Zhaoye Xu,Aiyan Qu,2,Kang An

1 College of Communications Engineering,Army Engineering University,Nanjing 210007,China

2 Jinling Institute of Technology,Nanjing 211169,China

3 Sixty-third Research Institute,National University of Defense Technology,Nanjing 210007,China

Abstract: In this paper, the physical layer secure transmission in multi-antenna multi-user cognitive internet-of-thing (IoT) network is investigated,where the coalitional game based joint beamforming and power control scheme is proposed to improve the achievable security of cognitive IoT devices.Specifically, the secondary network consisting of a muti-antenna secondary transmitter,multiple secondary users (SUs), is allowed to access the licensed spectrum resource of primary user(PU)with underlay approach in the presence of an unauthorized eavesdropper.Based on the Merge-Split-Rule, coalitional game is formulated among distributed secondary users with cooperative receive beamforming.Then,an alternative optimization method is used to obtain the optimized beamforming and power allocation schemes by applying the up-downlink duality.The simulation results demonstrate the effectiveness of our proposed scheme in improving the SU’s secrecy rate and system utility while guaranteeing PU’s interference threshold.

Keywords: physical layer secure transmission; IoT;coalitional game;alternative optimization method

I.INTRODUCTION

With the unprecedented development of the fifthgeneration (5G) infrastructure, tremendous attention has been paid to the Internet of Things(IoTs), whose capability of connecting things in physical world such as sensors, smart furniture and smart phones with wireless communication to exchange information.Various IoT applications can be extensively and effectively enabled with densely deployed infrastructure and advanced architecture[1].

However, numerous connecting demands of things will make spectrum resource exhausted [2], particularly for conventional spectrum management approaches.The exclusive assignment of spectrum resource and static utilization lead to inefficient and unbalanced utilization spectrum usage, which deteriorates the contradiction between continuous growth of interconnected IoT devices and the limited spectrum resources.Under this situation, cognitive radio (CR), which has been proved to be an effective approach in alleviating the spectrum scarcity via dynamic spectrum access,is regarded as a promising solution for IoT services.The overwhelming demand on the spectrum resource make it preferred to introduce CR technology to IoT[3].In this way,IoT devices,as SUs,share the licensed frequency band of pre-existing PN with its QoS met.[4] proposed a reliable energy efficient dynamic spectrum sensing method, and[5] presented a framework to design spectrum sensing and resource scheduling jointly for CR networks.In[6],the author jointly optimized the spectrum sensing time and packet error rate to maximize the cognitive effective-throughput.[7] derived a unique set of optimal sensing parameters to achieve the maximum throughput in a random access narrowband cognitive radio IoT network.Under jamming attacks,[8]proposed a novel probabilistic-based channel assignment mechanism, minimizing the invalidity ratio of CR packet transmissions subject to delay constraints.

In IoT network, constant information exchange makes it vulnerable to wiretapping attack since the broadcast propagation of electromagnetic.With decentralized users, traditional higher layers security techniques such as cryptography are complex and hard to implement[9–11].Different from the conventional cryptographic techniques which have inherent difficulties in secret key management[12],physical layer security (PLS) exploits a promising solution for secure IoT communication by exploring physical properties of wireless channels[13,14].Wyner firstly proposed the Wire-tap channel model based on Shannon’s information theory in [15].This model showed that when the eavesdropper channel is a degraded version of the main channel, the source and the destination can exchange perfectly secure messages at a non-zero rate,which is the basement of following physical layer security research.And there have been diversity techniques to improve PLS [16] and solve problems for Industrial Wireless Networks[17].

There has been several previous works focusing on the physical layer security of IoT based on CR network [18–26].Concerning IoT network, [12] proposed a leakage-based precoding scheme to eliminate the physical layer interference to PN,optimal the QoS for all the IoT devices and the signal-to-leakage-andnoise-ratio(SLNR)in MIMO-OFDM system.In[27],the nonorthogonal multiple access (NOMA) technology was proposed through accommodating multiple users in the same frequency.In downlink network,compared with OFDM,the NOMA can provide higher SE and more connectivity opportunities[28].

Game theory is an effective mathematical tool for studying and analyzing strategic interactions among decision-makers in wireless networks.Recently,there have been amounts of usages in physical layer security based on non-cooperative game theory such as zerosum game[29,30],and Stackelberg game in different scenes [31, 32].Also, cooperative game theory has been proposed to solve physical layer security problems.[33] introduced cooperation framework relying to protect the wireless transmission against eavesdropping.Considering the scenario of multiple source nodes and multiple eavesdroppers, distributed nodes with single antenna can adopt cooperative beamforming to improve secrecy rate in [34] and distributed merge-and-split algorithm, improving the average individual utility[35].In CR network, [36] proposed a novel distributed algorithm based on merge-and-split rule for collaborative spectrum sensing in CR network and improved the performance significantly.The authors in [9] demonstrated that cooperation between wireless network nodes can effectively improve the physical layer security of wireless transmission.When there is an eavesdropper in the SN trying to tap,the interference from the PN can be used by some means to help interference the eavesdropper to guarantee physical layer security transmission of SN.In[37],interference from SUs improved the PN secrecy capacity with the help of coalition formation game with nontransferable utility and beamforming technology.But only a part of trustworthy SUs can be selected to access the spectrum.

In this paper,we consider a game-theoretic physical layer secure transmission for cognitive IoT networks,where the SN consisting of a multi-antenna ST,multiple SUs and an unauthorized eavesdropper,is allowed to access the licensed spectrum resource of PN.The contributions of this paper can be summarized as follows:

? A coalitional game among distributed SUs is first formulated based on the Merge-Split-Rule,where distributed multiple SUs are divided into different coalitions with cooperative beamforming to receive signals transmitted from multi-antenna ST.

? Based on BC-MAC duality of MIMO downlinks system and up-down link duality between transmission and receiving beamforming, a joint optimization problem with respect to ST’s transmitting beamforming, ST’s power allocation schemes and SU’s receiving beamforming was proposed in the presence of PN’s interference constraint, which aims at improving SN secrecy rate and PN transmission rate simultaneously.

? Representative simulation results are provided to demonstrate the effectiveness of our proposed scheme,where both the SU’s secrecy rate and system utility are improved while guaranteeing PU’s interference threshold.

II.SYSTEM AND CHANNEL MODEL

For the system model under consideration,the PN consists of a PT,a PU while the SN consists of a ST,multiple SUs and a malicious eavesdropper as shown in figure 1.It is assumed that the ST is equipped withMantennas while other nodes are equipped with one single antenna each.In this paper, two receiving model,receiving as single node and receiving as coalition,are compared.

Figure 1. The considered system model.

In PN, the signal transmitted by PT can be represented asxP=, where the power ofsis normalized to one,i.e,=1,andPPis the transmission power of the PT.

In SN, x = Tdiag(p)1/2s is the transmitted signal.T = [t1,...,tk,...,tK] denotes the ST transmitting beamforming matrix,and thek-th transmitting beamforming vector is denoted bytk ∈CM×1with∥tk∥2= 1.s = [s1,...,sk,...,sK]TrepresentsKindependent signals and p = [p1,...,pk,...,pK]Tis the corresponding power allocation vector.

The signal arriving at the EVE and at the PU can be showed as the following respectively

The problem in this paper can be shown as:

where the SN’s secrecy rate and the PN’s transmission rate are involved.In a cognitive network, it is necessary to meet the QoS requirement of the PN.in this paper, the PN threshold rate is predefined asCΓ.The problem is to propose a proper scheme to guarantee the QoS of PN and achieve an improved secrecy rate of SN with maximum ST transmitting power constraint.Specifically,the problem can be convert to the maximization of the SN secrecy rate under the PN rate threshold and the ST maximum transmitting power constraint.The problem Eq.(3) can be shown as the following:

The following section will introduce two SU receiving models.

III.ANALYSIS TO RECEIVING AS SINGLE NODE

In SN,Ksingle nodes are selected to receiveKsignals from ST respectively.The signals received by thekth node can be showed as the following:

where hk ∈CM×1andgkdenote the channel from the ST and PT to thekth node respectively.nk ～CN(0)is the additive noise at the kth receive node.

Figure 1. System mode.

Therefor the SINR at thek-th SN receiving node can be shown as the following:

IV.ANALYSIS TO RECEIVING AS COALITION

By propose coalition game based on merge-and-split methods,distributed SUs cooperate to receive signals from the ST.There have been many distributed mergeand-split methods for coalition formation,and through these algorithms, wireless nodes can autonomously cooperate and self-organize into disjoint independent coalitions[9,35,36].So in this paper we only introduces simple merge-and-split rules for proposed coalition formation.

In this paper, Since the focus is on the coalitional beamforming performance, we are only interested in receiving as coalition rather than the detail of coalition formation algorithm.For convenience, we adopt the following scenario without loss of generality:

? In a coalition, we consider a TDMA receiving and transmission as in [9], a coalition receiving process is divided into two time slots: In the first slot,the coalition coalitions performs collaborative beamforming to receive information from ST; and in the second slot, nodes broadcast received information to the corresponding destination node.

? We consider the scenario where distances from eavesdroppers to the collations are far more than the coalition size, and therefore the transmitting power leakage when nodes communicating in a coalition in the second time slot can be neglected.This scenario is typical such as UAVs cluster communication in a small scope and other condition,as in[10,11].

Definition 1.A coalitional formulation game with transferable utility can be shown as(N,V(S)),whereNis the set of all the distributed nodes that join in the game,S = [S1,...,Sk,...,SK]denotes the formulated coalition, and V(S) =

It is obvious that distributed nodes have properties as following:

? The transmitting power leakage when nodes communicating in a coalition will cause interference to the other coalitions.

? The transmitting power of nodes communication in a coalition is finite.

? The interference to the other coalitions can be neglected if the transmitting nodes located in a coalition with proper size.

Based on properties above and merge-and-split rules, coalition formulation rules are proposed as the following:

? According to the property that the signal energy will decrease with the increasing of propagating distance, farer distance between two nodes in a coalition demands more transmitting power, resulting in more interference to other coalitions.Finding a proper size of coalition, the interference among coalitions and the security lose when exchanging information in a coalition can be ignored.Model the coalition as a circle,denote the max radius of a proper coalition asR,and denote the distance from thekth node to the topology center of a coalition asrk.Ifrk ≤R,thekth node will join in the coalition,otherwise won’t.Therefore the secrecy rate ofkth node can be written as

After distributed nodes formKdisjoin coalitions to cooperate to receiveKsignals from the ST,the Eq.(5)and Eq.(6)can be written as:where rk ∈CNk×1with∥rk∥2= 1 denotes the receiving beamforming vector of thekth coalition containingNksingle nodes, and all the receiving beamforming vectors can be collected in the vector ΥT=Hk ∈CNk×1and gk ∈CNk×1are the channel matrixes from the ST and PT to thekth coalition respectively.nk ∈CNk×1,nk ～is the additive noise at thekth coalition.

In cognitive network, for the underlay scheme, the SU coexists with the PU as long as no harmful interference is caused to the PU.In the following part,a joint transmission beamforming and the power allocation of ST scheme is proposed to reduce the interference to PN,guaranteeing the QoS of PN.

Beside, the effect of the interference from the PN to the SN can not be ignored.Both for SUs and the EVE, the interference from the PT is considered as detrimental factor that limits the rate.However,the interference can be beneficial to physical layer security in SN.A coalitional receiving beamforming scheme is proposed to reduce the interference to SUs, while the EVE can not diminish the interference,improving the secrecy rate of SN.

4.1 Analysis to MIMO Downlink Transmission

With proposed coalition formulation game, the distributed nodes formulateKdisjoint coalitions, building a MIMO downlinks transmission with the ST.

By optimizing ST downlinks beamforming vectors,the ST downlinks power allocation and receiving beamforming vectors of SU coalitions,we can reduce the interference among downlinks,the PN interference leakage to the SN and the SN interference leakage to the PN.

LetPint1andPint2denote the interference threshold at the PU and SU coalitions respectively,and therefore the problem can be written as the following:

It is difficult to optimize the transmission beamforming matrix T and the receiving beamforming vector Υ simultaneously.Therefore the alternative optimizing method is proposed.In this way, we fix one beamforming vector and optimize the other,then swap each other until the two beamforming vectors are optimal.

4.2 Initialize the Receiving Beamforming Vector

As analysis before,the proper receiving beamforming vectors should diminish the interference from PT as far as possible.Here SVD method[38]is proposed to initialize the receiving beamforming vectors: Firstly decompose the singular value of;Secondly choose one vector from,the matrix composed of right singular vectors of the zero singular values of, and normalize it to be the receiving beamforming vector rkof the kth coalition, where apparentlygk= 0; Finally initialize all the other coalitions receiving beamforming vectors by the same way.

4.3 Design the Transmission Beamforming Vector and the Power Allocation

Now the problem is to obtain the proper transmission beamforming vectors T and power allocation P.To simplify the analysis, combine the two power constraint to one power constraint[39],and then the problem can be transformed into the following structure

whereP1=a1Pint1+b1PSmax,anda1,b1>0 are the auxiliary variables.

From the SINR formula of the SN,it is apparent that the transmission beamforming vectors are coupling so that as one transmission beamforming vector changes,all the SINRs of downlinks change, which makes it difficult to obtain the transmission beamforming vector T and the power allocation P.[40, 41] proved that with settled transmission beamforming vector and sum power, the problem can be simplified by convert the downlink joint optimization to the uplink joint optimization based on BC-MAC duality.

4.4 Design the Receiving Beamforming Vector

whereP2=a2Pint2+b2Pmax, anda2,b2>0 are the auxiliary variables.When the interference from the PN to the coalitions meets the threshold, w has no influence toSo for convenience, let w=p/∥p∥1.

4.5 Alternative Optimization

The Eq.(12)and Eq.(13)can be written uniformly as

Inner cycleFirstly, fix the power allocation x with random but reasonable initialization values to obtain U,and then Eq.(14)can be written as

where ukcan be obtained by solve(ηk,βk)dominant generalized singular vectors.

Secondly,according to[39,42],the coupling matrix can be built as

We can obtain the following equation

Algorithm 1. Subgradient algorithm.1: inner cycle: solve Eq.(14) and Eq.(17) alternatively, update uk,?k and xext continuously until|λn ?λn|≤ε1,then turn to step 2;2: outer cycle: solve Eq.(18)to obtain yext,and update a, b by using Eq.(19).if meeting Eq.(20),finish the algorithm,otherwise turn to step 1.Algorithm 2. Alternative optimization algorithm.1: initialize the beamfroming vectors of coalitions by using SVD method,obtaining Υ0;2: fix Υn?1,and solve the problem Eq.(12)by using Subgradient algorithm, obtaining pn = yn T =U;3: fix Tn,make xn = pn,and solve the Eq.(20)by using Subgradient algorithm,obtaining Υ=U;4: judge the stop condition: if max k■■γnk ?γn?1k■■≤ε2,then stop the algorithm,or turn to step 2.

whereλis the greatest singular value of Λ,and=is the corresponding singular vector divided by its last element.

Outer cycleThe corresponding dual matrix of Eq.(17)is where V=is the dual power allocation of xextand can be obtained by using the same way as xext.

Update the auxiliary variables by using yextobtained:

wheretis the update step.And the stop conditions are as following

The algorithm step is shown in Algorithm 1.

Based on the analysis above, the alternative optimization algorithm of T, p and Υ can be shown in Algorithm 2.

V.NUMERICAL RESULTS

In this section,numerical simulations are carried out to investigate the performance of the coalition game and effectiveness of the alternative optimization algorithm.For convenience,we assume that the PT’s transmitting power is 1, i.e.PP=1, the total transmission power available of ST is 1,i.e.Pmax=1,all the noise powers are set to 0.1,i.e.==0.1,the weight to the secrecy rate of the SN and to rate of the PN in utility function are set to 1,i.e.α=β= 1,the band is set to 1, i.e.W= 1, and interference threshold at the PU and SN coalitions are set asPint1= 0.1 andPint2= 0.01.For coalition formation, let the max radius of a proper coalitionR=1km, that means if a node joining in a coalition makes the max radius of the coalition be more than 1km,the node will not choose to form the coalition.Consider the distances from the eavesdropper to coalitions are more than the coalition size, and therefore the distances are set all more than 3km.We will compute utilities when SUs receive signals as single node model and coalition model.Then all the utilities are compared to validate the proposed method.

Figure 2 shows a snapshot of the SN structure.According to the coalition formulation rule 1,there is no controversy on coalition 1 and coalition 2,while node 4 can not only form the coalitionS3={1,2,3,4},but also can form the coalitionR4={4,5,6}, resulting in two different coalition sets S={S1,S2,S3,S4}and R={R1,R2,R3,R4}.And the amounts of the node in two different coalition sets are={3,3,4,2}and={3,3,3,3}.In the following section, we firstly take coalition set S into consideration to show the performance of proposed method,then make a comparison between S and R in system utility to show the coalition conversion.

Figure 2. A snapshot example of coalition formation in SN.

Firstly, considering step2 in the algorithm 2, we construct the receiving beamforming vectors to obtain the transmission beamforming vectors and power allocation.Figure 3 shows the convergence of the Subgradient algorithm for uplink scenarios.For the convergence of the uplinks SINRs in figure 3(a),the different coalitions coincide together,justifies the efficient convergence.Figure 3(b) shows that the total transmission power increases with the optimization to transmission beamforming vectors until it reaches the maximal power of the SN.Figure 3(c)shows that through the proposed optimization algorithm, the interference from the ST to the PU decreases until it meets the threshold of the PN.

Figure 3. Verification of Subgradient algorithm for uplinks.

Considering step3 in the algorithm 2,figure 4 shows the convergence of the Subgradient algorithm for downlink scenarios.Figure 3(a) shows the convergence of the downlinks SINRs, where the D-value among downlinks SINRs decreases with optimization until convergence.Figure 4(b) shows that the total transmission power increases with the optimization to receiving beamforming vectors until it reach the maximal power of the SN.Figure 3(c)shows that by optimizing the receiving vectors,the interference from the PT to the SN decreases until it meets the threshold of the SN.

Figure 4. Verification of Subgradient algorithm for downlinks.

Figure 5 shows the variation of information rate at all receiving coalitions when optimizing transmission beamforming vectors, power allocation and receiving beamforming vectors alternatively.It can be observed that the D-values among receiving coalitions decreases to zero and the information rates of receiving coalitions increase, which shows that the proposed algorithm can effectively improve the information rate of the SN receiving coalitions.

Figure 5. The information rate at all receiving coalitions.

Figure 6 shows the variation of interference from the PT to the SU coalitions in the process of alternative optimization.As can be seen,the variation is different among various coalitions.While for the whole condition,the sum interference from the PT to the SN decreases.Therefor the algorithm indeed can decrease the sum interference from the PN to the SN.

Figure 6. The interference from the PT to SU coalitions.

Figure 7 shows the variation of secrecy rate in the process of alternative optimization.It is obvious that secrecy rates at all coalitions increase with optimization, and the sum secrecy rate of the SN increases accordingly, which confirms the effectiveness of pro-posed method.Also from Figure 7 and Figure 5, secrecy rate and information rates at SU coalitions have the synchronous variation, confirming analysis that the secrecy rate of the SN can be optimized through SINRs at SUs.

Figure 7. The secrecy rate at SU coalitions.

The comparison of coalition set R with S is shown in the Table 1.It is obvious that the coalition set R can achieve higher system utility.Hence, according to the merge-and-split rule, there is the transform :{S1,...,Sm}→{R1,...,Rn}.

Table 1. Simulation result of coalition set S and R.

As depicted in Section III,when receiving as single node,Ksingle nodes in SN are selected to receiveKsignals from ST respectively.then the SN system can be modeled as a typical downlink transmission problem in a cognitive radio network, where the existing downlink schemes in[39,42]can be proposed.In Table 2, as the comparison between case with receiving as coalition set R and case with single node shows,with the same PT rate,receiving based on coalition set R can improve the receiving SINRs,corresponding information rate,secrecy rate and system utility.

Table 2. Simulation results based on coalition set R and single node.

VI.CONCLUSIONS

In this paper, we have investigated the physical layer security in CR-based IoT network.Taking into account the distributed SUs,we have proposed coalition game and merge-and-split rule to formulate multiple coalitions to cooperate to receive signals from ST.For the case of improve utility value based on available sum secrecy rate in SN and transmission rate in PN,we proposed an alternative optimization algorithm to obtain proper transmission vectors, power allocation,and receiving vectors.For the case of MIMO downlinks problem, we simplified the problem based on BC-MAC duality and up-down-link duality.The simulation result conformed the performance of proposed algorithm.