source node is expected to transmit data to its destination node from K available channels, either with or without the assistance of a relay node, the complexity of exhaustive search is (28)Cexhaustive=2MKN.From (28), the complexity increases exponential with the number of sessions, which is intolerable when the number of sessions is large. To solve this problem, a joint relay selection and session grouping scheme is proposed based on QPSO.QPSO is a novel multiagent optimization system modified by PSO that is inspired by the social behavior of agents. Each agent, called quantum particle, files in a 2N-dimensional space according to the historical experiences of itself and of colleagues. 2N represents the dimension of the optimization problem [20, 21].We define the position of thejth quantum particle as (29)Lj=U⃑V⃑=μj1μj2⋯μjNεj1εj2⋯εjN,where μjn represents the relay number of session sn,dn and εjn represents the group number of session sn,dn. In QPSO algorithm, μjn and εjn are mapped into quantum particle’s bit position which can be expressed as(30)xjn=kmin+μjnkmax-kmin,yjn=mmin+εjnmmax-mmin,where kmax and kmin are the upper bound and lower bound of the relay node number, respectively. Similarly, mmax and mmin express the upper bound and lower bound of the group number.From (30), the quantum particle’s bit position is in the space of 1,K×0,M. Therefore, (29) can be simplified as (31)X⃑Y⃑=xj1xj2⋯xjNyj1yj2⋯yjN.We use the integral functionround(·) to find the optimal Θnrk,m. Thus, the expression of Θnrk,m is shown as(32)Θnrk,m=1,ifroundxjn=k,roundyjn=m,0,otherwise.We set the objective function in (27) as the fitness function. The local optimal bit position of the jth quantum particle is (33)P⃑Q⃑=pj1pj2pj3pj4⋯pjNqj1qj2qj3qj4⋯qjN.The global optimal bit position of the whole quantum particle population is(34)Pg⃑Qg⃑=pg1pg2pg3pg4⋯pgNqg1qg2qg3qg4⋯qgN.In this proposed algorithm, we consider the generation in two dimensions. The quantum rotation angles are calculated by (35)θjni+1=e1pjni-μjni+e2pgni-μjni,φjni+1=e4qjni-εjni+e5qgni-εjni,where e1 and e2 express the relative important degree of P⃑ and Pg⃑, and the updating process of the quantum particle can be expressed as(36)μjni+1=1-μjni2,ifpjni=μjni=pgni,e3<c1,μjnicos⁡θjni-1-μjni2sin⁡θjni,others,εjni+1=1-εjni2,ifqjni=εjni=qgni,e6<c2,εjnicos⁡φjni-1-εjni2sin⁡φjni,others,where e3 and e6 are uniform random number between 0 and 1 and c1 and c2 are mutation probabilities between 0 and 1/N.Assumption 1.
The power allocation process has finished.Assumption 2.
All the channel state information (CSI) is a priori known.Therefore, the process of QPSO algorithm is given in the following steps.Step 1.
Initialize quantum particle population, including the quantum particles’ bit positionsLj and the local optimal bit positions. Calculate the fitness of each quantum particle, and record the global optimal bit position from (27).Step 2.
Update the rotation angle for each quantum particle from (35). Update the bit positions for each quantum particle from (36).Step 3.
Calculate the fitness of all quantum particles based on updated positions.Step 4.
Update the local optimal quantum position for each quantum particle and the global optimal quantum position.Step 5.
If it reaches the predefined value of the maximum generation, stop the process, output the global optimal quantum position, and map it into the final transmission strategy by (30), (31), and (32); if not, go to Step 3.


## 4. Numerical Results

In this section, we show the simulation results to evaluate the performance of our proposed approach. As shown in Figure1, we consider our simulation within a 1000 × 1000 m2 square area. We consider a network randomly consisting of 50–200 sessions and 5–50 relays. For all network instances, we assume that the transmission power of each source node is 1 W and that the channel bandwidth is 22 MHz. The loss exponent α is 4. We assume that the white Gaussian noise at all nodes has a variance of 10−10 W [8]. The circuit power for each node is chosen as 110 mW. For QPSO, we set the maximal generation as 200, h=20, e1=0.15, e2=0.2, e4=0.6, e5=0.7, c1 = 1/(500K), and c2 = 1/(1000M). Each result is obtained from averaging over 50 realizations. Simulation parameters are provided in Table 1.Table 1
Simulation parameters.
Parameters Value Number of sessions 50–200 Number of relay nodes 5–50 Distribution area 1 000 × 1 000  m 2 Channel bandwidth 22 MHz Loss exponent 4 Transmit power of source node 1 W Circuit power 110 mW White Gaussian noise 1 × 10−10 W Number of quantum particles 20 Maximal generation 200 Rotating factor ofθ e 1 = 0.15 ,   e 2 = 0.2 Rotating factor ofφ e 4 = 0.6 ,   e 5 = 0.7 Mutation probability c 1 = 1/(500K) c 2 = 1/(1000M)


### 4.1. System Performance of Relay Node Selection and Session Grouping

First, we consider the system performance of relay node selection and session grouping. We analyze the energy efficiency, total throughput, and power consumption versus the number of sessions. The traditional direct transmission (DT) and opportunistic relay-selected cooperative transmission (CR) are used to provide performance reference for our proposed (NC) scheme. In addition, power allocations are preoptimized in DT, CR, and NC.In CR and NC, the source nodeSn can exploit a relay node based on the energy level at relay node and channel state information (CSI) when it sends data to its destination node. Since the bandwidths of different schemes may be different, the performance is measured in bit/s/Hz.Figure2 shows that the proposed scheme outperforms other two schemes apparently. Increasing number of sessions will increase the possibility of sessions being a reasonable group. As the number of sessions increases, the average throughput of our scheme increases as well. However, in a big number regime, the average throughput is saturated. This is because the increasing NC noise will affect the throughput.Figure 2
Throughput for three transmission schemes.Figure3 is the average power consumption of each transmission scheme. It shows that DT consumes the most power. The reason is that this scheme is transmitting the maximum number of sessions by occupying all possible channels to improve the energy efficiency. This figure also indicates that the average power of CR transmission is the minimum. It is because better cooperative relay nodes are selected to maximize the energy efficiency. Unlike CR transmission, the circuit energy consumption is considered in our scheme. The figure indicates that NC performs better than DT.Figure 3
Average power consumption for three transmission schemes.Figure4 shows the energy efficiency of different transmission schemes. It is observed that our proposed scheme achieves a higher energy efficiency than the other two schemes. This is because both the CSI and the energy level of relay nodes are considered in our scheme.Figure 4
Energy efficiency for three transmission schemes.


### 4.2. System Performance of Power Allocation

Next, we show the performance of power allocation for relay nodes. In Figure5, the proposed scheme is validated. Our approach always outperforms the NC transmission without power allocation for relay nodes. In Figure 5(a), when the number of sessions N increases, the throughput performance gap becomes larger because the efficient power allocation assures uniform distribution. Figure 5(b) presents the average power consumption versus the number of sessions. With increasing number of sessions, the power is continually increasing in both schemes. As shown in the figure, the power allocation scheme costs more power consumption than non-power allocation scheme, since higher throughput will consume more power. In Figure 5(c), the energy efficiency of power allocation scheme is superior to that of non-power allocation scheme. The energy efficiency begins to converge when the number of sessions becomes large, since the existence of NC noise could diminish the advantage of optimal power allocation.Figure 5
System performance of the policy with power allocation for relay nodes.
(a) (b) (c)


## 4.1. System Performance of Relay Node Selection and Session Grouping

First, we consider the system performance of relay node selection and session grouping. We analyze the energy efficiency, total throughput, and power consumption versus the number of sessions. The traditional direct transmission (DT) and opportunistic relay-selected cooperative transmission (CR) are used to provide performance reference for our proposed (NC) scheme. In addition, power allocations are preoptimized in DT, CR, and NC.In CR and NC, the source nodeSn can exploit a relay node based on the energy level at relay node and channel state information (CSI) when it sends data to its destination node. Since the bandwidths of different schemes may be different, the performance is measured in bit/s/Hz.Figure2 shows that the proposed scheme outperforms other two schemes apparently. Increasing number of sessions will increase the possibility of sessions being a reasonable group. As the number of sessions increases, the average throughput of our scheme increases as well. However, in a big number regime, the average throughput is saturated. This is because the increasing NC noise will affect the throughput.Figure 2
Throughput for three transmission schemes.Figure3 is the average power consumption of each transmission scheme. It shows that DT consumes the most power. The reason is that this scheme is transmitting the maximum number of sessions by occupying all possible channels to improve the energy efficiency. This figure also indicates that the average power of CR transmission is the minimum. It is because better cooperative relay nodes are selected to maximize the energy efficiency. Unlike CR transmission, the circuit energy consumption is considered in our scheme. The figure indicates that NC performs better than DT.Figure 3
Average power consumption for three transmission schemes.Figure4 shows the energy efficiency of different transmission schemes. It is observed that our proposed scheme achieves a higher energy efficiency than the other two schemes. This is because both the CSI and the energy level of relay nodes are considered in our scheme.Figure 4
Energy efficiency for three transmission schemes.


## 4.2. System Performance of Power Allocation

Next, we show the performance of power allocation for relay nodes. In Figure5, the proposed scheme is validated. Our approach always outperforms the NC transmission without power allocation for relay nodes. In Figure 5(a), when the number of sessions N increases, the throughput performance gap becomes larger because the efficient power allocation assures uniform distribution. Figure 5(b) presents the average power consumption versus the number of sessions. With increasing number of sessions, the power is continually increasing in both schemes. As shown in the figure, the power allocation scheme costs more power consumption than non-power allocation scheme, since higher throughput will consume more power. In Figure 5(c), the energy efficiency of power allocation scheme is superior to that of non-power allocation scheme. The energy efficiency begins to converge when the number of sessions becomes large, since the existence of NC noise could diminish the advantage of optimal power allocation.Figure 5
System performance of the policy with power allocation for relay nodes.
(a) (b) (c)


## 5. Conclusion

In this paper, we studied the energy efficiency problem in multiple relay cooperative networks with energy harvesting. The energy efficiency is taken as the classic network throughput per power allocation. In the optimization problem, network coding noise and receiver circuit power consumption were considered. This problem can be decomposed into a power allocation problem and an energy-efficient transmission optimization problem. We solved the first problem by proposing a time-power allocation algorithm based on directional water-filling algorithm. The second problem was solved by jointly considering relay selection scheme and session grouping based on quantum particle swarm optimization. Numerical results verified that the proposed transmission scheme effectively improved energy efficiency, compared with direct transmission scheme and opportunistic cooperative transmission scheme.



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*Source: 5618935-2016-12-25.xml*