Covert Communication in Integrated High Altitude Platform Station Terrestrial Networks

Zeke Wu,Kefeng Guo,Rui Liu and Shibin Zhu

1School of Space Information,Space Engineering University,Beijing,101416,China

2College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing,210016,China

ABSTRACT In recent years,Internet of Things(IoT)technology has emerged and gradually sprung up.As the needs of largescale IoT applications cannot be satisfied by the fifth generation(5G)network,wireless communication network needs to be developed into the sixth generation(6G)network.However,with the increasingly prominent security problems of wireless communication networks such as 6G,covert communication has been recognized as one of the most promising solutions.Covert communication can realize the transmission of hidden information between both sides of communication to a certain extent,which makes the transmission content and transmission behavior challenging to be detected by noncooperative eavesdroppers.In addition, the integrated high altitude platform station(HAPS)terrestrial network is considered a promising development direction because of its flexibility and scalability.Based on the above facts, this article investigates the covert communication in an integrated HAPS terrestrial network,where a constant power auxiliary node is utilized to send artificial noise(AN)to realize the covert communication.Specifically,the covert constraint relationship between the transmitting and auxiliary nodes is derived.Moreover,the closed-form expressions of outage probability(OP)and effective covert communication rate are obtained.Finally,numerical results are provided to verify our analysis and reveal the impacts of critical parameters on the system performance.

KEYWORDS Covert communication; the integrated HAPS terrestrial network; constant power auxiliary node; artificial noise(AN);effective covert communication rate

1 Introduction

The Internet of Things (IoT) is an information carrier based on the Internet and traditional telecommunication networks, which allows all ordinary physical objects that can be independently addressed to form an interconnected network.Nowadays, because the demand for large-scale IoT can not be satisfied by the fifth generation(5G)terrestrial mobile communication,the sixth generation (6G) terrestrial mobile communication development is becoming the general trend.Moreover,over recent years, high altitude platform station (HAPS) has been considered a critical part of the next-generation wireless communication networks for its high altitude, large capacity, flexible communication services, lower communication delay, and smaller terrestrial receiving antenna [1].Without loss of generality, HAPS can be regarded as a “pseudo satellite,” which is viewed as a supplement or substitute for satellites in many scenes [2].In addition, as an exemplary network architecture for future communications, the integrated HAPS terrestrial network has momentous practical significance,which can overcome obstacles and geographical constraints flexibly,compared with the integrated satellite-terrestrial network(ISTN)[3,4].Karabulut Kurt et al.[5]provided a vision and framework for the HAPS networks of the future,including highlighting the unrealized potential of HAPS systems and elaborating on their unique ability to serve metropolitan areas.Liu et al.[6]studied the performance of non-orthogonal multiple access (NOMA)-based integrated satelliteterrestrial relay network(ISTRN)in the presence of multiple primary users(PUs)under a spectrum sharing environment.Shuai et al.[7] investigated the performance of NOMA-based integrated satellite-HAPS-terrestrial networks with transmit antenna selection(TAS)in the presence of imperfect channel state information (CSI) and successive interference cancelation (SIC).Furthermore, the performance of the NOMA-based overlay cognitive integrated satellite-terrestrial relay network with secondary network selection was investigated by Liu et al.[8].The combined effects of channel estimation errors and hardware impairments on the secrecy performance of cognitive integrated satellite-terrestrial relay networks were researched by Guo et al.[9].Moreover,Guo et al.[10]studied the performance of the reconfigurable intelligent surface-assisted integrated satellite-unmanned aerial vehicle (UAV)-terrestrial networks with hardware impairments and interference in the presence of an unavailable direct link.Gao et al.[11] optimized the deployment of an aerial reconfigurable intelligent surface (ARIS) to assist the HAPS down-link transmission when the direct link was blocked.Pace et al.[12]investigated optimal routing issues in a multilayered terrestrial-HAPS-satellite network.The massive access for a satellite-aerial-terrestrial network (SATN) was investigated by Huang et al.[13], where a HAPS was deployed as a relay to assist the uplink transmission from terrestrial user equipment(UE)to satellite.

However, the openness of wireless communication and the broad coverage of the HAPS beam will lead to a series of security problems,such as channel monitoring,information eavesdropping,and malicious interruption.Generally,many traditional security policies focus on preventing the extraction of information, such as coding encryption or physical layer security technology using information theory.Popovic et al.[14]analyzed and compared the security features of network architectures based on HAPS and satellites by proposing a security comparison method for network architectures that were based on airborne infrastructure.A new selective encryption and decryption framework based on the start code for high-efficiency video coding was proposed by Lee et al.[15].On the other hand, Guo et al.[16] investigated the impacts of joint relay selection and user scheduling scheme on the physical layer security for a hybrid satellite-terrestrial relay system.Yerrapragada et al.[17]analyzed new schemes for securing applications at low latency by extending physical layer security(PLS)algorithms to beyond-5G/6G systems and designed protocols that advanced a specific form of PLS.The PLS performance of a wireless communication link through a large reflecting surface(LRS)with phase errors was analyzed by Vega Sanchez et al.[18].Zhang et al.[19]developed a novel layered physical layer security model to secure multiple messages simultaneously.

Nevertheless, preventing transmission from being perceived is considered a more direct and effective measure.Compared with the above means,covert communication has more advantages than other security policies,which can prevent transmission content and behavior from being detected by non-cooperative eavesdroppers to solve the problem of information security fundamentally.Based on this, many scientists and engineers have focused on the research of covert communication.Covert communication was first cited in military communications by Prescott et al.[20].Recently, the restriction theory of information transmission was being studied deeply by Bash et al.[21,22].It was proved that to meet the demands of covert communication in the AWGN channel,the transmission power of the transmitter decreased with the increase of codeword length, resulting in a near-zero effective covert communication rate on both sides of legal communication which is meaningless[23].Nevertheless,in the actual wireless communication environment,there are many interference signals which can be used to interfere with the eavesdropper’s communication signal[24].Namely,widespread interference can be used to hide the transmission of information.The interference was firstly proposed to be utilized to realize a positive covert communication by Li et al.[25].Topal et al.[26]provided a physical layer supported defense mechanism against traffic analysis attacks by exploring the covert communication capability of digital modulation schemes.Covert communication between a pair of legitimate transmitter-receiver against a watchful warden over slow fading channels was studied by Zheng et al.[27].Yang et al.[28]considered covert communications having uncertainty about the noise variance in fading channels where an eavesdropper used a radio-meter detector to detect the legitimate signal.Furthermore,Gao et al.[29]studied the performance of covert communication under a scenario consisting of a source-destination pair, a passive warden, and multiple relays.The requirement of information freshness in covert communications was considered for the first time by Wang et al.[30].Su et al.[31]investigated the covert communication performance in relay networks with relay selection.Zhang et al.[32]considered a covert mmWave communication system,where legitimate partiesAliceandBobadopted a beam training approach for directional link establishment.A new framework for jointly characterizing the covertness and timeliness of short-packet communications was developed by Yang et al.[33], in which a new metric named covert age of information (CAoI) was first proposed and derived.Channel uncertainty was exploited to achieve covert communication in relay networks by Wang et al.[34],in which a transmitter sent messages to the legitimate receiver with the help of a relay,and the eavesdroppers wanted to detect the existence of the transmission.

Inspired by the works mentioned above, this article considers an integrated HAPS terrestrial network with one constant power auxiliary node,a terrestrial eavesdropper,a HAPS as the transmitter,and a terrestrial user as the receiver.Moreover,all nodes are equipped with a single omnidirectional antenna and operate in half-duplex mode.Specifically,the significant contributions of this paper are summarized below:

1.Firstly,considering the single-user scenario,a novel integrated HAPS terrestrial covert communication network structure is established,and a constant power auxiliary node assists the covert communication between HAPS and the user.

2.Secondly,considering the actual situation of signal transmission,such as rainfall attenuation and free path loss,the statistical characteristics of the channel are given.In addition,the covert constraints on universal significance are derived.

3.Thirdly,based on the above,the closed expression of outage probability(OP)under this covert communication network is deduced to obtain more in-depth insights and laws.Furthermore,the index to measure the covert performance named effective covert communication rate is given.

4.Finally,the numerical simulation results are given further to analyze key parameters’impact on system covert performance.Moreover,the observation results are analyzed in detail.

2 System Model and Problem Formulation

As shown in Fig.1, an integrated HAPS terrestrial network is established, which consists of a HAPSA(Alice), a terrestrial userB(Bob), an auxiliary nodeC(Cora)near theA, and a terrestrial eavesdropperE(Eavesdropper).AliceandBobare legal communication parties, andAliceis a transmitter that wants to transmit information to the receiverBoband must be unknown to theEavesdropper.In general,Eavesdropperknows the location ofAliceand tends to detect its transmission behavior.Besides,Corais the jammer deployed byAliceandBob,which constantly emits a constant power of artificial noise (AN).Due to the persistent interference signal in the environment, it is assumed thatEavesdropperknows the existence ofCora.Moreover, all nodes are equipped with a single omnidirectional antenna and work in half-duplex mode.

Figure 1:System model

2.1 Channel Model

In order to get close to realistic transmission scenarios,the impacts of rain attenuation,free space loss,and antenna gain are considered in this system.Thus,the channel coefficient betweeni－thnode andj－thnode is given by

wheregijis the random channel coefficient of Shadowed-Rician(SR)fading,is the rain attenuation coefficient which undergoes lognormal random distribution,ωijrepresents the free space loss coefficient which is decided by carrier frequency and the distance,ξijdenotes the antenna gain ofi－thnode whileψijis the antenna gain atj－thnode,(ij∈{ae,ce,ab,cb}).

In Fig.1,all nodes are equipped with a single omnidirectional antenna and work in half-duplex mode.For specific analysis, it is assumed that there are discrete-time channels withNtime slots between each node, and each time slot hasntransmission symbol period or channel uses, which is expressed as the Fig.2.

Figure 2:N time slot discrete channel

Moreover,we assume that the channels within the system experience standard SR fading,which means that the channel gain of each time slot remains unchanged but varies independently from onetime slot to another.Based on the above,it can be considered that thehijis modeled by quasi-stationary SR fading, which is a complex Gaussian random variable with 1.Meanwhile, only a downlink time slot is considered in the subsequent analysis of covert communication performance.Finally, it is assumed that the time slots between the nodes are strictly synchronized, and the prior probability ofAliceperforming covert information transmission in each time slot is equal, which is 0.5.

Besides,following the general assumptions in covert communication theory[22],we assume thatAliceandBobshare a long enough key in advance so thatBobknows the transmission strategy ofAlice,butEavesdropperknows nothing about it.

2.2 Signal Model

Regarding a given maximum correct detection probabilityηofEavesdropper,there is a constraint on the average signal-to-noise ratio(SNR)ofAliceandCora.The information transmission process needs to be analyzed first to investigate the constraint relationship between them.And the received signal at userBobcan be given by

wherek= 1,2,...,nis the symbol subscript in one time slot,αdenotes the path loss coefficient,hij (ij∈{ae,ce,ab,cb})represents the channel fading coefficient,Dijis the node spacing,xaandxcdenotes the complex transmission signal ofAliceandCora,nbis the complex Gaussian white noise received byBobwithnb(k)～PaandPcdenote the transmission power ofAliceandCora,respectively.H1represents Alice sends valid signals to Bob andH0is the opposite.

Similarly,the received signal ofEavesdroppercan be given by

whereneis the complex Gaussian white noise received byEavesdropper,andne(k)～

2.3 Problem Formulation

In our model, only a single auxiliary node is considered, and the energy detection method is adopted byEavesdropper, which has been proved as the best method in quasi-stationary fading channel[25].

TheEavesdropperadopts the energy detection method to probe and judge whetherAliceis transmitting the information.Namely,when the average power of theEavesdropper’sreceived signal is larger than the preset energy detection threshold,EavesdropperconsidersAlice, andBobare transmitting signals to each other,and when the average power of theEavesdropper’sreceived signal is less than the preset energy detection threshold,Eavesdropperconsiders that there is no information transmission betweenAliceandBob,which is given by

Therefore,the error detection ofEavesdroppercan be divided into two categories as

wherePfais the false alarm probability andPmdis the missed detection probability.

On the above foundation,the requirements of covert communication can be expressed as

Furthermore, since the probability density functions of |hae|2and |hce|2are continuous and convergent,whenηis given,the following formulas can be satisfied,which is given by

where1χn2stands for the noncentralchi－squaredistribution with degrees of freedomn, while2χn2stands for thechi－squaredistribution with degrees of freedomn.

According to the weak law of large numbers and some mathematical steps,whenσc2≤andnis large enough,we can obtain

whereλ1＜σc2+σe2－θandθis a constant greater than zero.

Proof.See Appendix A.

whereλ2＞σa2+σc2+σe2+θ.

By means of(9)and(10),whennis large enough,we can derive

Moreover,the sufficient conditions of(11)can be expressed as

whereBCrepresents the complement of setB.

With the help of(12)and in the light of the different fading conditions involved,we can obtain

Proof.See Appendix B.

Then,the following formula can be obtained as

where Z is the set represents all the conditions in(12)hold together,andθ=according to formula(14).

Hence,the average error detection ofEavesdroppercan be expressed as

In conclusion,Aliceis able to meet the requirements of covert communication in(6)by controlling own transmit power,and due to the above formula(7),the covert constraint relationship betweenandis given by

3 Performance Analysis

In this section, the statistical properties of SR fading are provided.On this basis, the exact expression of OP for the covert communication in this integrated HAPS terrestrial network is obtained.Besides,we derive the closed-form expression of the effective covert communication rate to measure the system’s covert communication performance.

3.1 Statistical Properties of Channels

Firstly,the probability distribution function(PDF)and cumulative distribution function(CDF)of SR fading are obtained.From[35],the PDF ofgijis given by

Under the situation thatmijis an integer,with the utilizing of[36],1F1(mij;1;δijx)is represented as

According to(18)and(19),the PDF ofgabcan be re-written as

3.2 OP

OP can well evaluate the performance of the system, and in this paper we define the OP as the probability of the instantaneous capacity for any node lower than its excepted capacity.WhenAlicecommunicates withBoblegally,the SNR of the received signal atBobcan be given by

Assuming that the default coding rate ofAliceisthe OP of transmission betweenAliceandBobwhich is given by

whereCab=log2(1+γb).

By substituting(21)into(22),we can obtain the OP as

whereγth=2?Rab－1.

Furthermore,the final expression of OP can be derived as

where

3.3 Effective Covert Communication Rate

Effective covert communication rate is also a momentous and more intuitive index in the covert communication system, defined as the average ratio of practical transmission information to the transmission time from transmitter to the receiver under all fading conditions.Finally, the effective covert communication rateRabcan be expressed as

Furthermore,the final expression of the effective covert communication rate is given by

4 Numerical Results

In this section,the critical constraint relationship of average SNR between the transmitting node and the auxiliary node, and the effective covert communication rate of the considered system are proved through MC simulations.In general,we setDab

－α=Dcb－α=1 and it is assumed thathabandhcbown the same fading condition.In addition,we assume that a certain covert constraint is maintained in different fading channels.The SR fading channel parameters[38]are given by

· Frequent heavy shadowing(FHS):

mij=1,bij=0.063,Ωij=0.0007;

· Average shadowing(AS):

mij=5,bij=0.251,Ωij=0.279;

· Infrequent light shadowing(ILS):

mij=10,bij=0.158,Ωij=1.29.

Figure 3:Covert constraint of

Fig.4 depicts the relationship betweenandRabwith setting=20dB.It can be observed thatRabfirst increases and then degrades with the rise of.It is because there is an optimalwhich can be adjusted to obtain the maximum effective covert communication rate.Moreover,a largerηor the more serious fading conditions,which means more loose covert constraints or natural interference,can enhance the effective covert communication rate.

Figure 4:Rab vs.

Figs.5 and 6 plot thatRab vs.differentincluding linear and logarithmic forms,which can show different conclusions,respectively.We set the coding rate= 0.1bit/symbol.Under the givenη,it can be found thatRabreaches a stable limit value in high average SNR regimes from Fig.5, whereγbis approximately the proportional coefficient of the average SNR.In addition,it can be observed that the rise of the maximum allowable correct detection probabilityηloses the covert constraints,and a higher effective covert communication rate can be obtained.From Fig.6,we can realize that the worse fading condition in high average SNR regimes will lead to better performance, while the rate under FHS is lower than that under AS or ILS in low average SNR regimes.Due to that,much more serious fading conditions will prominently influence the quality of legitimate transmission service in a low SNR regime.In contrast,the worse channel condition will help implement covert communication easier.

Figure 5:Rab vs. (linear)

Figure 6:Rab vs. (logarithm)

5 Conclusions

This article systematically investigated the covert constraint and effective performance of covert communication in the integrated HAPS terrestrial networks, which utilized an auxiliary node with constant power.In particular, the covert constraint relationship between the transmitting node and the auxiliary node was discussed.Furthermore, the exact expressions of OP and effective covert communication rate were derived.According to numerical results, we found that the power of the transmitting node and auxiliary node under the covert constraint had a linear relationship.Secondly,the tightening of the covert constraint caused the deterioration of the achievable effective covert communication rate.Thirdly,there was an optimal preset coding rate to obtain the maximum effective covert communication rate.In addition,we knew that it was difficult for theEavesdropperto acquire correct judgment under severe fading conditions, which means natural interference, namely, covert communication, can be realized with less interference of the auxiliary node.Similarly, it was worth noting that the worse fading condition would enhance effective performance in the high average SNR regimes.

Acknowledgement:Thanks to all the authors for their contributions to this paper.The authors would like to thank the anonymous reviewers for their insightful suggestions that helped us improve this paper’s quality.

Funding Statement:This work was supported by the National Science Foundation of China under Grant 62001517, in part by the Research Project of Space Engineering University under Grants 2020XXAQ01 and 2019XXAQ05,and in part by the Science and Technology Innovation Cultivation Fund of Space Engineering University.

Conflicts of Interest:The authors declare that they have no conflicts of interest regarding the publication of this article.

Appendix A

Recalling the transmission model,under the condition ofH0,we can obtain

where1χn2stands for the noncentralchi－squaredistribution with degrees of freedomn, while2χn2stands for thechi－squaredistribution with degrees of freedomn.

Due to the weak law of large number andwe can get

Further,for ?θ ＞0,there is a constantN0which is large enough that for ?n ＞N0,we can derive

Moreover,for ?n ＞N0,we can get

Whenthere is

Therefore,at this time,for ?n ＞N0,we can obtain

whereλ1＜σc2+σe2－θandθis a constant greater than zero.

Similarly,under the condition ofH1,(10)can be proved by us.

Appendix B

Based on the previous Eq.(12)in this article,we have obtained

whereσc2=|hce|2Dce

－αPc.

Moreover,due to

we can get

Therefore,according to the scenario all we consider and the probability density distribution curve of|hce|2,We can deduce

Namely,