IRS-Aided SWIPT Systems with Power Splitting and Artificial Noise

Baogang Li,Fuqiang Si,Dongsheng Han,2,Wujing Wu,

1 Department of Electronic and Communication Engineering,North China Electric Power University,Baoding 071003,Hebei,China

2 Hebei Key Laboratory of Power Internet of Things Technology,North China Electric Power University,Baoding 071003,Hebei,China

Abstract:Intelligent refecting surface(IRS)is regarded as a promising technology because it can achieve higher passive beamforming gain.In particular,the IRS assisted simultaneous wireless information and power transfer(SWIPT)system can make the information decoding receivers(IDRs)have a higher signal-to-noise ratio(SNR),and the energy harvesting receivers(EHRs)have the guarantee of minimum harvested energy threshold.Motivated by the above,in this paper,we use the power splitting(PS)at the user and introduce artifcial noise(AN)into the access point(AP),so that the user in system can harvest energy and decode information simultaneously,further improve the security of user.We jointly optimize the beamforming matrix at AP,the refection phase shift at IRS and the PS ratio,in order to maximize the user’s achievable secrecy rate,subject to the user’s minimum harvested energy threshold and AP’s transmission power.Due to the introduction of PS ratio,the coupling between variables is increased,and the complexity of the problem is signifcantly increased.Furthermore,the problem is non-convex,so we propose an effcient algorithm based on Taylor Formula,semi-defnite relaxation(SDR)and alternating optimization(AO)to get the solution.Numerical results show that the proposed IRS-SWIPT system with PS and AN achieves signifcant performance improvement compared with other benchmark scheme.

Keywords:intelligent refecting surface(IRS);passive beamforming;power splitting;SWIPT

I.INTRODUCTION

With the rapid development of the Internet of Things(IoT),the number of mobile devices is increasing rapidly.Accordingly,there are a series of new challenges: due to the limited battery capacity,the task calculation in progress will be forced to terminate,and prolonging the lifetime of energy has become an urgent problem to solve.Because radio frequency(RF)signal can carry energy and information simultaneously,the use of RF signal for simultaneous wireless information and power transfer(SWIPT)is considered as a technology with enormous potential for development[1,2].For SWIPT system,the users are divided into two groups,a group of information decoding receivers(IDRs)for information decoding(ID)and a group of energy harvesting receivers(EHRs)for energy harvesting(EH).Meanwhile,as a new technology,intelligent refecting surface(IRS)has attracted wide attention[3–7].IRS is composed of a large number of low-cost passive refectors,which can be controlled by software to change the refecting phases and angles of the incident signal arbitrarily.In the early work on IRS,the active and passive beamforming of IRS-assisted systems was usually studied.Solve different problems by jointly optimizing the transmit beamforming of active antenna array at the AP and refect beamforming of passive phase shifter at the IRS[7].Recently,to make full use of the advantages of both technologies,the combination of IRS and SWIPT has become the focus of attention[8–12].

In the IRS-SWIPT system,according to different optimization objectives,the above papers studied the resource allocation problems in the system,such as beamforming matrix at access point(AP)and passive phase shift change at IRS.For instance,the authors of[8]maximized weighted sum rate(WSR)by using the block coordinate decent(BCD)method.[9]chose to minimize the transmission power at AP,and applied the penalty-based optimization method.Semi-defnite relaxation(SDR)and alternative optimization(AO)are used to maximize the minimum power received at EHRs in[10],and the work in[11]aimed to maximize the weighted sum-power received by EHRs.Different from the other articles,the author in[12]introduce a multi-objective optimization(MOOP)framework to investigate the fundamental trade-off between the data sum-rate maximization and the total harvested energy maximization.

Recently,physical layer security has emerged as an important secrecy criterion in the feld of wireless communication[13].In particular,[14–16]optimized the physical layer security of the SWIPT system.[14]and[15]took EHRs as a potential eavesdropper and maximized the security rate of the system.On the basis of ensuring that EHRs can harvest enough energy,it optimized the beamforming matrix at the AP and the transmission power to each user,so that the system has better security performance.In addition,in order to make the system have better performance,artifcial noise(AN)is applied to AP in[16],which greatly reduces the signal-to-noise ratio(SNR)of eavesdropper.

Furthermore,it is worth noting that due to the structure of the IRS,the direct signal from base station(BS)and the refected signal from IRS can be combined according to different demand.Compared with the traditional MIMO active relay,the IRS adopts the refection mode and does not need to amplify and regenerate the signal,so the energy consumption and the interference between signals are signifcantly reduced.Therefore,these characteristics make IRS a good choice to improve the physical layer security of system.The works in[17–23]studied the physical layer security in the IRS system,and improved the security performance of the system by jointly optimizing active and passive beamforming.The authors of[17]maximized the secrecy rate of the legitimate communication link by using the SDR and AO method.The work in[18]maximized the energy effciency,however[19,20]maximized the system secrecy rate and[21]minimized the transmit power.Particularly,the works in[22,23]applied AN technology in the IRS system to enhance physical layer security by deliberately impairing the channel of an eavesdropper.Their optimization goals are to maximize the achievable secrecy rate,and the methods used are roughly the same,such as AO,successive convex approximation(SCA),and SDR.

In addition,a lot of works[24–27]have studied the physical layer security of the IRS-SWIPT system.Because the characteristics of the two technologies can be effectively combined,so that the SNR at IDRs can be enhanced as needed in the IRS-SWIPT system,while the SNR at the eavesdropper can be weakened,at the same time,the energy collection at EHRs can be ensured.In particular,the works in[24]and[25]aimed to maximize the secrecy rate of IDRs,and proposed an inexact block coordinate decent(IBCD)method or penalty-based algorithm.The optimization problem in[26]was maximizing the system energy effciency(EE),the SDR and AO were used to solve the problem.[27]maximizing the minimum signal-tointerference-plus-noise ratio(SINR)among all IDRs.

However,even though the literatures on IRSSWIPT system are studied many methods to improve energy effciency,confdentiality or other performance indicators,it is still assumed that EHRs are potential eavesdroppers for optimization,which can not support the user ID and EH simultaneously.

In order to break through this bottleneck,two schemes are proposed in[28,29],namely time switching(TS)and power splitting(PS).TS divides the time of receiving signal into two time slots,one for EH and the other for ID.However,PS separates the received signal into two parts,one for EH and the other for ID.Therefore,how to design and apply TS or PS technology in IRS-SWIPT system to achieve the optimal performance balance of EH and ID for users is a new problem to be solved in the current literatures.Recently,some works have studied the combination of PS or TS technology and IRS-SWIPT system[30–33].The work in[30]and[31]maximized the energy effciency indicator(EEI)which is introduced to tradeoff between data rate and harvested energy.However,in[32]and[33],only a simple analysis of the feasibility and performance of PS or TS technology in the IRSSWIPT system.Therefore,there is no work that considers safety performance in the PS-aided IRS-SWIPT system and optimizes the achievable secrecy rate of the user.

Motivated by the above,in this paper,we study an IRS-SWIPT system,in which we use the PS at the user and introduce AN into the AP so that the user can ID and EH at the same time.In particular,due to the application of PS,the complexity of the algorithm has been inevitably increased because of the PS ratio and the coupling between variables.At the same time,because of the combination of IRS and SWIPT,the beamforming matrix at AP is refected by IRS,so that the signals at the receiver are coupled between vectors,which also increases the diffculty of solving the optimization problem.In addition,although the application of AN inevitably reduce the SNR of user and eavesdropper,the achievable security rate of the user in system still increase greatly by adjusting beamforming matrix at AP,refection phase shift at IRS and PS ratio.What is more different is that we assume that there is an external eavesdropper in the system,rather than assuming that EHRs are eavesdroppers in other articles like[24–27].Our main contributions are summarized as follows

·In order to improve the achievable security rate of user,we introduce IRS in the transmission path,apply AN in AP and PS in user,respectively.We assume that there is an external eavesdropper in the system,rather than assuming that EHRs are eavesdroppers.We also assume that the system experiences Rayleigh fading and obtain the expression of user’s achievable security rate subject to the user’s minimum harvested energy threshold,AP’s transmission power and the range of PS ratio.

·We solve the proposed non-convex problem by jointly optimize the beamforming matrix at AP,the refection phase shift at IRS and the PS ratio.By using Taylor Formula,SDR and AO methods,we fx other variables to optimize the target variables and propose their own algorithms.Then a global algorithm is proposed to solve the nonconvex primitive problem.

·Finally,the numerical results show that the proposed IRS-SWIPT system with PS and AN achieves signifcant performance improvement compared with the benchmark scheme.

The rest of the article is arranged as follows.In Section II,we describe the proposed IRS-SWIPT system model in detail,and present the problem formulation.In Section III,we transform the problem into a solv-able form and propose algorithm to solve the optimization problem.Then,the simulation results are shown in the Section IV.Finally,we summarize this paper in Section V.

II.SYSTEM MODEL AND PROBLEM FORMULATION

2.1 System Model

As shown in Figure 1,the IRS-SWIPT system based on PS and AN is composed of an AP equipped withNtantennas,an IRS equipped withMrefecting elements,a single antenna user and a single antenna eavesdropper.In order to prevent the information transmitted by AP from being decoded by the eavesdropper,AN will be transmitted with the information signal.In particular,the user adopts PS structure,which enables the user to decode information and harvest energy from the signal transmitted by the AP.Therefore,the signal transmitted by AP can be expressed as

Figure 1.The model for IRS-SWIPT system.

2.2 Problem Formulation

We aim to maximize the security rate of the system by jointly optimizing beamforming matrixω1andω2,PS ratioρand phase shiftθ.Therefore,the optimization problem is formulated as

where C1 is the transmission power constraint of AP and C2 is the user’s harvested energy threshold.The C3 is the user’s PS ratio,and C4 is the constraint of phase shift.

It is obvious that Problem(P1)is a non-convex problem because of the coupling among variables.Due to the addition of PS ratio and combination of IRS and SWIPT,the complexity of the problem is greatly increased.

III.THE OPTIMAL SOLUTION OF PROPOSED PROBLEM

In this section,we design an algorithm to solve the above problem by jointly optimizing beamforming matrixω1andω2,PS ratioρand phase shiftθ.Among them,for the optimization ofρ,we use the method of formula deformation and Taylor Formula.Subsequently,the original non-convex problem is transformed into a convex problem by SDR,and then AO is used for joint optimization ofω1,ω2andθ.

3.1 Optimizing PS Radio for Given Beamforming Matrix and Phase Shift

3.2 Optimizing Beamforming Matrix for Given PS Radio and Phase Shift

Algorithm 1.AO for solving(w1,w2).1: Initialization: Initialize the initial value of w1 and w2 by satisfying w1wH1 +w2wH2 ≤PA.2: Set m=1,W(0)1 =w1wH1 and W(0)2 =w2wH2 .3: Repeat:·t(m)U and t(m)E are calculated with W(m-1)1and W(m-1)2.· W(m)1 and W(m)2 are calculated with t(m)U and t(m)E .·m=m+1.4: Until(W1,W2)converges.5: Recover(w1,w2)from(W1,W2).

3.3 Optimizing Phase Shift for Given Beamforming Matrix and PS Radio

Algorithm 2.AO for solving f.1: Initialization: Initialize the initial value of ～F by satisfying η(1-ρ*)[Tr(HU～F+ ^HU～F)+σ2] ≥Ereq,～Fn,n =1 and ～F ■0.2: Set n=1 and ～F(0) = ～F.3: Repeat:·z(n)U and z(n)E are calculated with ～F(n-1).· ～F(n)are calculated with z(n)U and z(n)E .·n=n+1.4: Until ～F converges.5: Recover～f from ～F,and then calculate f.

Algo rithm 3.AO for solving the original problem.1: Initialization: Initialize the initial value of GAU,GAE,hAU,hAE, σ2, σ2ID, PA, Ereq and the coeffcients of ～F(0),W(0)1 ,W(0)2 and ρ(0).2: Set l=1.3: Repeat:· Solve ρ(l)for given ～F(l-1),W(l-1)1and W(l-1)2 .· Solve W(l)1 and W(l)2 for given ρ(l)and ～F(l-1).· Solve ～F(l)for given W(l)1 ,W(l)2 and ρ(l).·l=l+1.4: Until the maximum number of iterations is reached or all values converge.

IV.SIMULATION RESULTS

In this section,we show the simulation results to illustrate the performance of the proposed algorithm.The simulation setup is shown in Figure 2.We assume that AP,IRS,eavesdropper and user are located at(0,0),(2,2),(xE,0)and(xU,0)respectively,wherexE∈[3,5]andxU∈[10,20].In addition,we assume that the channel in the system experiences Rayleigh fading and can be expressed as

Figure 2.The simulation setup.

1.Without AN:AN is not applied;

2.Without IRS:IRS is not applied;

3.Without IRS and AN: IRS and AN are not applied.

In Figure 3,we study the convergence performance of the proposed algorithm.From the fgure,it can be seen that the algorithm has good convergence,and when the number of iterations reaches 14,the security rate is close to convergence.It can also be found that with the increase of the number of refecting elements,the achievable security rate will also increase.Similarly,the increase of the number of antennas at the AP will also increase the achievable security rate.This proves that IRS can effectively improve the security rate of the user.

Figure 3.The convergence behaviour of Algorithm 3.

Figure 4.Achievable security rate versus the number of reflecting elements.

Figure 5.Achievable security rate versus the maximum transmission power at AP.

Figure 6.Achievable security rate versus the minimum harvested energy threshold.

In Figure 4,we study the relationship between the number of refecting elements and achievable security rate.We can fnd that the performance of the proposed scheme is always better than that of other benchmark schemes.In addition,it can be seen that in the scheme with IRS,Rsecincreases with the number of refecting elementsM.We can also see the system with AN has higher security rate compared with the system without AN.These outstanding security performances are attributed to the fact that IRS greatly increases the SNR at the user and directionally reduces the SNR at the eavesdropper.Moreover,when the number of refective elements increases,the effect becomes more obvious.

In Figure 5,we investigate the infuence of the AP’s maximum transmission power on the achievable security rate.It is obvious that with the increase of the maximum transmit power,the security rate of all schemes shows an increasing trend.However,the proposed scheme is always better than other benchmark schemes.This is because when the user’s minimum harvested energy threshold is reached,the increased maximum transmission power can enable the user to allocate more power for ID.

In Figure 6,we show the achievable security rate versus the minimum harvested energy threshold.It can be seen from the fgure that the achievable security rate decreases with the increase ofEreq.This is because whenEreqincreases,the signals used for EH increase,which leads to a smaller proportion of signals for ID in the user’s received signals.It can be concluded that due to the application of PS,user can have EH and ID at the same time.But it is necessary to balance EH and ID to ensure that not only enough energy can be harvested,but also suffcient safety performance can be achieved.

Figure 7.Achievable security rate versus the x-axis coordinate position of user.

In Figure 7,we show the achievable security rate versus the x-axis coordinate position of user.The range of the user’s x-axis coordinate is[10,20],so we can study the impact of IRS on the user’s ID through this fgure.It can be observed from the fgure that as the distance between the user and the AP gradually increases,the achievable security rate under the four different schemes is decreasing.Obviously,the performance of the schemes with IRS is always better than the schemes without IRS.In the case of a large distance,the schemes without IRS can basically be regarded as unable to meet the safety needs of users.However,the proposed scheme can always maintain a good achievable security rate.It can be concluded that using IRS can signifcantly improve the working range of user equipment,which has practical application value.

V.CONCLUSION

In this paper,we investigate a IRS-SWIPT system using AN and PS,and study the achievable security of the user.In particular,to study the impact of IRS,AN and PS on system security,we jointly optimize the beamforming matrix at AP,the refection phase shift at IRS and the PS ratio,in order to maximize the user’s achievable secrecy rate,subject to the user’s minimum harvested energy threshold,AP’s transmission power and the range of PS ratio.We propose an effcient algorithm to optimize the variables in the system.Numerical results show that the proposed IRSSWIPT system with PS and AN achieves signifcant performance improvement compared with the benchmark scheme.

ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundation of China(No.61971190),the Fundamental Research Funds for the Central Universities(No.2019 MS089),the Hebei Province Natural Science Foundation(No.F2016502062)and the Beijing Natural Science Foundation(No.4164101).