# Simultaneous Wireless Information and Power Transfer Mechanism in Interference Alignment Relay Networks

Authors: Fahui Wu; Lin Xiao; Dingcheng Yang; Laurie Cuthbert; Xiaoping Liu
Journal: Mobile Information Systems
 (2016)

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## Abstract

This paper considers a simultaneous wireless information and power transfer (SWIPT) mechanism in an interference alignment (IA) relay system, in which source nodes send wireless information and energy simultaneously to relay nodes, and relay nodes forward the received signal to destination nodes powered by harvested energy. To manage interference and utilize interference as energy source, two-SWIPT receiver is designed, namely, power splitting (PS), and antennas switching (AS) has been considered for relay system. The performance of AS- and PS-based IA relay systems is considered, as is a new energy cooperation (ECop) scheme that is proposed to improve system performance. Numerical results are provided to evaluate the performance of all schemes and it is shown from the simulations that the performance of proposed ECop outperformed both AS and PS.


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## Body

## 1. Introduction

Recently, energy harvesting (EH) from radio-frequency (RF) signals has drawn significant attention as it is a promising solution to prolong the lifetime of energy constrained wireless networks, for example, sensor based wireless networks. Since it has practical valuable for enabling both wireless data and wireless energy transmission, EH has a promising future for green communications. Simultaneous wireless information and power transfer (SWIPT) was first proposed in [1], where SWIPT in a point-to-point single-antenna additive white Gauss noise (AWGN) channel was studied from an information-theoretic standpoint. In [2], Grover extended [1] to frequency-selective single-antenna AWGN channels, where nontrivial tradeoff between information rate and harvested energy was demonstrated by varying power allocation over frequency. Optimal designs that take into account cochannel interference of wireless information and power transfer were studied in [3] to achieve different outage energy tradeoff as well as rate-energy tradeoff.Since the application of multiple-input multiple-output (MIMO) technology could significantly enhance the transfer efficiency of both energy and information, SWIPT for MIMO channels has been investigated in [4–6]. In [4], Zhang and Ho studied the performance limits of a three-node MIMO. The work in [4] was extended to cases with imperfect channel state information (CSI) at the transmitter in [5]. In [6], when the CSI is not available at the transmitter, a transmitter design based on random beamforming is proposed for a multiple-input single-output (MISO) SWIPT system with artificial channel fading generated over quasi-static channels. SWIPT is studied in orthogonal frequency division multiplexing (OFDM) systems in [7–9], in broadcast channels [10], and in interference channels [11, 12]. In addition, [13] studied SWIPT in MIMO-OFDMA systems and proposed a SWIPT-enabled architecture to study the power control problem in broadband wireless systems. It is well known that MIMO relay networks can markedly improve spectrum utilization and simultaneously enhance link reliability [14, 15], as well as being an efficient way to provide high quality service at low cost [14–16]. More importantly, the concept of SWIPT is more applicable for short-distance applications since wireless power transfer (WPT) will suffer from high attenuation due to path-loss. MIMO relay systems involving an energy harvesting receiver were studied in [17], in which the joint optimal source and relay precode were designed to achieve different tradeoffs between the energy transfer and the information rate. In [18] a relaying protocol based on time switching (TS) and power splitting (PS) is proposed to enable energy harvesting and information processing at the relay. In [19], the throughput in a classic three-node Gaussian relay channel with decode-and-forward (DF) relaying is analyzed.Interference is well known as being one of the major challenges in the transceiver design of wireless communications. A promising solution to interference management in wireless networks is interference alignment (IA) that has proved its optimality to approach the Shannon capacity of interference networks at high signal-to-noise ratio (SNR) [20]. In IA, the transmitted signals of all the users are jointly designed to constrain all the interference into certain subspaces at the unintended receivers, and the desired signal can be obtained from the remaining interference-subspaces by the decoding matrices at each receiver. To obtain the coding and decoding matrices, numerical iteration is proposed in [20], and the feasibility conditions of IA in multiuser MIMO networks were studied in [21]. Due to its outstanding performance, IA has been successfully applied in various networks [22].The study of SWIPT in IA networks is still at an early stage: although some fundamental work has been done [23, 24], there is not much reported in the literature. In this paper, SWIPT in IA relay networks has been studied, with the performance of antennas switching (AS) and PS-based SWIPT being analyzed.The system sum-rate maximum problem is formulated as a three-step optimization problem. The problem is transformed to a convex problem that can be solved easily. Combining the transfer characteristic of AS and PS, an energy cooperation scheme is proposed that can achieve better performance than either the AS or PS scheme. Also, the degree of freedom (DoF) condition is more flexible than in the AS scheme.SWIPT has proved to be more efficient in spectrum usage than transmitting information and energy in orthogonal time or frequency channels [1]. To settle the interference issue in communication systems, existing interference management techniques, for example, interference cancellation, attempt to avoid or mitigate interference through spectrum scheduling. However, with RF energy harvesting, harmful interference can be turned into useful energy through a scheduling policy. This paper provides new vision to mitigate interference and facilitate SWIPT. Furthermore, cooperative relaying techniques can extend the coverage of source node and help to overcome fading and attenuation by using intermediate relay nodes, resulting in improved network performance in terms of efficiency and reliability. Our paper presents tentative exploration in interference management and improves energy efficiency in relay network; our results can be applied to next generation communication system with ultra-densification network infrastructure.This paper is organized as follows: Section2 introduces the system model and problem formulations; Section 3 presents the solutions for the formulated problems; Section 4 provides numerical examples to validate our results and compare the performances; and Section 5 concludes the paper.


## 2. System Model

As shown in Figure1, K-user interference relay channel is considered, that is, K transmission links of transmitter-relay-receiver.Figure 1
System model ofK-user interference relay channel.It is assumed thatMk, Nk, and Tk antennas are fitted at kth source node, relay node, and destination node, respectively; dkS and dkR data streams are transmitted by kth source node and relay node. We assume there is no direct link between the source and the destination node so that an intermediate DF relay assists the transmission of the source messages to the destination. The energy harvesting enabled relay nodes to first harvest energy and receive information simultaneously through RF signals from the source nodes. Next, the relay nodes use the harvested energy as a source of transmission power to forward the decoded source information to the destination nodes. It is assumed that the processing power required by the information decoding circuitry at the relay is negligible as compared to the power used for signal transmission from the relay to the destination.Communication is performed in two orthogonal time slots and it is assumed that perfect channel state information (CSI) of the network is available at all the nodes. In this paper, to avoid interference between users, linear IA in the spatial dimension is considered, that is, IA in multiuser MIMO systems. This paper mainly concentrates on the information and power transfer in the IA networks instead of degrees of freedom, so we assume that the streams for each node are the same; that is,dkS=dkS=d, ∀k=1,2,…,K. Moreover, symmetric networks are considered, and thus all the nodes have the same parameters; that is, Mk=M, Nk=N, and Tk=T, ∀k=1,2,…,K.Consider Slot 2 firstly that is the conventional IA network with only information transmission being performed. The received signal at destination nodek can be represented as (1)ykD=U2,kHGkkV2,kx2,k+∑i=1,i≠kKU2,kHGkiV2,ix2,i+U2,kHn2,k.x2,k is dkR×1 data symbol transmitted by the relay node. The average power constraint is denoted as Tr(E{x2,kx2,kH})=Tr(S2,k)=P2,k, where S2,k denotes the covariance matrix of x2,k. Gki∈CN×T is the channel gain matrix from relay node i to destination node k.For the arbitrarykth relay node, its signal x2,k is precoded by a precoding matrix V2,k∈CT×dkR. The coded signal V2,kx2,k is transmitted by the antennas from relay node k to destination node k, which will also cause interference at other unintended destination nodes. At kth destination node, the interferences from other relay nodes, GkjV2,jx2,j, ∀j≠k are constrained into the same subspace that is orthogonal to the unitary interference suppression matrix U2,k∈CN×dkR, through the cooperation of the precoding matrices of the other users. Thus, the desired signal of kth destination node can be recovered as U2,kHGkkV2,kx2,k at kth destination node. n2,k∈CN×1 represents the additive white Gaussian noise vector at destination node k with distribution CN0,σ2.When IA is feasible, the interferences among users can be assumed to be perfectly eliminated if the following conditions are satisfied [20, 21]:(2)U2,kGkjV2,j=0,∀j≠k,rankU2,kGkkV2,k=dkR.The feasible condition for IA can be given as(3)M+N≥K+1d.Then (1) can be simplified as(4)ykD=U2,kHGkkV2,kx2,k+U2,kHn2,k.The rate of kth destination node can be described as(5)R2,k=log⁡I+U2,kHGkkV2,kS2,kV2,kHGkkHU2,k,where Tr(S2,k)=P2,k≤Q and Q denotes the harvested energy in Slot 1.Next, consider the joint information and power transfer in Slot 1. Assume that each relay node can decode information and harvest energy at the same time. The source node transfers energy and information to the relay node through two mechanisms, AS and PS.In the AS scheme, receiving antennas are divided into two groups with one group switched to information decoding and the other group to energy harvesting as shown in Figure2.Figure 2
Antennas switching model.We assume that each relay node switchesL antennas from all N antennas for information decoding (ID), and the remaining N-L antennas are used for EH. The number of ID antennas should satisfy the feasible condition; that is,(6)L+M≥K+1d.The channel matrix between source nodej and the ID antennas of relay node k is denoted as HID-kj∈CL×M, which is composed by L rows of Hkj and adopted to obtain the coding matrices. Assume that the interference can be eliminated completely, and the rate of the kth relay noted can be described as(7)R1,AS-k=log2⁡Idk+U1,kHHID-kkV1,kSkV1,kHHID-kkHU1,k.For power transfer, the channel matrix between source nodej and the relay node k is HEH-kj∈C(N-L)×M. The harvested energy at relay node k can be described as(8)
Q
A
S
-
k
=
ζ
T
r
∑
i
=
1
K
H
E
H
-
k
i
V
i
S
i
V
i
H
H
E
H
-
k
i
H
,where ζ(0<ζ<1) is the energy conversion efficiency at the relay node and the background noise at the EH receiver is negligible and thus can be ignored.For the PS scheme, the received signal at each antenna is split into two separate signal streams with different power levels, one sent to the EH receiver and the other to the ID receiver, as shown in Figure3.Figure 3
Power splitting model.The received signal from the antenna is first corrupted by a Gaussian noise denoted bynA~CN0,σA2 in the RF-band. The RF-band signal is then fed into a power splitter, which is assumed to be perfect without any noise induced. The signal split to the ID receiver then goes through a sequence of standard operations to be converted from the RF band to baseband. During this process, the signal is additionally corrupted by another noise nP~CN0,σP2, which is independent of nA.Forjth antenna at kth relay node, the portion of power for EH is denoted as ρkj, 0≤ρkj≤1 and that for ID is 1-ρkj, 1≤j≤N. Then the rate of kth relay node can be calculated as(9)R1,PS-k=log⁡I+U1,kHΛ-k1/2Ψk1Λ-k1/2U1,kHUkHΛ-k1/2σA2I+Ψk2Λ-k1/2+σP2Uk-1,where (10)Ψk1=HkkV1,kS1,kV1,kHHkkH,Ψk2=∑i=1,i≠kKHkiViSiViHHkiH,where Λk=diag(ρk1,ρk2,…,ρkN) and Λ¯k=I-Λk represents the partition of power for all N receiving antennas at kth relay node. The harvested energy at kth relay node can be calculated similar to (8) as(11)QPS-k=ζTr∑i=1KΛkHkiV1,iS1,iV1,iHHkiH.For the relay system, we assume Slot 1 = Slot 2, so the system rate ofkth relay transmission link can be described as(12)Rk=12min⁡R1,k,R2,k.


## 3. Problem Formulation

### 3.1. Antenna Switching-Based Relaying

In AS, it supposed thatL antennas are selected from all N for ID; hence, there are a=CNLK feasible combinations totally. The optimal AS scheme can be found through searching the optimal one from all feasible antennas combinations. Assume that the global channel knowledge is available to all users. For a selected AS scheme, the optimization problem can be described as follows:P1maxS1,1,…,S1,K,S2,1,…,S2,K∑k=1Kmin⁡R1,k,R2,ks.t.TrS1,k≤P,k=1,…,KTrS2,k≤QAS-k,k=1,…,KS1,k⪰0,S2,k⪰0,k=1,…,K.Theorem 1.
The power allocation problemP1 can be divided into K independent subproblems for K links.Proof.
Since the transmission in Slot 2 is powered by the harvested energy in Slot 1, we haveP2,k=QAS-k. Moreover, consider perfect IA and optimal power allocation on Slot 2; the rate of kth link in Slot 2 is independent of any other link. The two-hop optimization problem can be regarded as a rate-energy tradeoff problem in Slot 1:P1-amaxS1,1,…,S1,K∑k=1KαkR1,k+1-αkQAS-ks.t.TrS1,k≤PS1,k⪰0,k=1,…,K,where 0≤αk≤1 denotes the weight allocated to the rate at kth relay, to make a tradeoff between EH and IT. For the AS combination determined, to achieve a maximum sum rate of K relay links, the value of αk should be proper setting.
For a givenαk, the power allocation problem P1-a can be divided into K independent subproblems for K links:P1-b∑k=1Kmax⁡αkRAS-1,k+1-αkQAS-k=∑k=1Kmax⁡αkRAS-1,k+1-αkζTr∑i=1KHEH-kiViSiViHHEH-kiH=∑k=1Kmax⁡αkRAS-1,k+Tr∑i=1K1-αiζHEH-ikVkSkVkHHEH-ikH=∑k=1Kmax⁡αkRAS-1,k+EAS-k.The decision variables are S1,k, k=1,…,K. Thus, the optimization problem can be rewritten as the following K parallel subproblems as(13)maxS1,kmax⁡αkR1,k+1-αkQAS-ks.t.TrS1,k≤P,S1,kS⪰0,where k=1,…,K.According to Theorem1, it is observed that, for a given antenna combination and weight value combination, each source node can determine its own power allocation simultaneously to achieve global optimization. Consider kth source node; the power allocation is denoted as (13) which is convex and can be solved effectively by the interior point method [25].


### 3.2. Power Splitting-Based Relaying

Consider the PS-based IA relay systems; to eliminate interference completely, uniform power splitting (UPS) should be used [24]; that is, ρk1=ρk2=⋯=ρkT.It is assumed first that each source node has only one data stream; that is,d=1. The optimal power splitting ratio at kth relay node is(14)ρk∗=ζTr∑i=1KHkiV1,iV1,iHHkiHζTr∑i=1KHkiV1,iV1,iHHkiH+U2,kHGkkV2,kV2,kHGkkHU2,k.Proof.
d = 1: the rate of kth user in Slot 1 is (15)R1,k=I+U1,kHΛ-k1/2HkkV1,kS1,kV1,kHHkkHΛ-k1/2U1,kH=I+P1,k1-ρkU1,kHHkkV1,kV1,kHHkkHU1,kH.
Corresponding harvested energy in Slot 1 is(16)QPS-k=ζTr∑i=1KΛkHkiV1,iS1,iV1,iHHkiH=P1,kρkζTr∑i=1KHkiV1,iV1,iHHkiH.
The rate ofkth user in Slot 2 is(17)R2,k=log⁡I+U2,kHGkkV2,kS2,kV2,kHGkkHU2,kH=log⁡I+QPS-kU2,kHGkkV2,kV2,kHGkkHU2,kH.
LetR1,k=R2,k; we have(18)P1,k1-ρkU1,kHHkkV1,kV1,kHHkkHU1,kH=QPS-kU2,kHGkkV2,kV2,kHGkkHU2,kH.
Substituting (16) into (18), the optimal power splitting ratio can be calculated and denoted as (14).Whend>1, the power allocation at each source node, PS ratio, and weight value at each relay node should be jointly optimized. For a give rate weight value, the optimization problem can be formulated asP
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.InP2, if ρk are given, P2 can be divided into K independent subproblems for K links as for P1. The optimal solution for PA SkS∗ can be obtained through applying the interpoint method for the UPS scheme.


### 3.3. Energy Cooperation

Since the AS scheme has better rate performance and PS scheme has advantages on the harvested energy [24], we consider an energy cooperation (ECop) scheme where the PS relays share harvested energy with AS relays.It is assumed that onlyKth relay node adopts AS scheme and the reminder relay nodes are PS schemes. The IA relay systems are still symmetric networks where all the nodes have the same parameters; that is, Mk=M, Tk=T, Nk=N, and dk=d, ∀k=1,2,…,K.Prior to describing the optimization problem, we first check the feasibility condition of DoF. Assume that theL antennas are selected for ID at Kth relay node, the symmetric networks become asymmetric systems, and the feasibility condition should be reconsidered. From [26], the total number of equations and the total number of variables are given by(19)Nv=∑i=1K-1diMi+Ni-2di+dKMK+L-2dK=KM+N-2d+L-Nd,Ne=∑i=1K∑j=1,j≠iKdidj.The IA condition is proper ifNv≥Ne; that is, (20a)M+NK+1-N-LKK+1≥d.Moreover, the ID receiver can simultaneously decode up toL streams, which is(20b)L≥d.Note that, in the energy cooperation IA, the feasibility condition is stricter than condition (6). Table 1 compares the highest achievable DoF for given M,N,L,K.Table 1
Comparison of highest DoF for different schemes.
M , N , L , K PS: properd given by (2) (3) AS: properd given by (6) ECop: properd given by (20a) and (20b) ( 6,6 , 5,3 ) 3 2 2 ( 5,5 , 2,3 ) 2 1 2 ( 6,4 , 3,3 ) 2 2 2 ( 4,4 , 3,3 ) 2 1 1 ( 6,6 , 2,4 ) 2 1 2 ( 6,3 , 2,4 ) 1 1 1It is observed that energy cooperation has a better DoF than AS IA and the energy cooperation network will always have a lower DoF than PS, sinceKth AS relay node prevents the network being symmetric anymore.Now consider the design problem for the ECoP IA; our aim is to maximize the sum-rate of all relay links subject to individual rate constraints at PS links, given byCk, k=1,…,K-1.Remark 2.
Forkth (k=1,…,K-1) PS relay link, if (21a)U1,kHHkkV1,k2>U1,KHHKKVKK2,k=1,…,K-1,(21b)U2,kHGkkV2,k2>U2,KHGKKV2,K2,k=1,…,K-1.
Specifically, ifkth (k=1,…,K-1) relay link has a better rate performance than Kth link in both slots, kth relay node would not share its harvested energy with an AS relay node. The design objective of kth (k=1,…,K-1) relay links is still energy-rate tradeoff.Now the energy cooperation scheme is described as follows.First, calculate the energy requirement to maximize the system rate of the AS link. More precisely, find an antenna combination that achieves the maximum rate in Slot 1 and then calculate the energy requirement gap at relay nodes for forwarding the received information.Next, consider how much energy should be shared for the ECop available relay node. We define a parameter called energy-rate ratio (ERR) to compare the instantaneous EH capacity to ID capability of a relay node. The ERR of relay nodek, k∈{1,…,K-1} in the network can be denoted as(22)ηk=ξ∑i=1KHkiV1,i2log⁡1+U1,kHHkkV1,k2.Forkth relay node, the energy that should be shared with AS relay node is(23)QReq,k=v-1ηk+.Andv makes ∑k=1K-1QReq,k=QReq.However, energy sharing is not always available for the PS relay node since there is a rate requirement at the PS link. Forkth link, assume that, when the link rate requirement is satisfied, the saved energy at relay is denoted as Qshare,kmax. Practically, the energy that can be saved in kth rely node is Qshare,k=min(Qshare,kmax,QReq,k).Remark 3.
If the relay node cannot save any energy when the rate requirement is satisfied, that is,Qshare,kmax=0, the AS relay node would not receive any energy from the corresponding relay node.Finally,Kth relay node received energy is Qreceived=∑k=1K-1Qshare,k. If the received energy is smaller than the energy requirement QReq (the energy cannot afford to forward the information) the AS relay links should be redesigned to maximize their information rate. The algorithm of energy cooperation scheme is concluded as Algorithm 1.Algorithm 1 (energy cooperation scheme).
( 1 ) Calculate AS user’s maximum rate RK∗ and corresponding harvested energy QK∗ in Slot 1.
( 2 ) Calculate the energy requirement Q that makes Slot 2 achieve the information rate RK∗.
( 3 ) For the PS relay nodes satisfy (21a) and (21b), they should totally share energy QReq=Q-QK∗ to AS relay node.
( 4 ) Calculate the energy that should be saved in kth relay node QReq,k by (23).
( 5 ) For kth relay node, calculate the energy that can be saved Qshare,kmax when kth relay node satisfied the rate requirement, and the energy that can be shared with AS relay node is Qshare,k=min(Qshare,kmax,QReq,k) actually.
( 6 ) Calculate the total received energy Qreceived=∑k=1K-1Qshare,k in AS relay.
( 7 ) If Qreceived=QReq, rate of AS link is RK∗. Else redesign the AS link to maximize their information rate.


## 3.1. Antenna Switching-Based Relaying

In AS, it supposed thatL antennas are selected from all N for ID; hence, there are a=CNLK feasible combinations totally. The optimal AS scheme can be found through searching the optimal one from all feasible antennas combinations. Assume that the global channel knowledge is available to all users. For a selected AS scheme, the optimization problem can be described as follows:P1maxS1,1,…,S1,K,S2,1,…,S2,K∑k=1Kmin⁡R1,k,R2,ks.t.TrS1,k≤P,k=1,…,KTrS2,k≤QAS-k,k=1,…,KS1,k⪰0,S2,k⪰0,k=1,…,K.Theorem 1.
The power allocation problemP1 can be divided into K independent subproblems for K links.Proof.
Since the transmission in Slot 2 is powered by the harvested energy in Slot 1, we haveP2,k=QAS-k. Moreover, consider perfect IA and optimal power allocation on Slot 2; the rate of kth link in Slot 2 is independent of any other link. The two-hop optimization problem can be regarded as a rate-energy tradeoff problem in Slot 1:P1-amaxS1,1,…,S1,K∑k=1KαkR1,k+1-αkQAS-ks.t.TrS1,k≤PS1,k⪰0,k=1,…,K,where 0≤αk≤1 denotes the weight allocated to the rate at kth relay, to make a tradeoff between EH and IT. For the AS combination determined, to achieve a maximum sum rate of K relay links, the value of αk should be proper setting.
For a givenαk, the power allocation problem P1-a can be divided into K independent subproblems for K links:P1-b∑k=1Kmax⁡αkRAS-1,k+1-αkQAS-k=∑k=1Kmax⁡αkRAS-1,k+1-αkζTr∑i=1KHEH-kiViSiViHHEH-kiH=∑k=1Kmax⁡αkRAS-1,k+Tr∑i=1K1-αiζHEH-ikVkSkVkHHEH-ikH=∑k=1Kmax⁡αkRAS-1,k+EAS-k.The decision variables are S1,k, k=1,…,K. Thus, the optimization problem can be rewritten as the following K parallel subproblems as(13)maxS1,kmax⁡αkR1,k+1-αkQAS-ks.t.TrS1,k≤P,S1,kS⪰0,where k=1,…,K.According to Theorem1, it is observed that, for a given antenna combination and weight value combination, each source node can determine its own power allocation simultaneously to achieve global optimization. Consider kth source node; the power allocation is denoted as (13) which is convex and can be solved effectively by the interior point method [25].


## 3.2. Power Splitting-Based Relaying

Consider the PS-based IA relay systems; to eliminate interference completely, uniform power splitting (UPS) should be used [24]; that is, ρk1=ρk2=⋯=ρkT.It is assumed first that each source node has only one data stream; that is,d=1. The optimal power splitting ratio at kth relay node is(14)ρk∗=ζTr∑i=1KHkiV1,iV1,iHHkiHζTr∑i=1KHkiV1,iV1,iHHkiH+U2,kHGkkV2,kV2,kHGkkHU2,k.Proof.
d = 1: the rate of kth user in Slot 1 is (15)R1,k=I+U1,kHΛ-k1/2HkkV1,kS1,kV1,kHHkkHΛ-k1/2U1,kH=I+P1,k1-ρkU1,kHHkkV1,kV1,kHHkkHU1,kH.
Corresponding harvested energy in Slot 1 is(16)QPS-k=ζTr∑i=1KΛkHkiV1,iS1,iV1,iHHkiH=P1,kρkζTr∑i=1KHkiV1,iV1,iHHkiH.
The rate ofkth user in Slot 2 is(17)R2,k=log⁡I+U2,kHGkkV2,kS2,kV2,kHGkkHU2,kH=log⁡I+QPS-kU2,kHGkkV2,kV2,kHGkkHU2,kH.
LetR1,k=R2,k; we have(18)P1,k1-ρkU1,kHHkkV1,kV1,kHHkkHU1,kH=QPS-kU2,kHGkkV2,kV2,kHGkkHU2,kH.
Substituting (16) into (18), the optimal power splitting ratio can be calculated and denoted as (14).Whend>1, the power allocation at each source node, PS ratio, and weight value at each relay node should be jointly optimized. For a give rate weight value, the optimization problem can be formulated asP
2
m
a
x
S
1,1
,
…
,
S
1
,
K
,
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1
,
…
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k
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.InP2, if ρk are given, P2 can be divided into K independent subproblems for K links as for P1. The optimal solution for PA SkS∗ can be obtained through applying the interpoint method for the UPS scheme.


## 3.3. Energy Cooperation

Since the AS scheme has better rate performance and PS scheme has advantages on the harvested energy [24], we consider an energy cooperation (ECop) scheme where the PS relays share harvested energy with AS relays.It is assumed that onlyKth relay node adopts AS scheme and the reminder relay nodes are PS schemes. The IA relay systems are still symmetric networks where all the nodes have the same parameters; that is, Mk=M, Tk=T, Nk=N, and dk=d, ∀k=1,2,…,K.Prior to describing the optimization problem, we first check the feasibility condition of DoF. Assume that theL antennas are selected for ID at Kth relay node, the symmetric networks become asymmetric systems, and the feasibility condition should be reconsidered. From [26], the total number of equations and the total number of variables are given by(19)Nv=∑i=1K-1diMi+Ni-2di+dKMK+L-2dK=KM+N-2d+L-Nd,Ne=∑i=1K∑j=1,j≠iKdidj.The IA condition is proper ifNv≥Ne; that is, (20a)M+NK+1-N-LKK+1≥d.Moreover, the ID receiver can simultaneously decode up toL streams, which is(20b)L≥d.Note that, in the energy cooperation IA, the feasibility condition is stricter than condition (6). Table 1 compares the highest achievable DoF for given M,N,L,K.Table 1
Comparison of highest DoF for different schemes.
M , N , L , K PS: properd given by (2) (3) AS: properd given by (6) ECop: properd given by (20a) and (20b) ( 6,6 , 5,3 ) 3 2 2 ( 5,5 , 2,3 ) 2 1 2 ( 6,4 , 3,3 ) 2 2 2 ( 4,4 , 3,3 ) 2 1 1 ( 6,6 , 2,4 ) 2 1 2 ( 6,3 , 2,4 ) 1 1 1It is observed that energy cooperation has a better DoF than AS IA and the energy cooperation network will always have a lower DoF than PS, sinceKth AS relay node prevents the network being symmetric anymore.Now consider the design problem for the ECoP IA; our aim is to maximize the sum-rate of all relay links subject to individual rate constraints at PS links, given byCk, k=1,…,K-1.Remark 2.
Forkth (k=1,…,K-1) PS relay link, if (21a)U1,kHHkkV1,k2>U1,KHHKKVKK2,k=1,…,K-1,(21b)U2,kHGkkV2,k2>U2,KHGKKV2,K2,k=1,…,K-1.
Specifically, ifkth (k=1,…,K-1) relay link has a better rate performance than Kth link in both slots, kth relay node would not share its harvested energy with an AS relay node. The design objective of kth (k=1,…,K-1) relay links is still energy-rate tradeoff.Now the energy cooperation scheme is described as follows.First, calculate the energy requirement to maximize the system rate of the AS link. More precisely, find an antenna combination that achieves the maximum rate in Slot 1 and then calculate the energy requirement gap at relay nodes for forwarding the received information.Next, consider how much energy should be shared for the ECop available relay node. We define a parameter called energy-rate ratio (ERR) to compare the instantaneous EH capacity to ID capability of a relay node. The ERR of relay nodek, k∈{1,…,K-1} in the network can be denoted as(22)ηk=ξ∑i=1KHkiV1,i2log⁡1+U1,kHHkkV1,k2.Forkth relay node, the energy that should be shared with AS relay node is(23)QReq,k=v-1ηk+.Andv makes ∑k=1K-1QReq,k=QReq.However, energy sharing is not always available for the PS relay node since there is a rate requirement at the PS link. Forkth link, assume that, when the link rate requirement is satisfied, the saved energy at relay is denoted as Qshare,kmax. Practically, the energy that can be saved in kth rely node is Qshare,k=min(Qshare,kmax,QReq,k).Remark 3.
If the relay node cannot save any energy when the rate requirement is satisfied, that is,Qshare,kmax=0, the AS relay node would not receive any energy from the corresponding relay node.Finally,Kth relay node received energy is Qreceived=∑k=1K-1Qshare,k. If the received energy is smaller than the energy requirement QReq (the energy cannot afford to forward the information) the AS relay links should be redesigned to maximize their information rate. The algorithm of energy cooperation scheme is concluded as Algorithm 1.Algorithm 1 (energy cooperation scheme).
( 1 ) Calculate AS user’s maximum rate RK∗ and corresponding harvested energy QK∗ in Slot 1.
( 2 ) Calculate the energy requirement Q that makes Slot 2 achieve the information rate RK∗.
( 3 ) For the PS relay nodes satisfy (21a) and (21b), they should totally share energy QReq=Q-QK∗ to AS relay node.
( 4 ) Calculate the energy that should be saved in kth relay node QReq,k by (23).
( 5 ) For kth relay node, calculate the energy that can be saved Qshare,kmax when kth relay node satisfied the rate requirement, and the energy that can be shared with AS relay node is Qshare,k=min(Qshare,kmax,QReq,k) actually.
( 6 ) Calculate the total received energy Qreceived=∑k=1K-1Qshare,k in AS relay.
( 7 ) If Qreceived=QReq, rate of AS link is RK∗. Else redesign the AS link to maximize their information rate.


## 4. Simulation Result and Discussions

In this section, we provide numerical results to compare the performance of investigated schemes.Firstly consider the achievable rate performances for different transmission strategies at different transfer power level.For the situation withd=1, a three-user IA relay network with M=N=T=3 is considered. Assume that, in AS, to meet the IA feasibility condition, L=2. For ECop, ID antennas are L=2 at the AS node, and receiving antennas at PS relay nodes are N=3.For the situation withd=2, assume that M=6, N=3, and T=6. In the AS scheme, L=2. In ECop, ID antennas are L=2 at the AS node, and receiving antennas at PS relay nodes are N=3. The conventional iterative algorithm is utilized to obtain the solutions for IA transceivers [20].Figure4 shows that the PS scheme always has a better performance than AS since the PS scheme makes a more flexible tradeoff between energy and information. Moreover, PS always has a higher DoF condition in any antenna situation. Since the system rate of a relay link depends on the smaller Slot, but both slots happen in the same transmission duration, the performance of PS and AS improves linearly with the increase of transfer power rather than logarithmically.Figure 4
Achievable sum system rate for different strategies.For ECop, the rate performance outperforms AS and PS. Since the AS node can achieve and maximize information due to no self-energy constraint, hence the ECop scheme achieves a better sum system rate.In the next experiment, users are distributed randomly in a one-dimensional region. The distance between source node and destination is 200 meters, which can be normalized to 1. The distance between source node and relay node is denoted ass and for the relay node to destination node denoted as 1-s. Suppose the large scale path-loss factor ϕ=3, and the channel coefficients between relay and users would have additional large scale path-loss Ω1=s-3, Ω2=(1-s)-3, respectively.Ford=1 and d=2, the network condition is the same as the previous experiment. It is observed from Figure 5 that, when relay nodes are closer to destination nodes, the AS scheme has a better performance, which indicates that the AS scheme has an advantage on information transmission. This conclusion is somewhat surprising when the UPS was superior to the AS in the conventional MIMO systems by maintaining spatial multiplexing gain at the cost of power loss. It is worth pointing out that AS has a better rate performance at the cost of lower DoF. In summary, AS has a better rate performance with hard DoF condition; on the other hand, UPS has an advantage on the harvested energy with a better DoF condition. For a real communication system, we should choose the receiving scheme according to the actual situations.Figure 5
Achievable sum system rate of the IA relay network for different schemes at different relay position.Furthermore, it is noted that ECop always has the highest rate which indicates that the proposed scheme can improve the system performance efficiently. ECop can also achieve higher DoF than that of AS.


## 5. Conclusions

In this paper, SWIPT in IA relay networks has been studied. Firstly AS- and PS-based SWIPT is analyzed to maximize the sum-rate of the networks, and a three-step optimization method is proposed. The simulation results show that PS will not always outperform the AS scheme. This conclusion is somewhat surprising when we remember that the UPS always have a bigger R-E region than AS in traditional scenario. These results show that these two schemes lead to a new transmission characteristic when interference is taken as the energy source in IA networks.To combine the advantages of AS and PS, a new ECop scheme is proposed to achieve better performance. Simulation results are presented to show the advantage of the ECop scheme in IA relay networks.



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*Source: 7281027-2016-11-01.xml*