Dual-Threshold Based Secure On-Off Transmission Scheme for Dense HCNs with Imperfect CSI

Yunjia Xu,Kaizhi Huang＊,Yi Zou,Xin Hu

National Digital Switching System Engineering & Technological Research Center,Zhengzhou 450002,China

Abstract:In this paper,we propose a dual-threshold based secure On-Off transmission scheme,where signals are transmitted only if the channel condition can guarantee secure and reliable communication.First,we present a dynamic access strategy to increase access efficiency,which provides an access region for the intended user.Then,we propose an emission control policy to transmit signals according to the current channel condition,which declines the influence of channel estimation errors and guarantees qualities of communication links.Furthermore,we give a comprehensive performance analysis for the proposed scheme in terms of connection outage probability (COP) and secrecy outage probability (SOP),and present a dual-threshold optimization model to further support the performance.Numerical results verify that the secure On-Off transmission scheme can increase the system secure energy efficiency and guarantee reliable and secure communication.

Keywords:physical layer security; imperfect CSI; dense heterogeneous cellular networks; On-Off transmission; secure energy efficiency

I.INTRODUCTION

Dense heterogeneous cellular networks (HCNs) can promote the system capacity and coverage effectively [1,2].However,the broadcast nature of wireless communication may lead to confidential information leakage.Therefore,the security in dense HCNs is of paramount importance.Traditional encryption methods are confronted with difficulties of key distribution when applied in dense HCNs,which seriously restricts the performance of the systems.As an important complement to traditional security approaches,physical layer security (PLS) technology employs the “basic attributes” of wireless channels to ensure secure communications.During the past decades,a framework of using PLS in dense HCNs has been developed in [3],and security performance has been analyzed in [4].On this basis,researchers have designed many methods to improve the security performance of dense HCNs,including multiple-input multiple-output (MIMO) [5,6],cooperative transmission [7-9],cooperative interference [10,11],resource allocation [12-14],signal processing [15,16] and so on.

1.1 Related works and motivation

Although a large number of secure transmission schemes have been proposed for dense HCNs,the above studies [3]-[16] are based on the hypothesis of perfect channel state information (CSI).In practice,complex interference may lead to channel estimation errors.In addition,small base stations (BSs) may not be able to do real-time processing of CSI,resulting in channel estimation errors.Therefore,the structure of dense HCNs determines such systems are more vulnerable to be affected by channel estimation errors than traditional cellular networks.To guarantee secure communication,[17] has analyzed the impact of artificial noise (AN) by a stochastic geometry approach.Based on this,[18] has presented an optimal power allocation scheme for artificial noise in multiple antenna systems.Nevertheless,the interferences caused by artificial noise leakage increases with the raise of the channel estimation errors,thus the AN-assisted schemes are not applicable in systems with large channel estimation errors.In point-to-point communication network,[19] put forward a secure On-Off transmission scheme to reduce the influences of channel estimation errors.In multi-antennas system,robust beamforming [20,21] and artificial noise assisted transmission scheme [22] have been applied.However,the proposed scheme only considers channel estimation errors in a fixed communication link,which ignores multi-link channel estimation errors caused by open access mechanism.In multi-cell system,secrecy performance analysis [23] and cooperative transmission schemes [24,25] have been applied to ensure secure communication with imperfect CSI.Nevertheless,all of the aforementioned works [19]-[25] only concentrate on networks with fixed location and number of communication nodes,which ignore the challenges when applying the above-mentioned methods to the system.

1) The random deployment of dense HCNs results in irregular locations and numbers of communication nodes,thus transmission schemes designed for fixed communication links are difficult to apply to networks with dynamic topologies.

2) In dense HCNs,multi-link channel estimation errors should be thought about due to the open access mechanism,hence the aforesaid works which only consider a fixed link with channel estimation error are incomplete.

As a result,the traditional transmission schemes are no longer applicable in dense HCNs with imperfect CSI.

In this paper,we propose a dual-threshold based secure On-Off transmission scheme of dense HCNs to decrease the influences of channel estimation errors,and improve the reliability and security performances of the system.

1.2 Our work and contributions

Motivated by the above observations and challenges,we apply PLS technology toK-tier dense HCNs with imperfect CSI,where the positions of BSs,users and eavesdroppers are all modeled as independent homogeneous Poisson Point Processes (PPPs).We provide a dual-threshold based secure On-Off transmission scheme of dense HCNs to improve the performance of the system,and provide a comprehensive performance analysis under a stochastic geometry framework.Our main contributions are summarized as follows:

1) A dynamic access strategy based on average received signal power is proposed to increase access efficiency.By setting access threshold,users cannot associate the BSs with bad channel condition,thus not only good communication link qualities but also efficient access efficiency can be guaranteed.On this basis,an emission control policy based on instantaneous estimated signal power is presented.By setting transmission threshold,only if communication links in good channel condition can transmit signals,which ensures reliable and secure communication.

2) Analyses of performance metrics including connection outage probability (COP) and secrecy outage probability (SOP) are conducted for the proposed scheme in the presence of co-channel interference and the most threatening eavesdroppers.

3) To further support the performance of the system,we present a dual-threshold optimization model,which maximizes the secure energy efficiency (secure EE) subject to the security and reliability requirements of the network.Besides,we introduce a two-dimensional search method to obtain the optimal thresholds.

This paper is organized as follows.Section 2 introduces the system model with multi-link channel estimation errors.Section 3 presents the secure On-Off transmission scheme.Section 4 explores the approach in dense HCNs by analyzing the COP and SOP.Simulation results are presented in Section 5.Section 6 concludes the paper.

II.SYSTEM MODEL

InK-tier dense HCNs,BSs in different layers are distinguished by transmission power,path loss coefficient,spatial distribution and number of antennas.As the locations of BSs and eavesdroppers are unplanned,we model them by random spatial point process.Positions of BSs,legitimate users and eavesdroppers in thei-th tier are modeled as homogeneous PPPs,i.e.Φi,Φuand Φe,with intensityλi,λuandλe.Taking them-th BS in thei-th tier as an example,i.e.Bim,the total transmission power and antennas number ofBimarePiandNi,respectively.Users and eavesdroppers are all equipped with single antennas.We consider large scale and quasi-static Rayleigh fading at the same time,and the large scale fading coefficient isα,α＞2.

In channel estimation phase,BSs transmit the pilot signals at each time slot.Users receive the pilot signals to estimate the current channels,and feed the estimated CSI to BSs through ideal backhaul links.The random deployment and overlapping coverage ranges of BSs cause users receive pilot signals from a plurality of neighboring BSs,which may cause channel estimation errors easily.We considerhuias the legitimate communication link,andas the estimated value ofhui,so the precoding matrix isThe relationship betweenandhuican be expressed as [19]:

whereni～CN(0,1-ρi),1-ρiis variance of the channel estimation errors.ρi(0 ≤ρi≤1) can be regarded as channel estimation accuracy,and higherρiindicates more accurate the channel estimation.

According to Slivnyak theorem,we consider a typical user accessing to base stationBim,the estimated SINRreceived by the legitimate user is:

whereiK∈[1,],～gamma(Ni,ρi).Xiis the distance from the legitimate user to the serving BS.denotes intra-interferences and cross-interferences received by the legitimate user,wherehujis the interference channel vector,～exp 1(),andZiis the distance between the interference BS and the legitimate user.σui2is the power of white Gaussian noise received by the user.

Due to channel estimation errors,the real SINRγUireceived by the legitimate user is:

Assume non-colluding eavesdroppers can estimate the channel accurately.Considering the worst case,we study the eavesdropping link with the largest SINR,which can be expressed as:

whereiK∈[1,],～exp 1(),Yiindicates the distance between the BS and the eavesdropper,denotes interference received by the eavesdropper,wherehejis the wiretap channel vector,～exp 1(),andMiindicates the distance between the interference BS and the eavesdropper,σei2is the power of white Gaussian noise receiving by the eavesdropper.

As green communications is proposed in the next generation cellular networks and the limited power of wireless nodes confines reliable and secure communication [26],some researchers consider secure EE as an important parameter to analyze the performance of dense HCNs.Secure EE is defined as average secrecy rate at which the confidential messages are reliably and securely transmitted from the transmitters to the legitimate receivers with unit energy consumption.Mathematically,secure EE of a typical link in thei-th tier is given by:

wherePi,totalis the total power consumption per unit area in thei-th tier.ptixis the transmission probability.pciois the connection outage probability.is the secrecy outage probability andis the secrecy rate of the legitimate user.

In dense HCNs,locations and numbers of nodes are no longer fixed,and channel estimation errors are different in multi links.Therefore,traditional transmission methods considering fixed communication link cannot be applied directly to the system.So we propose a dual-threshold based secure On-Off transmission scheme under a stochastic geometric framework,to ensure reliable and secure transmission in dense HCNs.

III.SECURE ON-OFF TRANSMISSION SCHEME

In this section,we put forward a dual-threshold based secure On-Off transmission scheme.First,we propose a dynamic access strategy to increase access efficiency.Then,we design an emission control policy to dominate the transmission only when BSs in good channel condition,which guarantees reliable and secure communication.

3.1 Dynamic Access Strategy

In the open network,users can choose arbitrary BSs to access.However,open access may greatly reduce access efficiency inK-tier dense HCNs.So we consider adopting a dynamic access strategy by installing an access thresholdτito ensure efficient access,where the access threshold is set according to the large-scale fading of communication link of each tier.The dynamic access strategy allows those users with receiving powerPrilarger thanτito access,which can be expressed as:

Specifically,it can be deduced that users can access BSs when the distancexifrom BSs is less thanDi,i.e.xi∈(0,Di],where

The legitimate user selects the BS providing maximum receiving powerPrias its serving BS,i.e.Pri＞Prj,j≠i.The association probability Aiand the probability density function (PDF)f Xi(x) of the distanceXifrom the user to the serving BS can be expressed as [3]:

3.2 Emission control policy

In the emission control policy,BSs implement emission control by comparing the estimated SINR with the transmission thresholdµi,where BSs transmit signals only if the estimated SINR of the legitimate user is greater thanµi.Otherwise,BSs suspend transmission as the current channel quality is not suitable for secure transmission.We define ℵ as a symbolic function to illustrate the state of the transmission in the current time slot,which can be expressed as:

It is obvious that the key of the emission control policy is to set an appropriate transmission threshold.Therefore,it is significant to design the optimal transmission threshold to decrease the influence of channel estimation errors and guarantee reliable and secure communication.

IV.PERFORMANCE ANALYSIS

In this section,we derive the analytical expressions of transmission probability,COP and SOP of the proposed scheme to analyze the reliability and security performances.Based on this,we present a dual-threshold optimization model to further support the performances of the system.

4.1 Transmission probability

Transmission Probability (TP) quantifies the probability that the messages can be transmitted at the serving BS.If the estimated SINR is larger thanµi,Bimcan transmit signals.

Proposition 1:The transmission probability of a typical link in thei-th tier is given by:

where

where

Remark 1:τiandµihave effects on TP from (11).AsTP decreases with the increase ofτi.This indicates that setting the access threshold can increase the probability of transmission.

Remark 2:SincesoTP of thei-th tier monotonically decreases withµi.Whenµi=0,the BSs transmit signals whenever a user access,and TP can be expressed asWhenµi→∞,=0,BSs do not transmit signals at this time slot.

4.2 Connection outage analysis

COP of a typical link in the i-th tier is given by:It measures reliability of communication link.Due to the system adopts the On-Off transmission scheme,there is no doubt that no connection outage occurs when there is no signal transmission,thus the COP of the system with the proposed scheme can be redefined as:

Proposition 2:The COP of the system employing the proposed secure On-Off transmission scheme is:

where (a) is based on the total probability formula,and (b) is based on the cumulative distribution function (CDF) of Gamma distribution,and

Remark 3:τiandµihave effects on COP.COP is negatively correlated withτiaccording to (15).Asτidetermines the access region,BSs outside the region cannot be accessed.Whenτi=0,arbitrary BSs in the system have chance to serve the legitimate user,thus BSs with poor communication link qualities may affect the reliability of the system.With the increase ofτi,COP decreases.

Remark 4:COP is negatively correlated withµiaccording to (15).Whenµi=0,there is no transmission constraint,thus signals may transmit at any time ignoring the current channel condition,which affects the reliable communication.With the increase ofµi,COP decreases.WhenµUi→∞,there is no signal transmission,thus there is no connection outage.

4.3 Secrecy outage analysis

SOP of a typical link in the i-th tier is given by:It is the principle performance metric in the passive eavesdropping scenario.As the proposed transmission scheme is used in the system,there is no doubt that no secrecy outage occurs when there is no signal transmission,thus the SOP of the system with the proposed scheme can be redefined as:

Proposition 3:The SOP of the system employing the proposed On-Off transmission scheme is (18) shown in the bottom at this page,where(a) is based on the PGFL (probability generating functional lemma) of PPP.

Remark 5:SOP decreases withτiincreases.This result can be explained that the number of eavesdroppers always decreases withτiincreases,which weakens the capacity of wiretap channel,thus the security of the system is guaranteed.

Remark 6:Since the encoding rateRUiis an increase function of transmission thresholdµiFor a given threshold,SOP is a decreasing function ofRUi,so we have the conclusion that SOP decreases withµi.

4.4 Performance optimization

The design problem is to maximize the secure EE by optimizingτiandµi,which is subject to security and reliability constraints.We consider the users have the same communication requirements in different layers,thus we assume the security constraint and reliable constraint areεandδrespectively.The optimization problem aims to maximize secure EE can be expressed as:

As we cannot obtain the analytical results from (19),we employ a search method to solve the numerical results of the optimalτi*,µi*in the feasible solutionsobtained by the constraintC1 in (19),which satisfies the security and reliability requirements of the network.The optimalτi*,µi*should be those in the setto maximize the secrecy throughput.Mathematically,we can get the optimal valuesby:

Algorithm 1.Search algorithm for obtaining optimal values τi*,µi*.ii,,τiup,µiup;2:Initialization:1:Input:K,ρi,α,Pi,λi,λe,Rb,Rs,ε,δ,Δ Δτ µup τi up C=Δ i τi,V=Δµµ,ξtemp=0;i 3:for iK=1:do 4:for cC=1:do 5:for vV=1:do 6:Calculate pco i in (18) and Ai in (8);7:if pco i in (15),pso i ≤ε then 8:update (τ µˆ ˆ i ≤δ and psoii,);9:end if 10:end for 11:end for 12:end for 13:Set Ω as the number of entries in the determined set (τ µˆ ˆ ii,) by putting Δ ⋅τi c,Δ ⋅µi v into (τ µˆ ˆ ii,).That is Ω==ˆ ˆ) ()14:for ω=Ω1:do 15:Calculate ξ by substituting the entries τ µCardCard (τµi i ωω,into (19) that lie in the set (τ µˆ ˆ ii ii,);16:if ξ ξ＞ temp then 17:ξξ temp=; Update τi*,µi* by τ τ µ µ*ω*ω,;18:end if 19:end for 20:Output τi*,µi*; (The optimal values are obtained.)==iiii

Fig.1.COP and SOP vs.channel estimation accuracy

Based on the above analysis,we present algorithm 1 to numerically determine the optimal valuesτi*,µi*of the power split factor in every tier,respectively.In algorithm 1,we respectively denote the step size ofτi*,µi*as Δτi,Δµi.

V.NUMERICAL RESULTS

In this section,we illustrate and analyze the numerical results of the proposed scheme.A 2-tier dense HCNs is taken as an example,in which the macrocell base stations (MBSs) and the picrocell base stations (PBSs) are deployed.The results shown in this section are all for the system withP1,total=20W,P2,total=2W,α=3,λ1=1π5002,λ2=3λ1,λ e=5λ1,N1=10,N2=5.

5.1 The eff ects of channel estimation accuracy

We plot the COP,SOP and secure EE versus channel estimation accuracy to show the effects of channel estimation in figure 1 and figure 2 respectively.Since MBSs and PBSs play similar parts in the system,we take tier 1 as an example to discuss the influence of channel estimation accuracy.It is obvious that COP and SOP are decreasing functions ofρ1,but secure EE is an increasing functions ofρ1.This implies that channel estimation errors influence the qualities of communication links,thus accurate channel estimation can improve the reliability and security performances and enhance secure EE at the same time.

Note thatτ1=0,µ1=0 means that the system is without the proposed transmission scheme,thus there is no On-Off transmission whenτ1=0,µ1=0.Comparing the curves ofτ1=0,µ1=0 withτ1=0,µ1=0.002 andτ1=0.001,µ1=0.002 in figure 1 and figure 2,we can observe that the system without the proposed transmission scheme has the highest COP/SOP but has the lowest secure EE among those with the proposed scheme.The curves illustrate that the proposed scheme can decrease COP by at most 33% and decrease SOP by at most 40%,which verifies that the proposed dual-threshold based On-Off transmission scheme can improve reliability and security performances of the network effectively.

Asτ1=0,µ1=0.002 means that the system is single-threshold based On-Off transmission scheme as in [19],we compare the curves ofτ1=0,µ1=0.002 withτ1=0.001,µ1=0.002,we can see that system with the proposed dual-threshold based transmission scheme has lower COP/SOP but higher secure EE than single-threshold scheme.This implies the superiority of the dual-threshold based transmission scheme.

The observations from the figure 1 and figure 2 illustrate the proposed transmission scheme can improve the performance of the system.In addition,it is always significant to improve channel estimation to increase the reliability and security performance of dense HCNs with imperfect CSI.

5.2 The eff ects of access threshold

We setτ1=τ2=τto analyze the influence of access threshold.We present TP,COP and SOP in each layer over varying access threshold in Fig.3.It is obvious the transmission probability decreases with the increase of access threshold.Comparing the curves ofτ=0 withτ≠0,we can see the increase of access threshold decreases COP and SOP of the system.It is because BSs with poor communication link qualities cannot be accessed by the intended user asτdetermines the access region.This implies the effectiveness of the proposed dynamic access strategy,which improves the reliability and security performances.

The secure EE versus varying access threshold is shown in Fig.4.We can see that the secure EE increases first and then decreases with the increase of the access threshold.This implies a proper access threshold can increase secure EE,and there exists an optimal access threshold to achieve the maximal secure EE.The observations from figure 3 and figure 4 show that access threshold influences reliability and security performance of the system.Therefore,it helps to perform load balancing and improve system performance by appropriately selecting the access threshold according to the preference for different requirements.

Fig.2.Secure EE vs.channel estimation accuracy.

Fig.3.Access probability vs.access threshold.

5.3 The eff ects of transmission threshold

We setµ1=µ2=µto analyze the inf luence of transmission threshold.We present TP,COP and SOP in each layer over varying transmission threshold in Fig.5.Comparing the curves of µ=0 with µ ≠0,we can see TP,COP and SOP are decreasing functions of transmission threshold.The increase of µ enhances the qualities of communication links but lowers the transmission probability.This implies the effectiveness of the proposed emission control policy,which improves the reliability and security performances.

Fig.4.Secure EE vs.access threshold.

Fig.5.TP,COP and SOP vs.transmission.

Fig.6.Secure EE vs.transmission threshold.

The secure EE over varying transmission threshold is shown in Fig.6.It is obvious the secure EE increases first and then decreases asµincreases.This signifies a proper transmission threshold can increase secure EE,and there exists an optimal transmission threshold to achieve the maximal secure EE.This implies that emission control policy can effectively improve the secure EE of the system,and it is significant to set a suitable transmission threshold.The observations from the figure 5 and figure 6 show that transmission threshold effects reliability and security performance of the system.Therefore,it can help the designers of real dense HCNs to find the optimal transmission threshold according to the preference for different requirements.

VI.CONCLUSION

In this paper,we propose a dual-threshold based secure On-Off transmission scheme of dense HCNs to decrease the influences of channel estimation errors,and improve the reliability and security performances of the system.First,a dynamic access strategy based on average received signal power is put forward,which benefits good communication link qualities and efficient access efficiency.Then,an emission control policy based on instantaneous estimated signal power is presented,which ensures reliable and secure communication.After that,comprehensive performance analyses under a stochastic geometry framework are conducted for the proposed scheme,and a dual-threshold optimization model is proposed to further support the performance of the system.Numerical results show the effectiveness of the proposed transmission scheme,where both the dynamic access strategy and the emission control policy can improve the performance of the system.

ACKNOWLEDGMENT

This work is supported in part by National Natural Science Foundation of China under Grants No.61871404,61401510,61521003,61501516.