Secure Beamforming Design for SWIPT in Cooperative D2D Communications

Li Jiang, Cheng Qin, Xixi Zhang, Hui Tian

State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, and Science and Technology on Information Transmission and Dissemination in Communication Networks Laboratory, Beijing, 100876, China.

* The corresponding author, email: tianhui@bupt.edu.cn

I.INTRODUCTION

1.1 Motivation

With the emergence of Internet of Things,billions of devices will be connected and managed by wireless networks [1]-[3].The vast proliferation of mobile devices which is mainly attributed to the explosive growth of mobile data traffics requirements, such as multimedia traffics.The very large number of devices with the huge network traffics has increased the need for higher data rates and capacity.Cooperative communication has been considered as one of the key technologies in the next generation wireless networks, in which network nodes help each other in relaying information to realize spatial diversity advantages and promise significant performance gains in terms of link reliability, spectral efficiency,system capacity and transmission range [4].Comparing with fixed terminal relaying which involves the deployment of low-power base stations (BS) to assist the communication between the source and the destination, the device relaying can realize the full potential of cooperation [5].Device relaying makes it possible for devices, including a cell phone or any other portable wireless device with cellular connectivity, to function as transmission relays for each other [6].For example, when a device is in a congested area or in a poor coverage area, this device can communicate with its destination via the cooperation of relays,which are another devices between the source device and the destination.Furthermore, the relay can also transmits its own information during the cooperation in order to further enhance the spectral efficiency [7].

In cooperative device-to-device (D2D)communications, the wireless devices are often powered by batteries with limited energy.The lifetime of the wireless devices remains the bottleneck in the provision of ubiquitous wireless communication services.If a device is an energy constrained node, it is difficult for this device to cooperate with the other device.Thus the battery energy should be consumed efficiently.In [8], an energy-efficient multimedia transmission scheme was proposed to optimize energy efficiency by exploiting user behavior.In [9], a user social pattern (USP)-based spectral efficiency and energy efficiency enhancement scheme was proposed for a HetNet of the LTE-A system.A macro-assisted data-only carrier for future 5G networks from green prospective was proposed in [10].

Recently, there has been an upsurge of research interests in radio frequency (RF)energy harvesting technique, which is the capability of covering the received RF signals into electricity.This technique is a promising approach to prolong the battery life of the battery equipped wireless devices and improve the network performance [11].Furthermore,RF energy harvesting technique facilitates the possibility of simultaneous wireless information and power transfer (SWIPT), in which the RF signals are in the dual use for delivering energy as well as for transporting information concurrently [25].In this paper, we consider a new cooperative D2D communications scenario, i.e., a cooperative D2D communications with SWIPT, in which a D2D transmitter assists a cellular downlink transmission by acting as an half-duplex (HD) relay between the BS and the cellular user.In return, the D2D transmitter is allowed to directly communicate with the desired D2D receiver by using the cellular users’ spectrum.At the same time,there exists multiple idle D2D users which need to harvest energy from the D2D transmitter’s signal and store the harvested energy for future use .However, the idle D2D users may decode the cellular message instead of harvesting energy, which results in cellular message security problem.In practice, the security of the cellular message need to be guaranteed since the cellular users are spectrum owner.Therefore, in addition to meeting the energy harvesting requirements of the idle D2D users,the cooperative D2D communication system with SWIPT should be optimally designed to guarantee the cellular message security in the presence of potential eavesdropping of the idle D2D users.

1.2 Related works

1) Energy harvesting in cooperative D2D communications:In conventional wireless networks, the wireless devices are powered by batteries.Finite network lifetime due to battery depletion becomes a fundamental bottleneck that limits the performance of energy-constrained networks, e.g., wireless sensor networks.Alternatively, energy harvesting technologies have received much interest in wireless networks [12], [13], where wireless devices are enabled to harvest energy from renewable energy sources, such as thermal,vibration, solar, acoustic, wind, and ambient RF signal to prolong the battery life of the battery equipped wireless devices.Wireless communication with energy harvesting in D2D networks have been considered in [14]-[16].In [14], cognitive and energy harvesting-based D2D communication in cellular networks was modeled and analyzed.The cognitive D2D transmitters harvest energy from ambient interference and use one of the channels allocated to cellular users to communicate with the corresponding receivers.The stochastic geometry was used to evaluate the performance of the proposed communication system model with general path loss exponent in terms of outage probability for D2D and cellular users.The results showed that energy harvesting can be a reliable alternative to power cognitive D2D transmitters while achieving acceptable performance.In [15], a D2D communication provided energy harvesting heterogeneous cellular network (D2D-EHHN) was proposed,where user equipment relay harvest energy from an access point and use the harvested energy for D2D communication.A framework for the design and analysis of D2D-EHHN by introducing the energy harvesting region and modeling the status of harvested energy using Markov chain was developed.The analysis result showed that having a high energy harvesting efficiency enhances the performance of D2D-EHHN.By considering downlink resource reuse and energy harvesting, the goal of [16] was to maximize the sum-rate of the D2D links, without degrading the quality of service (QoS) requirement of the cellular users.Based on the results of Lagrangian constrained optimization, joint resource block and power allocation algorithms for D2D links was proposed, when there is non-causal and causal knowledge of the energy harvesting profiles at the D2D transmitters.

2) Security transmission in cooperative D2D communications:Physical layer security has been proved to be an effective method to provide secure communications by exploiting the characteristics of wireless channels, such as fading, noise and interference [17].To make physical layer security viable, it needs that the legitimate user’s channel condition to be better than that the eavesdroppers’.However, it may not be always possible in practice.Current studies use the transmit beamforming of multi-antenna transmission to concentrate the transmit signal over the direction of the legitimate user while reducing signal leakage to the eavesdroppers at the same time [18].Secure beamforming schemes have been widely designed in multiple-input multiple-output(MIMO) broadcasting channel [19], MIMO relay channel [20] and MIMO OFDM channel[21].The efficiency of secure beamforming depends on how much the transmitter knows the eavesdroppers’ channel state information(CSI).For a case that the transmitter cannot obtain the full CSI of eavesdropper channel,paper [22] designed robust secure beamforming scheme.In addition, the notion of using artificial noise (AN) to enhance physical layer security has also received much attention in recent years, in which artificially generated noise is added into the transmit signal so as to interfere the eavesdroppers deliberately[23].In the SWIPT system, information and energy are carried by the same RF signal.The information is recovered at the information receivers and the electromagnetic energy is harvested and converted into electric energy at the energy receiver.However, the energy receivers may decode the signal instead of harvesting energy, which results in information leakage.Therefore, in addition to meeting the energy harvesting requirements of the energy receivers, the SWIPT system should be optimally designed to guarantee the information security in the presence of potential eavesdropping of the energy receivers.Yet,the SWIPT technology raises a demand for redesign of existing wireless networks due to the imposed new security challenge.The secure communication in SWIPT systems has been studied in different contexts.In[24], the physical layer security problem was addressed in a multiuser multiple-input single-output (MISO) SWIPT system, where one multi-antenna transmitter sends information and energy simultaneously to an information receiver (IR) and multiple energy receivers(ERs).In [25], the secure communication of MISO downlink system with SWIPT and in the presence of passive eavesdroppers and potential eavesdroppers was considered.The resource allocation algorithm formulation took into account artificial noise and energy signal generation for protecting the transmitted information against both considered types of eavesdroppers when imperfect CSI of the potential eavesdroppers and no CSI of the passive eavesdroppers are available at the transmitter.Besides, the problem formulation also took into account different QoS requirements.In[26], the secure relay beamforming scheme for SWIPT in nonregenerative relay networks was studied.A constrained concave convex procedure (CCCP)-based iterative algorithm was proposed, where the secrecy rate is maximized and the relay transmit power and energy harvesting constraints are satisfied.In [27], secure D2D communication in energy harvesting large-scale cognitive cellular networks was investigated, where the energy constrained D2D transmitter harvests energy from multiantenna equipped power beacons (PBs), and communications with the corresponding receivers using the spectrum of the primary base stations.A power transfer model and an information signal model to enable wireless energy harvesting and secure information transmission were introduced.

However, our scenario differs from these previous studies in that the device transmitter performs double roles as a relay and a transmitter.Specifically, the D2D transmitter sends its own message to a D2D receiver while relaying the cellular downlink message to a cellular user.The D2D pair is considered as the MISO link [28], [29].The main contributions of our paper are as follows.

1.3 Contributions

• We consider a new security problem in the cooperative D2D communication with SWIPT, whereKidle D2D users exist to harvest energy from the received signal.However, the idle D2D users can be malicious and decode the cellular downlink massage without permission.

• We aim to achieve the secure cellular message transmission and guarantee the minimum required amounts of energy simultaneously transferred to the idle D2D users by designing the optimal forwarding beamformingand the transmitting beamformingat the D2D transmitter.

• We formulate the optimization problem to maximize the desired D2D user data rate subject to a secrecy rate constraint of the cellular user and individual harvested energy constraints of the idle D2D users.The formulated optimal problem is non-convex.A semi-definite programming relaxation(SDR) approach is adopted to obtain the optimal solution.Furthermore, we propose two suboptimal secure beamforming scheme with low computational complexity.Simulation results demonstrate the efficiency of our proposed beamforming schemes.

The rest of this paper is organized as follows.In Section II, we will describe the system model and formulate an optimization problem.Solutions of the optimization problem are proposed in Section III.Section IV presents simulation results.Section V concludes the paper.

II.SYSTEM MODEL AND PROBLEM FORMULATION

We consider cooperation between a cellular downlink communication and a D2D communication.The cellular downlink communication system consists of a source (S) and a cellular user (CU), while the D2D communication system has a D2D transmitter (DT) who serves one desired D2D user (DU).There existsKidle DUs.All terminals have a single antenna except that the DT hasNantennas.The S intends to send a confidential message,to the CU while the DT transmits a non-confidential message,, to the desired DU.For example, in a small cell area, a small cell access point (AP) equipped with single antenna serves CUs.However, the cellular link is so worse that it needs the DT to relay the cellular message.As a return, the DT can transmit its own message by using the spectrum of the cellular link [30].

In this paper, we consider a two-phase transmission.At the first phase, the S transmits signalto all the receivers.At the second phase, the DT concurrently transmits both the cellular confidential message and its own message to the CU and to the desired DU, respec-tively.TheKidle DUs harvest energy from the received signal.However, the idle DUs may decode the cellular confidential message instead of harvesting energy.Thus, the idles DUs may be potential eavesdroppers which should be taken into account for providing secure D2D cooperative communications with SWIPT.

The channel coefficients of the S-CU, the S-DU and thelinks are denoted by the complex scalarandrespectively.For simplicity, the complex scalar of the channel coefficientsandis written asThecomplex channel vectors of the S-DT, DT-CU, DT-DU andlinks are represented byandrespectively, in whichandare further denoted asIn order to satisfy the energy harvesting requirements, the idle DUs feedbacks their channel state information (CSI) to the DT to design the transmit beamforming.Thus, the DT knows the full CSI of all the receivers.

As shown in Fig.1, at the first phase, the received signal at the CU, the DT, the desired DU and thekth idle DU are given by, respectively,

At the second phase, the DT concurrently transmits both the cellular confidential message and its own message by using the forwarding beamforming vectorand the transmitting beamforming vectorThe resulting transmit signal vector at the DT is given by,

with average power

Fig.1 System model of cooperative D2D communications with SWIPT.The black solid lines denote the first phase and the red dotted lines denote the second phase

The achievable SINR of the D2D message at the desired DU is expressed as,

Suppose that thekth idle DU is an eavesdropper and decodes the cellular confidential message instead of harvesting energy.The received signal at thekth idle DU is,

The achievable SINR of the cellular confidential message at theth idle DU is,

Thus the achievable secrecy rate at the CU is given by [31],

On the other hand, the harvested energy of theth idle DU in each slot is given by

The secure beamforming is designed to maximize the desired DU data rate subject to the secrecy QoS requirement for the CU and the individual harvested energy constrains for all the idle DUs.The optimization problem can be formulated as (P1),

III.SOLUTIONS OF THE OPTIMIZATION PROBLEM

In this section, we present both optimal and suboptimal solutions to (P1).

3.1 Optimal solution to (P1):

In this subsection, we utilize the semi-definite programming relaxation (SDR) [32] to obtain the optimal solution for problem (P1).

Problem (P1)can be equivalently written as,

If the optimal solution of problem (P2)areandsatisfyingandthen the optimal forwarding beamformingand the optimal transmitting beamformingcan be obtained from the the eigenvalue decomposition (EVD) ofandrespectively; otherwise, ifand, then the optimal value of problem (P2) only serves as an upper bound on that problem (P1).However, we provide the method to construct the optimal solution with

Problem (P2) is still non-convex since its objective function, the constraint C1 and the constraint C2 are non-concave overand.However, we can apply the Charnes-Cooper transformation [33] to reformulate (P2) as an equivalent convex problem.

Lemma 1:Problem (P2) is equivalent to the following problem (P3).

Proof:First, given any feasible solutionto problem (P2), it can be shown that with the solutionandproblem (P3)achieves the same objective value as that of problem (P2).Second, given any feasible solutionto problem (P3), problem(P2) achieves the same objective value as that of (P3).Thus, problem (P2) and problem (P3)have the same optimal value.

In the following, we provide the method for constructing the optimal solutionwith rank-one.Letanddenote the dual variables of (P3) associated with C1-C5, respectively.Then the Lagrangian of (P3)is,

where

Algorithm 1 The proposed optimal algorithm for problem (P3)

Proposition 1:The optimal solutionsto problem (P3) satisfy the following conditions:

Proof:Please refer to Appendix A.

The optimal transmitting beamforming and forwarding beamformingcan be obtained by EVD ofThe specifical procedure of the proposed optimal scheme to solve problem (P3) is presented inAlgorithm1.

3.2 Suboptimal solution I to (P1):

In this subsection, we propose a suboptimal solution I for problem (P1) with lower complexity.In our proposed suboptimal solution,the forwarding beamformingis restricted to lie in the null space of the desired DU and the idle DUs’ channelsin order to eliminate the interference of the cellular message to the desired D2D user and the leakage of the cellular message to the idle D2D users.Note that the proposed suboptimal solution is only applicable whenWe present the proposed suboptimal solution in details.

The suboptimal solution aims to solve problem (P1) with the addition constrains:To satisfy this, the beamforming vectoris chosen as,

The suboptimal problem is formulated as(P4),

Assuming that (P4-SDP) is feasible, then it can be solved via CVX.Denote the optimal solution asThen the optimalcan be obtained by the EVD of

3.3 Suboptimal solution II to (P1):

In this section, we propose the second sub-optimal solution, in which there should be no interference between the cellular transmission and the D2D transmission.Thus, problem(P1) adds with the additional constraints:The beamforming vectoris chosen as,

Due to the fact that both constraints C1 and C3 should hold with equality,can be expressed respectively as

IV.NUMERICAL RESULTS

In this section, we evaluate the performance of the proposed secure beamforming design schemes by providing numerical results.We assume that the DT is equipped withN=5 antennas and there isK=1 idle D2D user.We consider a scenario where the distance from the DT to all the other terminals are 10 m,while the distance from the S to the CU is 20m.The channel between a transmit-receive antenna pair is modeled aswheredis the distance,is the path loss exponent, chosen as 3.5, andwis uniformly distributed overThe variance of noise are set asN0= -35 dBm.The power of the S and the DT are set to beand.The energy harvesting efficiencyis set to be 0.5.The maximum allowable SINR for thekth idle DU to eavesdrop the cellular message is set to beThe minimum required energy harvesting at thekth idle DU is 0 dBm.

Fig.2 depicts the achievable secrecy rate of the CU versus the minimum required SINR of the CU,for different beamforming schemes.It can be observed that the achievable secrecy rate of the CU is a monotonically non-decreasing withThis is mainly due to the fact that with increasingmore power will be used for satisfy the minimum required SINR of the CU in the constraint one in the original problem.Besides, suboptimal solution I is observed to perform better than suboptimal solution II.However, it is worth noting that suboptimal solution II has the lowest complexity among the three proposed solutions,since the closed form solutions of the forwarding beamformingand the transmitting beamformingare obtained in (31) and (32),respectively.

Fig.2 The achievable secrecy rate of the CU vs the minimum required SINR of the CU

Fig.3 The achievable data rate of the desired DU vs the minimum required SINR of the CU

Fig.4 The total harvested energy of the idle DUs vs the minimum required SINR of the CU

Fig.3 illustrates the achievable data rate of the desired DU versus the minimum required SINR of the CU,for different secure beamforming schemes.It can be seen that the achievable data rate of the desired DU decreases with the increasing ofsince most of the power of the DT is used for meeting the minimum required SINR of the CU in the constraint one in the original problem.The achievable data rate of the desired DU in the optimal beamforming scheme is higher than that in the suboptimal beamforming scheme I and that in the suboptimal beamforming scheme II.In the suboptimal beamforming scheme II, the idle D2D users only harvest energy from thedue to the fact that both the transmitting beamformingand the forwarding beamformingare designed in the channel null space.A small value of thecan meet the energy harvesting amount requirement in constraint three in the original problem, thus the change of the achievable data rate of the desired D2D user is not obviously.However, we plot a sub figure to show the decrease of the data rate of the desired DU in the suboptimal beamforming scheme II with the increasing of

Fig.4 shows the total harvested energy of the idle DUs versus the minimum required SINR of CU,for different secure beamforming schemes.It is expected that the total harvested energy of the idle DUs decreases with the increasing ofThe total harvested energy of the idle DUs in the optimal beamforming scheme is higher than that of the suboptimal beamforming scheme I and that of the suboptimal beamforming scheme II.The change of the total harvested energy of the idle DUs is still not obviously in the suboptimal beamforming scheme II.It is similar to Fig.3,we plot a sub figure to show the decrease of the total harvested energy of the idle DUs in the suboptimal beamforming scheme II with the increasing of

In the following numerical results, we will observe the affect of the number of idle D2D users on the performance of the proposed three beamforming schemes.We set the transmit antennas at the D2D transmitterand the number of idle D2D usersFig.5 depicts the achievable secrecy rate of the CU versus the number of the idle D2D users for the three proposed beamforming schemes.It can be observed that the achievable secrecy rate of the CU decreases with the increasing number of the idle D2D users for all the three beamforming schemes.The reason is that with the increasing number of the idle D2D users,there is higher probability of existing idle D2D users with better channel gains.Thus the D2D transmitter needs to allocate more power to the transmitting beamformingto combat the cellular information leakage to the idle D2D users.Moreover, It is observed that when the first idle D2D user is activated, there is a drastic decrease in the secrecy rate achieved in suboptimal solution II.However, the optimal beamforming scheme performs better than other two suboptimal schemes.

Fig.6 shows the achievable data rate of the desired DU versus the number of the idle D2D users for the three proposed beamforming schemes.It is similar to Fig.5 that the achievable data rate of the desired DU still decreases with the increasing number of the idle D2D users, since most of the D2D transmitter’s power is used for combatting the cellular information leakage to the idle D2D users.In addition, the data rate of the desired DU achieved by the optimal beamforming scheme is higher than that of the other two suboptimal beamforming schemes.

Fig.7 shows the total harvested energy of the idle DUs versus the number of the idle D2D users for the three proposed beamforming schemes.From the figure we can see that the total harvested energy of the idle DUs increases with the increasing number of the idle DUs.The total harvested energy of the idle DUs in the optimal beamforming scheme is higher than that of the suboptimal beamforming scheme I and that of the suboptimal beamforming scheme II.From the results in above figures, it is inferred that our proposed optimal beamforming scheme achieves good performance due to the jointly optimized forwarding beamformingand transmitting beamforming.

V.CONCLUSION

Fig.5 The achievable secrecy rate of the CU vs the number of the idle D2D users

Fig.6 The achievable data rate of the desired DU vs the number of the idle D2D users

In this paper, we considered a new security problem in cooperative D2D communications with SWIPT, in which the multiple idle DUs may eavesdrop the cellular confidential message instead of harvesting energy from the received signal.We aimed to design secure beamforming to maximize the D2D users data rate subject to the secrecy rate requirements of the cellular user and the minimum required amounts of power transferred to the idle DUs.To solve this non-convex problem, a SDR approach was adopted to obtain the optimal solution.Furthermore, we proposed two suboptimal secure beamforming scheme with low computational complexity.Simulation results demonstrated that comparing with the two suboptimal secure beamforming scheme, our proposed optimal secure beamforming scheme achieves a significant data rate of the desired DU while provides a high secrecy rate for the cellular users and facilitates the efficient power transfer for the idle DUs.

Appendice A Proof of Proposition 1

The Karush-Kuhn-Tucker (KKT) conditions of problem (P3) are expressed as,

According to (17), we have,

Next, we prove the second part of Proposition 1.Define

Last, we prove the third part.Forandwe construct another solution of the problem (P3),Then substituting them into the objective function and constraints in (P3) which achieves the same optimal value as the optimal solution and satisfies all the constrains.Thus,are also optimal solutions to (P3) but withand

This work is supported in part by National Natural Science Foundation of China under Grants 61602048, by National Natural Science Foundation of China under Grants 61471060,by Creative Research Groups of China under Grants 61421061, by National Science and Technology Major Project of the Ministry of Science and Technology of China under Grants 2015ZX03001025-002.

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