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SECRECY RATE ANALYSIS FOR JAMMING ASSISTED RELAY COMMUNICATIONS SYSTEMS

SECRECY RATE ANALYSIS FOR JAMMING ASSISTED RELAY COMMUNICATIONS SYSTEMS
SECRECY RATE ANALYSIS FOR JAMMING ASSISTED RELAY COMMUNICATIONS SYSTEMS

SECRECY RATE ANALYSIS FOR JAMMING ASSISTED RELAY COMMUNICATIONS

SYSTEMS

?Jingping Qiao?Haixia Zhang?Dalei Wu?Dongfeng Yuan

?School of Info.Sci.&Eng.,Shandong University,Jinan,China

?Mechatronics Research Lab,Massachusetts Institute of Technology,USA

ABSTRACT

The secrecy rate optimization of wireless communication sys-tems with full-duplex(FD)relays and jamming signals is in-vestigated in this work.Cooperated with FD relays,a novel secrecy transmission mechanism is proposed targeting at cre-ating interference at eavesdroppers by adopting jamming sig-nals.In the proposed mechanism,relays work in FD mode to receive information signals and forward them together with extra jamming signals.The global channel state information (CSI)is assumed available at all transmit nodes.Based on the proposed scheme,the secrecy rate of relay communica-tion system is analyzed.Simulation results are also included to support the theoretical analysis.Results show that the pro-posed scheme can obviously enhance the secrecy rate of relay communication systems.

Index Terms—Physical layer security,secrecy rate,full-duplex,jamming

1.INTRODUCTION

Security has attracted considerable attention because of the broadcast nature of wireless communications.Traditionally, cryptographic approaches are employed in the upper layers for information security.Due to the ever improving com-puting ability of users,there are more challenges to design secret keys.This therefore will lead to high risk of informa-tion security.As a newly booming technique,physical layer security which makes use of channel conditions to improve secrecy rate can avoid such kind of risk and nowadays is of growing interests.Wyner has proved in[1]that if the wire-tap channel was a degraded version of the main channel,the security could be guaranteed and eavesdroppers could learn almost nothing about information from the source.Other-wise,the secrecy rate would be zero.To solve this problem,a large amount of work has focused on node cooperation[2–4], The work presented in this paper was supported in part by the International Science and Technology Cooperation Program of China (2014DFA11640),the National Natural Science Foundation of China(No. 61371109),the Outstanding Youth Fund of Shandong province with No. JQ201315,and the New Century Excellent Talents from the Ministry of Ed-ucation of China(NCET-11-0316).such as amplify-and-forward(AF),cooperative jamming(CJ) and decode-and-forward(DF),and all proved that introducing jamming signals into cooperative systems is an ef?cient way to degrade the channel conditions of eavesdroppers.

To take advantages of jamming signals,jamming nodes are introduced into DF and AF relay systems[5–7].Although jamming nodes can further increase secrecy rates of cooper-ative systems,they can also interfere with relays when they interfere with eavesdroppers.In addition,there is no closed form solution for secrecy rate optimization in such kind of systems.To solve this problem,a smart jamming algorithm has been proposed to schedule the interaction between relays and jamming nodes[8–11].Moreover,[12–14]proposed a novel self-protection scheme,where destinations transmitted jamming signals to interfere with eavesdroppers and protected itself from being interfered.All the previous work made con-tributions to enhance the physical layer security,yet few of them payed attention to advantages of jamming signals in full-duplex(FD)relay systems.Inspired by[14],jamming signals can also be introduced into FD relay systems to enhance the system security.This paper offers an extension work of[15]. Here,the jamming scheme in our method is cooperated with FD relays.That is,FD relays can transmit information signals with extra jamming signals.As a result,the channel condition of eavesdropper can be degraded by jamming signals,and the secrecy rate performance can be improved.

Notation:x denotes the transmit signal of the source and z represents the jamming signal.h?ij denotes the channel be-tween i node and j node,i={S,R},j={R,D,E}.(·)?denotes the conjugate transpose,(·)?conjugate,(·)T trans-pose.And CN(0,σ2)represents a circularly symmetric com-plex Gaussian distribution with zero mean and varianceσ2. And diag{w}denotes the operation to construct a diagonal matrix which elements on the main diagonal are the elements of vector w.I N is the identity matrix of size N by N,and log(·)represents the logarithm base2.

2.SYSTEM MODEL

We consider a cooperative communication system as shown in Fig.1,where there are one source node S,one destina-

tion node D,one eavesdropper node E and N available relay nodes R,all working in FD mode.The source,destination and eavesdropper nodes are all equipped with single antenna, while the relay nodes are all with two antennas,one transmit antenna and one receive antenna.Through out this work,we assume that all the relays work in FD mode.Let the trans-mission power of the source node be P s in Watt and assume that the total transmission power constraint for the whole sys-tem is P0.Therefore,relay nodes will transmit signals with power P0?P s.Both the destination and the eavesdropper can receive signals from both the source and relays.

(

Source Destination

Fig.1.System model:the eavesdropper is located at some-

where between the source and the destination.

For easy denotation,the power of transmit signal x and

jamming signal z are normalized to1.That is E{|x|2}=1,

E{|z|2}=1,respectively.Let h?SR∈C N×1denote the

source-relay channel.It is assumed that each relay can receive

signals from itself and other relays.Then the received signal

vector at relays can be written as

y′R=

P s h?SR x+y RR+n R,(1)

where n R∈C N×1denotes the noise vector at relays,

n R~CN(0,σ2I N).And y RR represents the received

signal vector,which is transmitted from all the relays,y RR=

[y RR(1),...,y RR(k),...,y RR(N)]T∈C N×1,where the

parameter k=1,2,...,N.Since the relay knows its own

received signal,y RR can be cancellated by using interfer-

ence cancellation algorithm[16].Thus,the received signal at

relays,denoted by y R,can be written as

y R=y′R?y RR

=

P s h?SR x+n R.

(2)

As it is known that the full-duplex relay nodes can retrans-

mit their received signals with very small delay,meaning that

the source and relays can almost simultaneously transmit

their signals.And the signal transmitted by each relay is the

weighted version of the received signal with the jamming sig-

nal,i.e.,w(k)y R(k)+w J(k)z.Thus,the signals transmitted

by all relays can be denoted as diag{w}y R+w J z,where

w=[w(1),...,w(k),...,w(N)]T denotes the weight vec-

tor at all relays,and w J=[w J(1),...,w J(k),...,w J(N)]T

represents the jamming weight vector.Let h?Rj

1

∈C N×1de-

note the channel between relays and the j1node for transmit-

ting information signals and jamming signals,j1∈{D,E}.

Therefore,the destination can receive signals both from the

source and all relays.Received signal at the destination can

be written as

y D=

P s h?SD x+h?

RD

(diag{w}y R+w J z)+n D

=

P s h?

RD

diag{h?SR}w x+

P s h?SD x

+n T R diag{h?RD}w+h?RD w J z+n D.

(3)

Similarly,the version of the received signal at the eavesdrop-

per is

y E=

P s h?SE x+h?

RE

(diag{w}y R+w J z)+n E

=

P s h?

RE

diag{h?SR}w x+

P s h?SE x

+n T R diag{h?RE}w+h?RE w J z+n E,

(4)

where n D~CN(0,σ2)and n E~CN(0,σ2)represent the

additive noise at the destination and eavesdropper,respec-

tively.And according to(3)and(4),the jamming signals

interfere with both received signals at the eavesdropper and

the destination.If the interference of jamming signals to the

eavesdropper is maximized and in the same time the inter-

ference to the destination is minimized,the performance of

secrecy rate will be optimized.

3.RATE OPTIMIZATION AND SYSTEM DESIGN

In this work,we assume there is only one eavesdropper,and

the global channel state information(CSI)is available for all

transmitters,including the source node and relay nodes.The

de?nition of the secrecy rate can be denoted as the difference

between rate of destination and rate of eavesdropper,

R s=R D?R E.

From the security point of view,more information received

at legitimate receiver is expected,while the less information

should be received at the eavesdropper.Thus,the optimal

problem to maximize the secrecy rate can be formulated as

arg max

w,w J

R s.(5)

In the following,this optimal problem for the described

model in Fig.1will be analyzed.The given total transmit

power constraint is P0,and it is assumed that the power of

signal diag{w}y R is P R,i.e.,w?Tw=P R,where T=

P s diag{h?

SR

}diag{h SR}+σ2I N.At receiver sides,includ-

ing the destination node and the eavesdropper node,in or-

der to simplify the expression of information rate,we de?ne

a=

P s diag{h SR}h RD.Thus the rate at the destination

can be written as

R D=log

(

1+

w?R a w

σ2w?R RD w+w?

J

h RD h?

RD

w J

)

,(6)

where R a=P s|h SD|2

P R T+aa?,R RD=P?1

R

T+diag{h RD}·

diag{h?

RD }.

De?ne b=√

P s diag{h SR}h RE,the rate at the eaves-

dropper can be represented as

R E=log (

1+

w?R b w

σ2w?R RE w+w?

J

h RE h?

RE

w J

)

(7)

where R b=P s|h SE|2

P R T+bb?,and R RE=P?1

R

T+

diag{h RE}·diag{h?RE}.

Based on(5),the maximization of the secrecy rate is an joint optimization problem of the weight vector w J and w, which is very dif?cult to solve.In order to simplify this prob-lem,we will try to achieve the optimization problem in two steps.Firstly,based on the weight vector w J,the interference at the eavesdropper can be maximized.The objective function can be described as

arg max

w J

|w?J h RE|2,

s.t.{

w?

J

h RD=0

w?

J

w J=P0?P s?P R.

(8)

By solving the above optimization problem,the interference at the destination can be nulled out,and the optimal jamming weight vector can be obtained and written as

w J=μ1∥h RD∥2h RE?μ1h?RD h RE h RD,(9)

whereμ1=√

P0?P s?P R

∥h RD∥4∥h RE∥2?∥h RD∥2|h?

RD

h RE|2

.

Let Q J=w?

J h RE h?

RE

w J represent the interference at

the eavesdropper caused by the jamming signals,then the se-crecy rate can be rewritten as

R s=log (

1+

w?R a w

σw?R RD w

)

?

log (

1+

w?R b w

σw?R RE w+Q J

)

=log (

w??R a w

w?R RD w

·w

??R

RE

w

w??R b w

)

(10)

where?R a=σ2R RD+R a,?R b=σ2R RE+R b+Q J

P R

T,

and?R RE=R RE+Q J

σ2P R T.Thus the objective function of

the optimization problem of secrecy rate can be simpli?ed as

arg max

w w??R RE w

w?R RD w

·w

??R

a

w

w??R b w

,

s.t.w?Tw=P R.(11) Considering that if A∈C n×n and B∈C n×n are arbi-trary n-dimensional diagonal matrix,the sum matrix A+B is also diagonal.It is easy to get that?R RE and R RD are both diagonal matrix,therefore the objective function in(11) is a product of two correlated Rayleigh quotients,which is in general intractable[17].To solve this optimization prob-lem,in this work we propose a sub-optimal solution.As it is known that the maximum value and the minimum value of the ratio w??R RE w/w?R RD w are corresponding to the max-imal eigenvalueλmax and the minimal eigenvalueλmin of the matrix R?1

RD

?R

RE

,respectively[4].With this,the lower and upper bounds of the objective function can be written as

λmin

w??R a w

w??R b w

≤w

??R

RE

w

w?R RD w

·w

??R

a

w

w??R b w

≤λmax w

??R

a

w

w??R b w

.

(12) Based on the above derivation,we can get that the weight vector maximizing the lower or upper bounds is

w=μ2q unit,(13)

where q unit is the unit-norm eigenvector of the matrix ?R?1

b

?R

a

corresponding to its largest eigenvalue.μ2can be determined by the power constraint,and is equal to

μ2=

P R

(q unit)?Tq unit

.(14)

With the obtained w,we get the tight rate bounds,as well as the maximized secrecy rate.This scheme has been proved to be sub-optimal and the bounds are also proved to be tight by[5].These properties keep unchanged for our system with full-duplex relays.

4.NUMERICAL RESULTS

To evaluate the performance of the proposed scheme,we as-sume that the channel between any two nodes is of line-of-sight transmission,described by h=d?c/2e jθ,d is the dis-tance between two nodes,and c represents the path loss expo-nent and is set to3.5,θdenotes the phase offset and follows a uniform distribution in the interval[0,2π).The distance between relay nodes is assumed much smaller than the dis-tance between relays and other nodes.It is also assumed that the path losses between N relays and the source or the des-tination are almost the same.In this section,the location of source node is always(0,0),where the unit is meters,and the total transmit power constraint is P0=10?3Watt.All per-formance results presented in the following are obtained by taking the average over1000independent Monte Carlo ex-periments.

Since locations of nodes in the system are?xed,we as-sume that the eavesdropper is located between relays and the destination.System performances in terms of the secrecy rate are shown in Fig.2,from which we can see that increasing the number of relays can improve the secrecy rate.In the lower power regime,the secrecy rate increases rapidly with the source power P s increase,while when the source power

Fig.2.Secrecy rate versus the source power.The source power varies form ?20dBm to ?1dBm,and relays and the destination are located at (25,0)and (50,0),respectively.And the eavesdropper is ?xed at (40,0)

.

Fig.3.Secrecy rate versus source-relay distance.The des-tination is located at (50,0)and the eavesdropper ?xed at (40,0).The source power is equal to ?4dBm.

is approximately ?4dBm,the secrecy rate reaches its max-imum value.However,due to the total power constraint,in-creasing the source power will result in the power decrease of relays,with the information transmitted by relays decreas-ing.So it is not bene?cial for security if the source power increases continually.Based on the aforementioned experi-ment,P s will be set to ?4dBm in the following analysis.The secrecy rate performance of the FD relay system in [15]and the proposed scheme is displayed in Fig.3.In the FD relay system described in [15],relays work in FD mode and transmit only information signals.It can be seen as a special case of the proposed scheme,i.e.,relays transmit information signals with the total relay power P 0?P s and jamming signals with 0power.The secrecy rate of the FD relay system can be expressed as

R s =log (

1+w ?R a w

σ2w ?R RD w )?log (1+w ?R b w σ2w ?R RE w ).In this work,we compare the secrecy rate of the proposed system with the FD relay system,results are shown in Fig.3.It can be seen that for the given total power

constraint

Fig.4.Secrecy rate versus source-destination distance.The source power is equal to ?4dBm.Relays are ?xed at (25,0).The location of the eavesdropper is (40,0).

P 0the proposed scheme achieves better performance than the FD relay system in terms of secrecy rate.Since the FD relay system transmits information signals with higher power than the proposed scheme,its maximal secrecy rate is greater than that of the proposed scheme,which is in agreement with the simulation results shown in Fig.3.

The secrecy rate performance is also simulated when the source-destination distance varies.Results are included in Fig. 4.For comparison purpose,we also simulate the se-crecy rate of the FD relay system.With the help of relays,the secrecy rate of two schemes is almost stable when the des-tination is located between the source and relays.From the simulation results,we can also see that secrecy rates decrease when the destination moves far away from both the source and relays.Obviously,the secrecy rate of the proposed scheme is much better than that of the simple FD relay system when the destination is close to the source.On the contrary,since they have the same total power constraint,relays in the FD relay system transmit information signals with much more power than that in the proposed scheme.This therefore will lead to better secrecy rate.That is also why the FD relay system per-forms better than the proposed scheme in the condition that the destination is far away from the source node.

5.CONCLUSION

In this work,by introducing the jamming signals,we pro-posed a novel transmission mechanism to improve the secrecy rate performance of relay communication systems.With the proposed scheme,secrecy systems can bene?t from both the FD relays and jamming signals and thus are of better per-formance.Theoretical analysis and simulation results have shown that the proposed scheme performs better than the FD relay system when the destination is not much far away from the source or the relays are close to the source.Due to the better performance brought by the jamming signals,it will be widely used in the future studies for secrecy communication.

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