# Transmission Strategy Design and Resource Allocation in D2D Multicast Cooperative Communications with SWIPT

Authors: Chenfan Weng; Dingcheng Yang; Jun Wan; Lin Xiao; Chuanqi Zhu
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

This paper proposes a new transmission strategy for device-to-device (D2D) multicast cooperative communication systems based on Simultaneous Wireless Information and Power Transfer (SWIPT) technology. The transmission block is divided into two slots. In the first slot, the source user transmits the information and energy to the help user by SWIPT. In the second slot, the help user uses the cellular spectrum and forwards the information to multiple receivers by using harvested energy. In this paper, we aim to maximize the total system rate, and to tackle the problem, we propose a two-step scheme: In the first step, the resource allocation problem is solved by linear programming. In the second step, the power-splitting coefficient value is obtained by taking the benefit of help user into account. Numerical results show that the proposed strategy not only effectively improves the overall throughput and spectrum efficiency but also motivates the cooperation.


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## Body

## 1. Introduction

Wireless Power Communication (WPC), where the smart terminals can harvest the energy from the far-field Radio-Frequency (RF) signals provided by energy access point, becomes a new approach to avoid replacing or recharging the batteries, reduce total cost, and prolong the lifetimes [1]. Simultaneous Wireless Information and Power Transfer (SWIPT) is a kind of WPC, where wireless devices can collect energy and receive information from RF signals at the same time [2–5]. In [6], Ioannis Krikidis team discussed the SWIPT technology and made a preliminary study on the allocation of wireless resources in SWIPT. Time switching and power-splitting model were proposed in [7]. Cooperative technology is also widely used in communication systems based on SWIPT. [8] studied cooperative communication system with Decode-and-Forward (DF) mode.With the help of the fast growth of wireless communication technology, smart devices can easily access the network anywhere anytime, which makes people’s sharing become ubiquitous [9]. Device-to-Device (D2D) communication was proposed to exchange information directly. The technology has several benefits, such as saving resources, improving spectral efficiency, and reducing transmission delay. Based on the transmission mode, it can be divided into unicast transmission and multicast transmission. In unicast transmission mode, a transmission channel is established between the Base Station (BS) or the sending user and each requesting user. Each channel takes a different frequency band that is orthogonal to each other, presenting a waste of spectral resources to some extent. Some works such as [10] consider throughput maximization while allowing D2D communication to underlay the cellular network; the results show that the total throughput can be increased. Some other works such as [11] consider throughput maximization under the spectral efficiency and energy constraints. Only one Cellular User (CU) and a D2D pair are considered at this scheme. [12] extends it to the general situation with multiple D2D users and CUs for maximizing the overall throughput. These works either improve network throughput [10–12] or ensure the reliability of D2D communications [13–15]. The works in [11, 16] take these two indicators into account at the same time. [16] has proposed an algorithm to solve a Mixed Integer and Nonlinear Programming (MINLP) resource allocation problem. But the algorithm does not consider the collaboration between CUs and D2D pair. Based on [11, 16], a maximum weight bipartite matching was proposed in [12]; the system of performance of D2D access rate and the total throughput improved significantly. While in multicast transmission mode the BS or the sending user is transmitting through the same frequency band with each request user, saving a certain spectrum resource, however, D2D multicast will meet more challenges which are different from unicast D2D (see, e.g., [11, 12]). As the number of receivers increases, the transmission rate tends to decrease. Some works have been investigated in cooperative D2D communication [17–19]. Authors in [17] proposed a cooperative caching strategy to analyze the network capacity and present an architecture to improve the network capacity. In [18], the author considers cooperative D2D communication in downlink cellular networks where the D2D transmitter is equipped with an energy-harvesting capability. A network model is proposed in [19], analyzing D2D communication with RF energy harvesting.In [20], a SWIPT-based D2D cooperative network is proposed. In SWIPT-based energy-harvesting D2D underlay network [21], the problem of joint power control and spectrum resource allocation is solved. A framework for optimal resource allocation in multicast D2D communications is presented to maximize the total throughput of D2D multicast groups and CUs in [22]. In fact, cooperative communication is hard to be realized to motivate the mobile terminals, due to the lack of incentives. Therefore, in this paper, we fully consider the benefits of the help users and aim at maximizing their benefits. Different from the previous works on cooperative communication, we proposed an innovation transmission strategy and incentive mechanism via combined D2D multicast technology with SWIPT, which can effectively improve the spectrum efficiency, lower the energy consumption, reduce the communication delay, largely release the burden of the BS, and thus reduce the cost of communication. Likewise, in order to lower the burden of the back-haul link, we assume that the content is stored locally. In addition, we will focus on the analysis of the cochannel interference brought by D2D multicast transmission and study the mechanism in user’s collaboration.


## 2. System Model and Transmission Protocol

As shown in Figure1, a cellular network is modeled in this section, consisting of a BS in the cellular center, M CUs (denoted as C={C1,C2,C3,...,CM}), and a D2D multicast group. The D2D multicast group is composed of a D2D multicast source user (denoted as DS), a D2D multicast help user (denoted as DT), andK D2D multicast receivers (denoted as DRk), and we define the set K≜DR1,DR2,...,DRK. We assume that D2D multicast transmission needs to be assisted by DT because there is no direct link due to some uncertain factors between DS and DRK. Therefore, this paper considers DT between DS and DRK to cooperate the transmission. On the other hand, in a cellular network, since help user is always selfish, DT does not want to cooperate with DS by using his own energy. For this reason, we consider that DT collects energy and data from DS by SWIPT and then complete D2D multicast by using the harvested energy. And DT can store the excess energy in a rechargeable battery for his own use. The antenna equipped at DS has the function of transmitting energy and transmitting data simultaneously. DT is equipped with batteries, and its antenna has the function of harvesting energy. Members distributed evenly and closely in the group have the same interest. Considering there are M CUs and M orthogonal channels, each occupied by one CU, which are denoted as sets R={R1,R2,R3,...,Rm}, in this paper, we consider uplink resource sharing since reusing downlink resources will greatly reduce the spectrum efficiency according to [23].Figure 1
System model.We assume that all channels are quasistatic channels, that is, the channel coefficients remain constant for a period of transmission time. It is assumed that the channel between all users contains three kinds of loss: small-scale Rayleigh fading, the distance-dependent path loss, and long-term shadowing with loss exponentα≥2. Here, let rS,T be the distance between DS and DT and hS,T be the channel coefficients between the two channels; similarly, let rT,k be the distance between DT and Kth DRk and hT,k be the channel coefficients between the two channels.In order to accomplishDRk’s downlink data transmission, this paper proposes a transmission strategy as shown in Figure 2.Figure 2
Transport protocol of WPC D2D network.The transmission block can be divided into 3 slots, which contains control signaling exchange process, SWIPT, and D2D multicast. In the first slot, the signaling exchange process consists of spectrum allocation, resource allocation, and link setup, which will be introduced in detail in Section3. Suppose that the amount of time in the first slot is too small and therefore it can be negligible.We assume that the total time resource meets the following constraints:(1)τ0+τ1≤T.Without loss of generality, letT=1 for calculation convenience.In the second slot, also known as SWIPT stage,DS transmits RF signals to DT with a transmit power P0. Since SWIPT is prone to generating cochannel interference, it is assumed that DS transmits information and power simultaneously by the dedicated channel. Set the DT receiver to work in power-splitting (PS) mode. The RF signals have two uses in DT receiver: one is energy harvesting, and the other is information decoding, as shown in Figure 3.Figure 3
Receiving antenna of multicast help user.The received signal atyT by DT can be expressed as(2)yT=P0hS,TXi+n,wherexi denotes the signal that DS transmitted and n represents the additive Gaussian noise of the antenna that complies with the form of n~CN0,σ2. Assume that all the receiver noise satisfies this formula in this paper.Denote the power split factor asρ with 0≤ρ≤1, and the energy ET harvested by DT is expressed as(3)ET=ρηTτ0P0hS,T,whereηT is the energy conversion efficiency of DT. Because the interference noise takes a tiny proportion in the received signal, the received noise is ignored when considering the collected energy.In information decoding,1-ρ is the information split factor of DT, so the signal receiving rate RS,T is expressed as(4)RS,T=τ0log21+1-ρP0hS,Tσ2.In the stage ofD2D multicast, or the τ1 stage, DT forwards data to all DRk in the group with the energy received by the SWIPT stage by the transmitting power of PT.According to the energy constraint, the energy consumption ofDT during multicast communication must be less than or equal to the energy harvested at the stage τ0, so we must meet the following constraints:(5)PTτ1≤ET.Considering the need to reuse the CU channel in the D2D multicast transmission,δii∈R is assumed to be a binary variable. Let δi=1 be that the D2D multicast transmission is using the cellular channel Ri; then, δi=0 indicates the opposite.In the process of D2D multicast communication, there are two kinds of interference in the system: (1) the cochannel interference to the BS when receiving the signals sent by the CUs and (2) the cochannel interference brought byCm to DRk when receiving the multicast signals.Suppose that D2D multicast communication can reuse Z cellular channels at most, that is,(6)∑Mδi≤Z,i∈R.In order to avoid the mass CU interference caused by D2D multicast communication, this paper only considers the situation ofZ=1; that is, D2D multicast can only choose one cellular channel to communicate.Setβk,m as a channel quality coefficient of DRk when occupying channel Rm, and(7)βk,m=hT,kσ2+Pmhm,k,∀k∈K,m∈C,wherePm is the uplink transmission power of Cm and hm,k is the channel coefficient between Cm and DRk.In D2D multicast group, due to different channel coefficients ofDRk and DT, each DRkreceives a different rate during multicast transmission. In order to ensure that each DRk can complete multicast communication, we define the multicast channel quality coefficient βmD as that of the receiver with the worst channel quality in the group related to DT, which will meet the following:(8)βmD=minβk,m,∀k∈K.Therefore, the normalized rateRT,R of multicast D2D group can be written as follows:(9)RT,R=∑m-1Mδmτ1log21+PTβmD.Meanwhile, it should also meet the information constraints in stageτ1:(10)RT,Rτ1≤Rp,Tτ0.The multicast communication rateRT,R of D2D multicast group meets the following constraints:(11)RT,Rsum≤∑m-1MδmKτ1log21+PTβmD.For CUs, letrp,m and hp,m denoted the distance and the channel coefficient between Cm and BS respectively, rT,p and hT,p denoted the distance and the channel coefficient between BS and DT respectively, then the channel quality coefficient between Cm and BS can be formulated as follows:(12)βm=hp,mσ2+δmPThT,pAssuming that the transmission powerCm remains unchanged during the whole transmission process T, then the transmission rate is(13)Rm=log21+Pmβm.In order to ensure the service quality of CUs and D2D during the communication, the following constraints should be met:(14)RT,R≥RminCU.(15)Rm≥Rmin,∀m∈MTable1 lists the variables and parameters used in the paper.Table 1
Table of notations.
Notation Description C Set of cellular users (CU) K Set of D2D multicast receivers R Set of orthogonal channels DS D2D multicast source user DT D2D multicast help user DRk D2D multicast receivers rS,T The distance betweenDS  and   DT hS,T The channel coefficients between the two channels rT,k The distance betweenDT  and Kth  DRk hT,k The channel coefficients between the two channels ρ The power split factor ET The energy harvested byDT ηT The energy conversion efficiency ofDT RS,T The signal receiving rate PT The transmitting power δi A binary variable βk,m A channel quality coefficient ofDRk Pm The uplink transmission power ofCm hm,k The channel coefficient betweenCm and  DRk ρmD Multicast channel quality coefficient RT,R The normalized rate of multicast D2D group RT,Rsum The summation of normalized rate


## 3. Problem Description and Optimization

In this paper, we endeavor to maximize the total system rate by combining the optimization of frequency resources, power split factors, and transmission power in the case of satisfying the constraints mentioned above. Thus, the optimization problem can be formulated as follows:(16)P1maxmizeδm,ρ,PT,PmRT,R+∑m-1MRms.t.PTτ1≤ET∑Mδi≤1,i∈RRT,Rτ1≤RS,Tτ0RT,R≥RminCURm≥RminCU,∀m∈Mδm∈0,1βmD2D=minβk,m,∀k∈K0≤PT≤PTmax0≤Pm≤Pmmax.In general, MINLP is NP-hard problem, but in this paper, we consider the problem of MINLP for the special case (each D2D group can reuse the channels of at most one CU and each CU can share their channels with at most one D2D group); it is a bipartite problem.The algorithm proposed in (16) will be divided into three steps: first, fix the value of δi; then optimize the value of each δi, and if the optimization is not feasible, the channel will be eliminated; finally, the channel that has the best effect in the remaining feasible solution is selected as the reusable channel.Whenδi is fixed, that is, (17)δi=1i=m0else,with only one cellular channel Rm being reused, we just take the rate of the CUs in the reused band among the targeted users that are being optimized.For the constrained condition (8), to obtain βmD, we have to find out the channel quality coefficient of the receiver with the worst channel quality and compare the interference values between all DRk. When considering the reuse of a cellular channel, formula (7) shows that, for each DRk under the same Pm, βk,m is only associated with hm,k and hT,k. The smaller hT,k and the larger hm,k become, the smaller the value of βk,m will be. To conclude, we define γk=hT,k/hm,k which means when γk picks the minimum value, the receiving user βk∗,m goes to βmD.The original optimization problem (16) is simplified as follows:(18)P2maxρm,PT,Pmτ1log21+PThT,k∗σ2+Pmhm,k∗+log21+Pmhp,mσ2+PThT,ps.t.PTτ1≤ρmηTτ0P0hS,Tτ1log21+PThT,k∗σ2+Pmhm,k∗≤τ0log21+1-ρmP0hS,Tσ2τ1log21+PThT,k∗σ2+Pmhm,k∗≥RminD2Dlog21+Pmhp,mσ2+PThT,p≥RminCU0≤PT≤PTmax,0≤Pm≤Pmmaxk∗=argmink⁡γk.From the objective function expression and the constraints, the problem is still a nonconvex problem and cannot be solved by the traditional convex optimization method. Therefore, in this paper, we are going to divide the problem into two subproblems.


### 3.1. Optimization Algorithm for D2D Interference

Firstly, the problem of D2D interference is to be optimized. Problem (18) simplifies subproblem (19):(19)P3maxPT,Pmτ1log21+PThT,k∗σ2+Pmhm,k∗+log21+Pmhp,mσ2+PThT,ps.t.Ca1:τ1log21+PThT,k∗σ2+Pmhm,k∗≥RminD2DCa2:log21+Pmhp,mσ2+PThT,p≥RminCUCa3:0≤PT≤PTmaxCa4:0≤Pm≤Pmmax.The formulasCa1 and Ca2 are simplified as(20)PT≥Aσ2+Pmhm,k∗(21)Pm≥Bσ2+PThT,p,whereA=2RminD2D/τ1-1/hT,k∗ and B=2RminCU/τ1-1/hp,m. Combined with (Ca3), (Ca4), (20), and (21), it is known that the constraints are all linear, which are divided into 6 cases as shown in Figures 4–9. The line la represents constraint (20) with equality, the slope is Ahm,k∗, and the intersection point with the PT axis is 0,Aσ2. When constraint (20) is met, the feasible solution is in the upper side of the line la. The line lb represents constraint (21) with equality and the intersection point with the Pm axis, and the slope is 1/B. When constraint (21) is met, the feasible solution is on the right side of the line lb.Figure 4
Case 1.Figure 5
Case 2.Figure 6
Case 3.Figure 7
Case 4.Figure 8
Case 5.Figure 9
Case 6.In Figure4, point C coordinates at (PTmax/A-σ2)/hm,k∗,PTmax, and point B coordinates at Bσ2+PTmaxhT,p,PTmax. Therefore, case 1 meets the following conditions:(22)PTmax/A-σ2hm,k≤PmmaxBσ2+PTmaxhT,p≤Pmmax.SupposeP^T∗ and P^m∗ are the best solutions for problem (19). In Figures 4–6, the blue part represents a feasible value region. In Figures 7-8, there is no value region that meets the constraints; in other words, there is no solution to the problem.In Figure5, point B coordinates at Bσ2+PTmaxhT,p,PTmax, and point C coordinates at Pmmax,Aσ2+Pmmaxhm,k∗. Therefore, case 2 meets the following constraints:(23)Bσ2+PTmaxhT,p≤PmmaxAσ2+Pmmaxhm,k∗≤PTmax.In Figure6, point B coordinates at Pmmax,Aσ2+Pmmaxhm,k∗, and point C coordinates at Pmmax,Pmmax/B-σ2/hT,p. Thus, case 3 meets the following constraints:(24)Aσ2+Pmmaxhm,k∗≤PTmaxPmmax/B-σ2hT,p≤PTmax.All the situations from Figures7–9 do not meet the requirements ranging from (22) to (24), and it is known from the function curve (19) that there is no feasible solution.Next, we analyze the objective function (19). According to [24], we can prove that when a set of solutions Pm,PT is taken within the feasible solution region, another set of solutions μPm,μPT will be found in the feasible region and meets the condition of fμPm,μPT≥fPm,PT, in which(25)fPm,PT≜τ1log21+PThT,k∗σ2+Pmhm,k∗+log21+Pmhp,mσ2+PThT,p.Therefore, at least one of the optimal solutionsP^T∗ and P^m∗ of problem (19) can take the maximum value; that is, constraints in Ca3 or Ca4 can be set equal.(i)
For case 1, the optimal solution (P^T∗,P^m∗) lies in the line BC; then P^T∗=PTmax. When PT is fixed, the objective function (19) is a convex function, so the optimal solution (P^T∗,P^m∗) can only be point B or point C.(ii)
For case 2, the optimal solution (P^T∗,P^m∗) may be in line BD or CD, and similar to case 1, the optimal solutions only may be B,C or D.(iii)
For case 3, the optimal solution (P^T∗,P^m∗) lies in the segment BC, and similar to case 1, the optimal solution is only possible for B or C.In summary, we can find that the optimal solution of subproblem (16) is as follows.WhenPTmax/A-σ2/hm,k∗≤Pmmax and Bσ2+PTmaxhT,p≤Pmmax, (26)P^T∗,P^m∗=argmaxfPTmax/A-σ2hm,k∗,PTmax,fBσ2+PTmaxhT,p,PTmax.WhenBσ2+PTmaxhT,p≤Pmmax and Aσ2+Pmmaxhm,k∗≤PTmax, (27)P^T∗,P^m∗=argmaxfBσ2+PTmaxhT,p,PTmax,fPmmax,Aσ2+Pmmaxhm,k∗,fPmmax,PTmax.WhenAσ2+Pmmaxhm,k∗≤PTmax and (Pmmax/B-σ2)/hT,p≤PTmax, (28)P^T∗,P^m∗=argmaxfPmmax,Aσ2+Pmmaxhm,k∗,fPmmax,Pmmax/B-σ2hT,p.When the abovementioned three conditions are not met, there is no solution to the original problem.


### 3.2. Joint Power Split Factor and D2D Interference Optimization Algorithm

According to the optimization results of Section3.1, this section will optimize the power split factor ρ; then, the optimization problem will become(29)P4Findρms.t.P^T∗τ1≤ρmηTτ0P0hS,Tτ1log21+P^T∗hT,k∗σ2+P^m∗hm,k∗≤τ0log21+1-ρmP0hS,Tσ2.The following constraints can be derived:(30)P^T∗ηTτ0P0hS,T≤ρm≤1-σ2P0hS,T2τ1-τ01+P^T∗hT,k∗σ2+P^m∗hm,k∗-1.Whenρm meets constrained condition (30), the original problem (18) has feasible solutions.In order to encourageDT to carry out cooperative communication and ensure the best benefits of its users, it should get the maximum energy in the process of cooperation, so let the energy harvested be △, that is,(31)△=ρmηTτ0P0hS,T-P^T∗τ1.Whenρm is maximized, △ goes to the maximum, so set(32)ρm∗=1-σ2P0hS,T2τ1-τ01+P^T∗hT,k∗σ2+P^m∗hm,k∗-1Thus, problem (18) is solved.Next, leti=m+1, then, changing the value of δm and continuing to solve problem (18).After traversing all channels, find out the best reuse cellular channelm∗=argmaxRsumm and output the global optimal solution.Hence, original problem (16) is solved.To conclude, the algorithms proposed in this paper are summarized as shown in Algorithm1.Algorithm 1:Joint Power Split Factor and D2D Interference Optimization Algorithm.
1. Initializem=1. 2. Ifm<M, order δi=1i=m0else, if not, jump to step 5. Solve problem(19): When the restricted condition (22) is satisfied, the optimal solution  P^T∗,P^m∗  is equation (26); When the restricted condition (23) is satisfied, the optimal solution  P^T∗,P^m∗  is equation (27); When the restricted condition (24) is satisfied, the optimal solution  P^T∗,P^m∗  is equation (28); If the above restricted conditions are not satisfied, output the optimal solution  Om=∅. 3.If the solution of step 2 satisfies the condition (30), output ρm∗ is equation (32). Or else,   Om=∅. 4.Here, the optimal solution of problem (18) is an array O m = P ^ T ∗ , P ^ m ∗ , ρ m ∗, calculate Rsumm by formula (19). Updatem=m+1, return step 2. 5.Find the best channelm∗=argmaxRsumm, and output the optimal solutionOm∗=Om.


## 3.1. Optimization Algorithm for D2D Interference

Firstly, the problem of D2D interference is to be optimized. Problem (18) simplifies subproblem (19):(19)P3maxPT,Pmτ1log21+PThT,k∗σ2+Pmhm,k∗+log21+Pmhp,mσ2+PThT,ps.t.Ca1:τ1log21+PThT,k∗σ2+Pmhm,k∗≥RminD2DCa2:log21+Pmhp,mσ2+PThT,p≥RminCUCa3:0≤PT≤PTmaxCa4:0≤Pm≤Pmmax.The formulasCa1 and Ca2 are simplified as(20)PT≥Aσ2+Pmhm,k∗(21)Pm≥Bσ2+PThT,p,whereA=2RminD2D/τ1-1/hT,k∗ and B=2RminCU/τ1-1/hp,m. Combined with (Ca3), (Ca4), (20), and (21), it is known that the constraints are all linear, which are divided into 6 cases as shown in Figures 4–9. The line la represents constraint (20) with equality, the slope is Ahm,k∗, and the intersection point with the PT axis is 0,Aσ2. When constraint (20) is met, the feasible solution is in the upper side of the line la. The line lb represents constraint (21) with equality and the intersection point with the Pm axis, and the slope is 1/B. When constraint (21) is met, the feasible solution is on the right side of the line lb.Figure 4
Case 1.Figure 5
Case 2.Figure 6
Case 3.Figure 7
Case 4.Figure 8
Case 5.Figure 9
Case 6.In Figure4, point C coordinates at (PTmax/A-σ2)/hm,k∗,PTmax, and point B coordinates at Bσ2+PTmaxhT,p,PTmax. Therefore, case 1 meets the following conditions:(22)PTmax/A-σ2hm,k≤PmmaxBσ2+PTmaxhT,p≤Pmmax.SupposeP^T∗ and P^m∗ are the best solutions for problem (19). In Figures 4–6, the blue part represents a feasible value region. In Figures 7-8, there is no value region that meets the constraints; in other words, there is no solution to the problem.In Figure5, point B coordinates at Bσ2+PTmaxhT,p,PTmax, and point C coordinates at Pmmax,Aσ2+Pmmaxhm,k∗. Therefore, case 2 meets the following constraints:(23)Bσ2+PTmaxhT,p≤PmmaxAσ2+Pmmaxhm,k∗≤PTmax.In Figure6, point B coordinates at Pmmax,Aσ2+Pmmaxhm,k∗, and point C coordinates at Pmmax,Pmmax/B-σ2/hT,p. Thus, case 3 meets the following constraints:(24)Aσ2+Pmmaxhm,k∗≤PTmaxPmmax/B-σ2hT,p≤PTmax.All the situations from Figures7–9 do not meet the requirements ranging from (22) to (24), and it is known from the function curve (19) that there is no feasible solution.Next, we analyze the objective function (19). According to [24], we can prove that when a set of solutions Pm,PT is taken within the feasible solution region, another set of solutions μPm,μPT will be found in the feasible region and meets the condition of fμPm,μPT≥fPm,PT, in which(25)fPm,PT≜τ1log21+PThT,k∗σ2+Pmhm,k∗+log21+Pmhp,mσ2+PThT,p.Therefore, at least one of the optimal solutionsP^T∗ and P^m∗ of problem (19) can take the maximum value; that is, constraints in Ca3 or Ca4 can be set equal.(i)
For case 1, the optimal solution (P^T∗,P^m∗) lies in the line BC; then P^T∗=PTmax. When PT is fixed, the objective function (19) is a convex function, so the optimal solution (P^T∗,P^m∗) can only be point B or point C.(ii)
For case 2, the optimal solution (P^T∗,P^m∗) may be in line BD or CD, and similar to case 1, the optimal solutions only may be B,C or D.(iii)
For case 3, the optimal solution (P^T∗,P^m∗) lies in the segment BC, and similar to case 1, the optimal solution is only possible for B or C.In summary, we can find that the optimal solution of subproblem (16) is as follows.WhenPTmax/A-σ2/hm,k∗≤Pmmax and Bσ2+PTmaxhT,p≤Pmmax, (26)P^T∗,P^m∗=argmaxfPTmax/A-σ2hm,k∗,PTmax,fBσ2+PTmaxhT,p,PTmax.WhenBσ2+PTmaxhT,p≤Pmmax and Aσ2+Pmmaxhm,k∗≤PTmax, (27)P^T∗,P^m∗=argmaxfBσ2+PTmaxhT,p,PTmax,fPmmax,Aσ2+Pmmaxhm,k∗,fPmmax,PTmax.WhenAσ2+Pmmaxhm,k∗≤PTmax and (Pmmax/B-σ2)/hT,p≤PTmax, (28)P^T∗,P^m∗=argmaxfPmmax,Aσ2+Pmmaxhm,k∗,fPmmax,Pmmax/B-σ2hT,p.When the abovementioned three conditions are not met, there is no solution to the original problem.


## 3.2. Joint Power Split Factor and D2D Interference Optimization Algorithm

According to the optimization results of Section3.1, this section will optimize the power split factor ρ; then, the optimization problem will become(29)P4Findρms.t.P^T∗τ1≤ρmηTτ0P0hS,Tτ1log21+P^T∗hT,k∗σ2+P^m∗hm,k∗≤τ0log21+1-ρmP0hS,Tσ2.The following constraints can be derived:(30)P^T∗ηTτ0P0hS,T≤ρm≤1-σ2P0hS,T2τ1-τ01+P^T∗hT,k∗σ2+P^m∗hm,k∗-1.Whenρm meets constrained condition (30), the original problem (18) has feasible solutions.In order to encourageDT to carry out cooperative communication and ensure the best benefits of its users, it should get the maximum energy in the process of cooperation, so let the energy harvested be △, that is,(31)△=ρmηTτ0P0hS,T-P^T∗τ1.Whenρm is maximized, △ goes to the maximum, so set(32)ρm∗=1-σ2P0hS,T2τ1-τ01+P^T∗hT,k∗σ2+P^m∗hm,k∗-1Thus, problem (18) is solved.Next, leti=m+1, then, changing the value of δm and continuing to solve problem (18).After traversing all channels, find out the best reuse cellular channelm∗=argmaxRsumm and output the global optimal solution.Hence, original problem (16) is solved.To conclude, the algorithms proposed in this paper are summarized as shown in Algorithm1.Algorithm 1:Joint Power Split Factor and D2D Interference Optimization Algorithm.
1. Initializem=1. 2. Ifm<M, order δi=1i=m0else, if not, jump to step 5. Solve problem(19): When the restricted condition (22) is satisfied, the optimal solution  P^T∗,P^m∗  is equation (26); When the restricted condition (23) is satisfied, the optimal solution  P^T∗,P^m∗  is equation (27); When the restricted condition (24) is satisfied, the optimal solution  P^T∗,P^m∗  is equation (28); If the above restricted conditions are not satisfied, output the optimal solution  Om=∅. 3.If the solution of step 2 satisfies the condition (30), output ρm∗ is equation (32). Or else,   Om=∅. 4.Here, the optimal solution of problem (18) is an array O m = P ^ T ∗ , P ^ m ∗ , ρ m ∗, calculate Rsumm by formula (19). Updatem=m+1, return step 2. 5.Find the best channelm∗=argmaxRsumm, and output the optimal solutionOm∗=Om.


## 4. Simulation Result

Figure10 simulates a wireless cellular D2D cooperative communication system with a size of 550∗500m2 with the BS located at 0,0. The abscissas of DS, DT, and DRk are 500. The coordinates of several CUs are between the BS and D2D users. The number of multicast transmission receiving users is 5, and all the users are within the radius of 10m. Set both the maximum transmission power PTmax and Pmmax of the user as 24dBm and τ0 and τ1 as 0.5. Assume the value of RminD2D and RminCU obeys the uniform distribution of [0,5] (bps/Hz). All channels meet hij=βijθijrij-α, in which βij is large-scale fading and θij is small-scale fading. The noise of all the received antennas is -114dbm.Figure 10
Wireless cellular D2D cooperative communication system.Figure11 is a simulation diagram under the scenario where the number of CUs is 15 when α=3. As shown in the figure, the blue baseline, about 9.301bps/Hz, is the rate of CUs when there is no interference from D2D multicast communication. When the average distance between DT and DRk increases, due to D2D cochannel interference, the rate of CUs is slightly lower than the baseline but generally remains the same. In this band, the rate of D2D multicast users can be greatly improved, remarkably increasing the spectrum utilization rate of the system. What is more, because of the influence of propagation path loss, the propagation rate of multicast is reduced when the average distance between DT and DRk increases, but a certain communication rate can be still guaranteed.Figure 11
System transmission rate (a).The simulation scenario in Figure12 shows the total system rate when the distance between DT is 50m. It can be drawn that when the number of CUs increases, D2D multicast communication will have more probability to reuse cellular channels with smaller cochannel interference, so the system rate will rise obviously at the beginning. But when the number of CUs rises to around 40, the system tends to a stable value. At this point, D2D multicast communication can select a better channel transmission from 40 CUs, ensuring that the system has a large total transmission rate. Therefore, without the occurrence of network congestion, the number of the best CUs in the communication system in this area is 40. In addition, it can be seen from the figure that the change of the channel coefficient will significantly affect the total rate of the system.Figure 12
System transmission rate (b).Figure13 is a help user benefit with a distance between DT and DRk of 50m and a number of 15 CUs when α=3. It can be seen from the graph that when the distance between DS and DRk increases, the energy harvested by ​T will be greatly reduced due to the influence of path loss, resulting in its lower revenue. And Figure 13 shows that when P0 is set as 30dBm-40dBm, and the distance between DS and DT is too long, the energy revenue is reduced to 0, and at this point DT is very likely to consume its own energy for cooperative communication, thus reducing the enthusiasm of the user’s collaboration. Therefore, when we find that the distance between DS and DT is too far, we should increase transmission power and ensure DT’s cooperative revenue.Figure 13
Energy benefits of collaborative users.


## 5. Conclusion

In this paper, SWIPT, D2D multicast technology, and user collaboration technology are combined to build up a D2D multicast cooperative communication system based on SWIPT, and a new transmission strategy is proposed. The objective of the research is to maximize the total system rate. Because of the problem of MINLP, the rate optimization problem is divided into D2D interference problem and power split factor optimization problem in this paper. To solve the D2D interference problem, we use linear programming to figure out the optimal transmission power and the optimal reusable cellular channel. In order to optimize the power split factor, we fully consider the benefits of the help users and aim at maximizing their benefits, figuring out the optimal power split factor. The simulation results show that the strategy proposed in this paper can significantly increase the total rate and spectrum utilization of the system, ensuring the benefits of the help users to a certain extent.



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*Source: 6790978-2018-11-01.xml*