Generalized Secure Transmission Protocol for Flexible Load-Balance Control with Cooperative Relays in Two-Hop Wireless Networks

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by  Yulong Shen

1
Generalized Secure Transmission Protocol for
Flexible Load-Balance Control with Cooperative
Relays in Two-Hop Wireless Networks
Yulong Shen∗‡, Xiaohong Jiang† and Jianfeng Ma∗
∗School of Computer Science and Technology, Xidian University, China
†School of Systems Information Science, Future University Hakodate, Japan
‡Email:[email protected]
3
1
0
2 Abstract—Thisworkconsiderssecuretransmissionprotocolfor problem,alotofprotocolswereproposedtobalancethetraffic
flexible load-balance control in two-hop relay wireless networks across the various relay nodes and avoids overloading any
n
without the information of both eavesdropper channels and
a relaynodeinvariouswirelessnetworks,especiallyenergycon-
locations. The available secure transmission protocols via relay
J strainedwirelessenvironments(likewirelesssensornetworks)
cooperationinphysicallayersecrecyframeworkcannotprovidea
9 flexible load-balance control, which may significantly limit their [7-16](see Section V for related works). We notice there is

application scopes. This paper extends the conventional works tradeoff between the load-balance capacity and transmission
]
R and proposes a general transmission protocol with considering efficiency and still no approaches can flexibly control it.
load-balance control, in which the relay is randomly selected
C Regarding the secrecy, the traditional cryptographic approach
from the first k preferable assistant relays located in the circle
can provide a standard information security. However, the
. area with the radius r and the center at the middle between
cs sourceanddestination(2HR-(r,k)forshort).Thisprotocolcovers everlasting secrecy can not be achieved by such approach,
[ the available works as special cases, like ones with the optimal becausetheadversarycanrecordthetransmittedmessagesand
relay selection (r = ∞, k = 1) and with the random relay try any way to break them [12]. Especially, recent advances
1 selection (r = ∞, k = n i.e. the number of system nodes) in in high-performance computation (e.g. quantum computing)
v the case of equal path-loss, ones with relay selected from relay
6 selection region (r ∈ (0,∞),k = 1) in the case of distance- further complicate acquiring long-lasting security via cryp-
4 dependentpath-loss.Thetheoreticanalysisisfurtherprovidedto tographic approaches [13]. This motivates the consideration
7 determine the maximum number of eavesdroppers one network of signaling scheme in physical layer secrecy framework to
1 can tolerate to ensure a desired performance in terms of the provide a strong form of security, where a degraded signal
. secrecy outage probability and transmission outage probability.
1 at an eavesdropper is always ensured such that the original
Theanalysisresultsalsoshowtheproposedprotocolcanbalance
0 data can be hardly recovered regardless of how the signal is
loaddistributedamongtherelaysbyapropersettingofr andk
3
underthe premiseof specified secure and reliable requirements. processed at the eavesdropper[14][15][16].
1
The secure and reliable transmission in physical layer
: Index Terms—Two-Hop Wireless Networks, Relay Cooper-
v secrecy framework for two-hop relay wireless networks has
ation, Physical Layer Secrecy, Transmission outage, Secrecy
i
X Outage. been studied and a lot of secure transmission protocols were
proposed in [17-28](see Section V for related works). These
r
a works mainly focus on the maximum secrecy capacity and
I. INTRODUCTION minimumenergyconsumption,inwhichthesystemnodewith
Wireless networks have the promising applications of in the bestlink conditionto sourceand destinationis selected as
many important scenarios (like battlefield networks, emer- information relay. These protocols are attractive in the sense
gencynetworks,disasterrecoverynetworks).However,Due to that provides very effective resistance against eavesdroppers.
theenergyconstrainedandbroadcastproperties,theconsidera- However,sincethechannelstateisrelativelyconstantduringa
tionofsecrecyandlifetimeoptimizationinsuchnetworksisof fixedtime period,some relaynodeswithgoodlinkconditions
greatimportanceforensuringthe hightransmissionefficiency always prefer to relay packages, which results in a severe
and confidentiality requirements of these applications. Two- load-balance problem and a quick node energy depletion.
hop wireless networks, as a building block for large multi- Such,theseprotocolisnotsuitableforenergy-limitedwireless
hopnetworksystem, havebeen a class ofbasic andimportant networks (like wireless sensor networks). In order to realize
networkingscenarios[1].Theanalysisanddesignoftransmis- load-balance, Y. Shen et al. further proposed a random relay
sion protocol in basic two-hop relay networks serves as the selectionprotocol[29][30],inwhichtherelaynodeisrandom
foundation for secure information exchange of general multi- selected from the system nodes. However, this protocol has
hop network system. lower transmission efficiency. Such, it is only suitable for
For the lifetime optimization, an uneven use of the nodes largescalewirelessnetworkenvironmentwithstringentenergy
may cause some nodes die much earlier, thus creating holes consumption constraint.
in the network, or worse, leaving the network disconnected, In summary, the available secure transmission protocols
which is critical in military or emergency networks. For this cannot provide a flexible load-balance control, which may
2
significantlylimittheirapplicationscopes.Thispaperextends
conventional secure cooperative transmission protocols to a R5 E2 E3
general case to enable the load-balance to be flexibly con-
tkrnoollwedledingethoef etawvoe-shdoropppreelraychawninreellessasnndeltowcoartkiosnsw.iTthhoeutmtahine S E5 R1 R2 D
contributions of this paper are as follows:
This paper proposes a new transmission protocol 2HR- R3 E1 R4 E4
•
(r,k) for two-hop relay wireless network without the
knowledge eavesdropper channels and locations, where Fig. 1. System scenario: Source S wishes to communicate securely with
destination D with the assistance offinite relays R1, R2, ···,Rn (n=5in
the relay is randomly selected from the first k preferable thefigure)inthepresenceofpassiveeavesdroppers E1,E2,···,Em (m=5
assistant relays located in the circle area with the radius inthefigure).Cooperativerelayschemeisusedinthetwo-hoptransmission.
r and the center at the middle between source and
destination. This protocol is general protocol, and can
flexibly control the tradeoff between the load-balance destinationDandprovideflexibleload-balancecontrolamong
amongrelaysandthetransmissionefficiencybyaproper the relays.
setting of k and r under the premise of specified secure
and reliable requirements. B. Transmission Model
In case that the path-loss is identical between all pairs
• Considerthetransmissionfromatransmitter Atoareceiver
of nodes, theoretic analysis of 2HR-(r,k) protocol is B, and denotethe ith symboltransmittedby node A by x(A).
providedto determinethe correspondingexactresults on i
We assume that all nodes transmit with the same power E
s
the numberof eavesdroppersone networkcan tolerate to
and path-loss between all pairs of nodes is independent. We
satisfy a specified requirement and shows that the 2HR-
denote the frequency-nonselective multi-path fading from A
(r,k)protocolcoversalltheavailablesecuretransmission
to B by h . Under the condition that all nodes in a group
A,B
protocolsasspecialcases,likeoneswiththeoptimalrelay
of nodes, , are generating noises, the ith signal received at
selection (r = ∞, k = 1) [19][20][27][29] and with the node B froRm node A, denoted by y(B), is determined as:
random relay selection (d = , k = n i.e. the number i
∞
of system nodes)[29][30].
h h
In case that the path-loss between each pair of nodes y(B) = A,B E x(A)+ Aj,B E x(Aj)+n(B)
• also dependson the distance between them, a coordinate i dα/2 s i dα/2 s i i
system is presented and the theoretic analysis of 2HR- A,Bp AXj∈R Aj,Bp
where d is the distance between node A and B, α 2
(r,k) protocol is provided to determine the correspond- is the path-Alo,Bss exponent, h 2 is exponentiallydistribu≥ted
ing exact results on the number of eavesdroppers one A,B
| |
network can tolerate to satisfy a specified requirement and without loss of generality, we assume that E hA,B 2 =
| |
and shows that the 2HR-(r,k) protocol covers all the 1.Thenoisen(B) atreceiverB isassumedtobeih.i.dcompilex
i
available secure transmission protocols as special cases,
Gaussian random variables with mean N . The SINR C
0 A,B
like ones with relay selected from relay selection region
from A to B is then given by
(r (0, ),k =1)[30].
∈ ∞
Theremainderofthispaperisorganizedasfollows.Section C = Es|hA,B|2d−A,αB
IIIIIprperseesnetnstssytshteemthmeoordeetilcsaanndaltyhseis2HinRc-a(rs,eko)fpreoqtuoaclolp.aStehc-tlioosns A,B Aj∈REs hAj,B 2d−Ajα,B +N0/2
between all node pairs. Section IV presents the theoretic For a legitimatPe node and(cid:12) an ea(cid:12)vesdropper, we use two
(cid:12) (cid:12)
analysis in case that path-loss between each node pair also separate SINR thresholds γR and γE to define the minimum
dependsontheirrelativelocations.SectionV isrelatedworks SINR required to recover the transmitted messages for legiti-
and Section VI concludes this paper. matenodeandeavesdropper,respectively.Therefore,asystem
node (the selected relay or destination) is able to decode
a packet if and only if its received SINR is greater than
II. SYSTEMMODELSAND2HR-(r,k)PROTOCOL γ , whereas each eavesdropper try to achieve target SINR
R
A. Network Model γE to recover the transmitted message. However, from an
information-theoretic perspective, we can map to a secrecy
A Two-hop wireless network scenario is considered where
rate formulation R 1log(1+ γ ) 1log(1 +γ ) [31].
asourcenodeS wishestocommunicatesecurelywithitsdes- ≥ 2 R − 2 E
Hence, we can also think the γ and γ can be set by the
R E
tinationnodeD withthehelpofmultiplerelaynodesR ,R ,
1 2 desired secrecy rate of the system.
,R .Alsopresentintheenvironmentaremeavesdroppers
n
···
E ,E , ,E withoutknowledgeofchannelsandlocations.
1 2 m
The rela·y··nodes and eavesdroppers are independent and also C. 2HR-(r,k) Protocol
uniformly distributed in the network, as illustrated in Fig.1. Notice the available transmission protocols have their own
Our goal here is to design a general protocol to ensure the advantages and disadvantages in terms of the transmission
secureandreliableinformationtransmissionfromsource S to efficiency and energy consumption, and thus are suitable for
3
different network scenarios. With respect to these protocols upperbound ε on P(T), we call the communicationbetween
t out
as specialcases, a generaltransmission protocol2HR-(r,k) is S and D is reliable if P(T) ε . Similarly, we define the
proposedto controlthe balance of load distributed among the transmission outage evenotustO≤(T)t and O(T) for the
relays and works as follows. transmissions from S to the selSe→ctRedj∗relay R Rja∗n→dDfrom R
j j
∗ ∗
1) Relay selection region determination: The circle area, to D, respectively. Due to the link independence assumption,
withradiusr andthecenteratthemiddlepointbetween we have
source S and destination D, is determined as relay
selection region.
2) Channel measurement: The source S and destination P(T) =P O(T) +P O(T)
D broadcast a pilot signal to allow each relay to mea- out S→Rj∗ Rj∗→D (1)
sure the channel from S and D to itself. The relays, (cid:16)P O(T) (cid:17) P(cid:16) O(T) (cid:17)
which receive the pilot signal, can accurately calculate − S→Rj∗ · Rj∗→D
(cid:16) (cid:17) (cid:16) (cid:17)
h ,j =1,2, ,n and h ,j =1,2, ,n.
S,Rj ··· D,Rj ··· Regarding the secrecy outage, we call secrecy outage
3) Candidate relay selection: The relays with the first k
happens for a transmission from S to D if at least one
largemin hS,Rr 2, hD,Rr 2 formthecandidaterelay eavesdropper can recover the transmitted packets during the
| j| | j|
set R. Her(cid:16)e,Rjr denotesthe j-(cid:17)th relaynodein the relay process of this two-hop transmission. We define the secrecy
selection region. outage probability, denoted by P(S), as the probability that
out
4) Relay selection: The relay, indexed by j∗, is selected secrecy outage happensduringthe transmission from S to D.
randomly from candidate relay set R. Using the same Forapredefinedupperboundε onP(S),wecallthecommu-
s out
method with Step 2, each of the other relays Rj,j = nication between S and D is secure if P(S) ε . Similarly,
5) 1T,w2o,-·H··op,n,trja6=nsmj∗isisnionne:twTohrek esxoaucrtcley kSnotwrasnshmRijt,sRjt∗h.e fwoer dtheefintreanthsmeissesciorencsyfrooumtagSe etovetnhtes sOelS(eS→oc)utRetdj∗≤realnsadyORR(Sj)∗→anDd
message to R , and concurrently,the relay nodes with j∗
indexes in j∗ = j =j : h 2 <τ transmit from Rj∗ to D, respectively. Due to the link independence
R1 6 ∗ | Rj,Rj∗| assumption, we have
noise to generate interference at eavesdroppers. The
(cid:8) (cid:9)
relay R then transmits the message to destination
j∗
D, and concurrently, the relay nodes with indexes in
R2 = j 6=j∗ :|hRj,D|2 <τ transmit noise to gener- Po(uSt) =P OS(S→)Rj∗ +P OR(Sj)∗→D (2)
ate inte(cid:8)rference at eavesdropp(cid:9)ers. (cid:16)P O(S) (cid:17) P(cid:16) O(S) (cid:17)
Remark 1: The load is completely balanced among the − S→Rj∗ · Rj∗→D
relays in the candidate relay set R whose size is determined (cid:16) (cid:17) (cid:16) (cid:17)
byparameterr andk inthe2HR-(r,k)protocol.Noticethata
toolargerrandkmayleadtolargersizeofthecandidaterelay III. EQUAL PATH-LOSSBETWEENALLNODE PAIRS
set R. Thus, the load-balance can be flexibly controlled by a
proper setting of the parameter r and k in terms of network In this section, we analyze 2HR-(r,k) protocol in the case
performance requirements. where the path-loss is equal between all pairs of nodes in the
Remark 2: The parameter τ involved in the 2HR-(r,k) system. The Remark 3 shows 2HR-(r,k) protocol is castrated
protocol serves as the threshold on path-loss, based on which as 2HR-( ,k) in case of equal path-loss between all node
∞
the set of noise generating relay nodes can be identified. pairs. We now analyze that under the 2HR-( ,k) protocol
∞
Notice that a too large τ may disable legitimate transmission, the numberof eavesdroppersonenetworkcan tolerate subject
while a too small τ may not be sufficient for interrupting all to specified requirements on transmission outage and secrecy
eavesdroppers.Thus,theparameterτ shouldbesetproperlyto outage. The following two lemmas regarding some basic
ensure both secrecy requirement and reliability requirement. propertiesof Po(uTt), Po(uSt) and τ are first presented, which will
Remark 3: In the case that there is equal path-loss between help us to derive the main result in Theorem 1.
all pairs of nodes, i.e., d = 1 for all A = B, the channel Lemma 1: Consider the network scenario of Fig 1 with
A,B
6
state information is independent of the parameter r in 2HR- equal path-loss between all pairs of nodes, under the 2HR-
(r,k) protocol. Since the parameter r is no effect on relay (r,k) protocol the transmission outage probability P(T) and
out
selection, the relay selection regionis the whole networkarea secrecy outage probability P(S) there satisfy the following
out
with r = . Therefore, 2HR-(r,k) protocol is castrated as conditions.
∞
2HR-( ,k)in case ofequalpath-lossbetweenallnodepairs.
∞
D. Transmission Outage and Secrecy Outage k n
1 n
P(T) 2 [1 Ψ]iΨn i
For a Two-hop relay transmission from the source S to out ≤ k i − − 
destination D, we call transmission outage happens if D can Xj=1(cid:20)i=nX−j+1(cid:18) (cid:19) (cid:21) (3)
notreceivethe transmittedpacket.We definethe transmission   2
k n
1 n
outage probability, denoted by Po(uTt), as the probability that −k i [1−Ψ]iΨn−i 
transmission outage from S to D happens. For a predefined j=1(cid:20)i=n j+1(cid:18) (cid:19) (cid:21)
X X−
 
4
here Ψ=e−2γR(n−1)(1−e−τ)τ, and
n n!
P(S) 2m 1 (n−1)(1−e−τ) 1≤ n(cid:0)−ii(cid:1)j ≤ (n−j)!j!
out ≤ · 1+γ
(cid:18) E(cid:19) (4) Substitu(cid:0)ting(cid:1)into formula (6), we have
1 (n−1)(1−e−τ) 2
m
−" ·(cid:18)1+γE(cid:19) # 1 k n−j n n j
The proof of Lemma 1 can be found in the Appendix A. k 1− nij −i (1−Ψ)iΨn−j−iΨj
Lemma2:ConsiderthenetworkscenarioofFig1withequal Xj=1(cid:20) Xi=0 (cid:0)−i(cid:1) (cid:18) (cid:19) (cid:21)
Ppao(tuSht)-lo≤ssεbsetwunedeenratlhlepa2iHrsRo-f(rn,okd)esp,rtootoecnoslu,rtehPeo(puTat)ra≤mεettearnτd ≤ k1 j=k1(cid:20)1−Ψ(cid:0)j ·ni=(cid:1)−0j(cid:18)n−i j(cid:19)(1−Ψ)iΨn−j−i(cid:21)
must satisfy the following condition. X X
k
1
=1 Ψj
− k
1
log k 1+k√1 ε k 1 Xj=1 (7)
τ ≤vuu− (cid:18)h(cid:0)⌊k2⌋(cid:1)2(cid:0)γR(n 1)− t(cid:1)i − (cid:19) =1− k1 k 1k kj Ψj −1
and ut − (cid:20)Xj=0 j (cid:18) (cid:19) (cid:21)
1 1 (cid:0) (cid:1)k k
1 Ψj 1
≤ − k k j −
log 1−√m1−εs (cid:20) ⌊k2⌋ Xj=0(cid:18) (cid:19) (cid:21)
τ ≥−log1+ (n 1(cid:16))log(1+(cid:17)γ ) =1 1 (cid:0) 1 (cid:1)(1+Ψ)k 1
− E − k k −
(cid:20) k (cid:21)
  ⌊2⌋
here, is the floor function.
⌊·⌋ According to(cid:0)form(cid:1)ula (5), (6) and (7), in order to ensure
Proof:
the reliability, we need
The parameter τ should be set properly to satisfy both
reliability and secrecy requirements.
Reliability Guarantee 1 1
•To ensure the reliability requirement Po(uTt) ≤ εt, we know 1− k(cid:20) kk (1+Ψ)k−1(cid:21)≤1−√1−εt
from formula (3) in the Lemma 1, that we just need ⌊2⌋
or equally,(cid:0) (cid:1)
k n
1 n
2 [1 Ψ]iΨn−i 1
k i −  k k
j=1(cid:20)i=n j+1(cid:18) (cid:19) (cid:21) Ψ 1+k√1 ε 1
X X− ≥ k − t −
 1 k n n  2 (cid:20)(cid:18)⌊2⌋(cid:19)(cid:0) (cid:1)(cid:21)
[1 Ψ]iΨn i that is,
−
−k i − 
j=1(cid:20)i=n j+1(cid:18) (cid:19) (cid:21)
X X−
ε  1
Thu≤s, t e−2γR(n−1)·(1−e−τ)τ ≥ kk 1+k√1−εt k −1
(cid:20)(cid:18)⌊2⌋(cid:19) (cid:21)
(cid:0) (cid:1)
Therefore
k n
1 n
[1 Ψ]iΨn i 1 √1 ε (5)
− t
k i − ≤ − −
Xj=1(cid:20)i=nX−j+1(cid:18) (cid:19) (cid:21) log k 1+k√1 ε k1 1
Notice that 1−e−τ τ ≤ − (cid:18)h(cid:0)⌊k2⌋(cid:1)2(cid:0)γ (n 1)− t(cid:1)i − (cid:19)
R
−
k n (cid:0) (cid:1)
1 n By using Taylor formula, we have
(1 Ψ)iΨn−i
k i −
j=1(cid:20)i=n j+1(cid:18) (cid:19) (cid:21)
X X−
k n j 1
= k1 Xj=1(cid:20)1−Xi=−0(cid:18)ni(cid:19)(1−Ψ)iΨn−i(cid:21) (6) τ ≤vuu−log(cid:18)h(cid:0)⌊kk2⌋(cid:1)2(cid:0)γ1R+(nk√11)−εt(cid:1)ik −1(cid:19)
= k1 Xj=k1(cid:20)1−nXi=−0j n(cid:0)n−ii(cid:1)j (cid:18)n−i j(cid:19)(1−Ψ)iΨn−j−iΨj(cid:21) •ToSeecnrseuutcrye Gthueasreacnrteecey requirem−ent Po(uSt) ≤ εs, we know
We alsonoticethe(cid:0)i ca(cid:1)ntake from0to n j,thenwehave from Lemma 1 that we just need
−
5
From formula (9) and (10), we can get
1 (n−1)(1−e−τ)
2m 1 √1 ε
s
· 1+γ m − −
(cid:18) E1(cid:19) (n−1)(1−e−τ) 2 ≤ 1+1γE (n−1)(1−e−τ)
−"m·(cid:18)1+γE(cid:19) # (cid:16) (cid:17) 1−√1−εs (11)
≤ 1
≤εs −log"(⌊kk2⌋)(1+k√1−εt)#k−1
1  2γRτ 
Thus, 1+γE
(cid:16) (cid:17)
Bylettingτ takeitsmaximumvalueformaximuminterfer-
1 (n−1)(1−e−τ) ence at eavesdroppers, from formula (8) and (11), we get the
m 1 √1 ε following bound
s
· 1+γ ≤ − −
(cid:18) E(cid:19)
That is, 1 √1 ε
s
m − −
≤ 1
τ ≥−log1+ (nlog1(cid:16))1lo−g√m(11−+εs(cid:17)γ ) 1+1γE vuuut−(n−1)log"(⌊kk2⌋2)γ(R1+k√1−εt)#k−1
− E (cid:16) (cid:17)
 
Based on the above analysis, by simple derivation, we can
Based ontheresultsofLemma2,we nowcanestablish the get the follow corollary to show our proposal is a general
followingtheorem regardingthe performanceof the proposed protocol.
protocol in case of equal path-loss between all node pairs. Corollary 1. Consider the network scenario of Fig 1 with
equalpath-lossbetweenallpairsofnodes,theanalysisresults
Theorem 1. Consider the network scenario of Fig 1 with
of the proposed protocol is identical to that of protocols with
equal path-loss between all pairs of nodes. To guarantee
P(T) ε and P(S) ε under 2HR-(r,k) protocol, the the optimal relay selection presented in [19][20] by setting of
out ≤ t out ≤ s k = 1 and r = , and is identical to that of protocols with
number of eavesdroppers m the network can tolerate must
∞
the random relay selection presented in [29][30] by setting of
satisfy the following condition.
k =n and r = .
∞
Remark 4: In case of equal path-loss of all pairs of nodes
1 √1 εs and the parameter r = , we notice that the larger k
m − − ∞
≤ 1 meansthe betterload-balanceamongthe relaysand the lower
1 vuuu−(n−1)log"(⌊kk2⌋2)γ(R1+k√1−εt)#k−1 tkra=ns1m,i2ssHioRn-(re,ffikc)ipenroctyo,coanldhavsitcheevweorsrsae. lIonadp-abratilcaunlcaer,amwohnegn
1+γE t the relays and the highest transmission efficiency, and when
(cid:16) (cid:17)
Proof: k = n, 2HR-(r,k) protocol has the best load-balance among
From Lemma 2, we know that to ensure the reliability the relays and the lower transmission efficiency.
requirement, we have
IV. GENERALCASE TOADDRESSINGPATH-LOSS
Inthissection,weconsiderthemoregeneralscenariowhere
1
log k 1+k√1 ε k 1 the path-loss between each pair of nodes also depends on
τ ≤vuu− (cid:18)h(cid:0)⌊k2⌋(cid:1)2(cid:0)γR(n 1)− t(cid:1)i − (cid:19) (8) tfhuerthdeirstapnrocevidbeedtwteoendethteermm.inTehteherelnautemdbethreoofreteiacveasndarloypsipseriss
u −
t onenetworkcan tolerantbyadoptingthe 2HR-(r,k)protocol.
and
To address the distance-dependent path-loss, we consider a
coordination system shown in Fig 2, in which the two-hop
1 relay wireless networks employed in the 2-D plane of unit
log k 1+k√1 ε k 1
(n−1) 1−e−τ ≤ − (cid:18)h(cid:0)⌊k2⌋(cid:1)(cid:0) 2γRτ − t(cid:1)i − (cid:19) asoreuar,cecoSnsliostciantgedofatthceoosrqduinaarete[−(−00.5.5,,00.5)]w×is[h−e0s.5to,0e.s5t]a.bTlihshe
two-hoptransmissionwithdestinationD locatedatcoordinate
(cid:0) (cid:1) (9)
(0.5,0).
To ensure the secrecy requirement, we need To address the near eavesdropper problem and also to
simply the analysis for the 2HR-(r,k) protocol, we assume
that there exits a constant d >0 such that any eavesdropper
0
1 (n−1)(1−e−τ) 1−√1−εs (10) falling within a circle area with radius d0 and center S or
(cid:18)1+γE(cid:19) ≤ m Rj∗ caneavesdropthetransmittedmessagessuccessfullywith
6
(-0.5,0.5) (0.5,0.5)
0.5 0.5 1
ϕ = dxdy
2 α
Ei Z−0.5Z−0.5 (x−0.5)2+y2 2
(x ,y ) h i
Ei Ei
(x ,y ) 0.5 0.5 1
Rj* Rj* ψ = dxdy
α
d0 (0,0) Rj*d0 D Z−0.5Z−0.5 (x−0.5)2+(y−0.5)2 2
S
Relay (0.5,0) The proof of Lemmha 3 can be found in the iAppendix B.
selected
(-0.5,0) r Lemma4:ConsiderthenetworkscenarioofFig2,toensure
from this
P(T) ε and P(S) ε by applying 2HR-(r,k) protocol,
region out ≤ t out ≤ s
the parameter τ must satisfy the following condition.
R dy
j
(x,y)dx
log k2√ν12+4(1−εt)ν2−k2ν1
(-0.5,-0.5) (0.5,-0.5) τ ≤vuuγ−R(n(cid:20) 1)(ϕ1+2ϕν22)(0.5+r)(cid:21)α
u −
t
and
Fig.2. Coordinatesystemforthescenariowherepath-lossbetweenpairsof
nodesisbasedontheirrelative locations.
log 1−√m1−εs−πd02
τ log1+ (cid:18) 1−πd02 (cid:19) 
probability 1, while any eavesdropper beyond such area can ≥− (n 1)log(1+γ ψd α)
E 0
−
only successfully eavesdropperthe transmitted messages with  
 
a probability less than 1. Based on such a simplification, we  
here, ϕ , ϕ , and ψ are defined in the same way as that in
1 2
can establish the following two lemmas regardingsome basic
Lemma 3, and
properties of P(T), P(S) and τ under this protocol.
out out
Lemma3:ConsiderthenetworkscenarioofFig2,underthe
k
a2nHdRs-e(crr,ekc)yporuottaogceolprthoebatbrailnitsymPis(sSio)nthoeuretasgaetispfryobthaebifloitlyloPwoi(unTtg) ν1 =k2 nl πr2 l 1−πr2 n−l
out l=1(cid:18) (cid:19)
condition. X (cid:0) (cid:1) (cid:0) (cid:1)
n
ν2 =k2 n πr2 l 1 πr2 n−l
k l −
P(T) 1 Υϕ1+ϕ2 n πr2 l 1 πr2 n−l l=Xk+1(cid:18) (cid:19)(cid:0) (cid:1) (cid:0) (cid:1)
out ≤ − l − Proof:
Xl=1(cid:18) (cid:19)(cid:0) (cid:1) (cid:0) (cid:1) (12) The parameter τ should be set properly to satisfy both
Υ2(ϕ1+ϕ2) n n πr2 l 1 πr2 n−l reliability and secrecy requirements.
− k2 l − Reliability Guarantee
l=Xk+1(cid:18) (cid:19)(cid:0) (cid:1) (cid:0) (cid:1) •To ensure the reliability requirement P(T) ε , we know
out ≤ t
from formula (12) in Lemma 3 that we just need
(S)
P
out ≤
2m πd 2+ 1 (n−1)(1−e−τ) 1 πd 2 1 Υϕ1+ϕ2 k n πr2 l 1 πr2 n−l
" 0 (cid:18)1+γEψd0α(cid:19) − 0 # − l=1(cid:18)l(cid:19) −
−"m πd02+(cid:18)1+γE1ψd0α(cid:19)(n−1)(1−e−(cid:0)τ) 1−π(cid:1)d02 !#2 − ΥX2(ϕk12+ϕ2)(cid:0)l=Xkn+1(cid:1)(cid:18)(cid:0)nl(cid:19)(cid:0)πr2(cid:1)(cid:1)l(cid:0)1−πr2(cid:1)n−l
(cid:0) ((cid:1)13) εt
≤
Thus,
here,
k2 ν 2+4(1 ε )ν k2ν
Υ=e−γRτ((n0.−51+)r()1−−αe−τ) Υϕ1+ϕ2 ≥ p 1 2ν−2 t 2− 1
here
k
ϕ1 =Z−00..55Z−00..55 (x2+1y2)α2 dxdy ν1 =k2Xl=1(cid:18)nl(cid:19)(cid:0)πr2(cid:1)l(cid:0)1−πr2(cid:1)n−l
7
ν2 =k2 n nl πr2 l 1−πr2 n−l m≤ πd 21+−√11−πdεs2 ω
l=k+1(cid:18) (cid:19) 0 − 0
X (cid:0) (cid:1) (cid:0) (cid:1)
That is, here (cid:0) (cid:1)
e−γRτ(n−1()0(.15k−+2er−)−ταν)(1ϕ21++ϕ24)(1 εt)ν2 k2ν1 ω = 1+γ1ψd α vuut−(n−1)logγR"k(ϕ2√1+νϕ122)+(40(.251ν+−2rε)tα)ν2−k2ν1#
− − (cid:18) E 0 (cid:19)
≥ 2ν
p 2
ϕ , ϕ , ν ,ν and ψ are defined in the same way as that in
1 2 1 2
Thus,
Lemma 3 and Lemma 4.
Proof:
log k2√ν12+4(1−εt)ν2−k2ν1 From Lemma 4, we know that to ensure the reliability
− 2ν2 requirement, we have
τ 1 e τ (cid:20) (cid:21)
− − ≤ γ (n 1)(ϕ +ϕ )(0.5+r)α
R 1 2
−
(cid:0) (cid:1)
By using Taylor formula, we have log k2√ν12+4(1−εt)ν2−k2ν1
v− 2ν2 (14)
v −log k2√ν12+4(21ν−2εt)ν2−k2ν1 andτ ≤uuutγR(n−(cid:20) 1)(ϕ1+ϕ2)(0.5+r)(cid:21)α
τ ≤uuγR(n(cid:20) 1)(ϕ1+ϕ2)(0.5+r)(cid:21)α
u −
t
Secrecy Guarantee
fro•Tmofeonrsmuurelat(h1e3)seicnreLceymrmeqau3irethmaetnwtePjo(uuSst)t n≤eedεs, we know (n−1) 1−e−τ ≤ −lγogτ(cid:20)k(ϕ2√ν+12ϕ+4)(21(ν−02ε.t5)ν+2−rk)2αν1(cid:21)
R 1 2
(cid:0) (cid:1) (15)
2m πd 2+ 1 (n−1)(1−e−τ) 1 πd 2 To ensure the secrecy requirement, we need
" 0 (cid:18)1+γEψd0α(cid:19) − 0 #
(cid:0) (cid:1)
−"m πd02+(cid:18)1+γE1ψd0α(cid:19)(n−1)(1−e−τ)(cid:0)1−πd02(cid:1)!#2 m·"πd02+(cid:18)1+γE1ψd0α(cid:19)(n−1)(1−e−τ) 1−πd02 #
≤εs 1 √1 ε (cid:0) (cid:1)
s
≤ − −
Thus, (16)
From formula (15) and (16), we can get
m πd 2+ 1 (n−1)(1−e−τ) 1 πd 2
·" 0 (cid:18)1+γEψd0α(cid:19) − 0 #
(cid:0) (cid:1) 1 √1 εs
1 √1 ε m − −
≤ − − s ≤ πd 2+ 1 (n−1)(1−e−τ) 1 πd 2
that is, 0 1+γEψd0α − 0
(cid:16) (cid:17)1 √1 εs(cid:0) (cid:1)
− −
τ ≥−log1+ (nlog1(cid:18))l1o−g√m1(1−1−επ+sd−0γ2πdψ02d(cid:19)α) ≤ πd02+ 1+γE1ψd0α −log"γkR2√τ(νϕ112++ϕ42(2)1ν(−02.ε5t+)νr2)−αk2ν1# 1−πd02
− E 0 (cid:16) (cid:17) (cid:0) (17) (cid:1)
 
 
  By letting τ take its maximum value for maximum inter-
ference at eavesdroppers, from formula (14) and (17), we get
Based ontheresultsofLemma4,we nowcanestablish the
the following bound
following theorem regarding the performance of 2HR-(r,k)
protocol.
Theorem 2. Consider the network scenario of Fig 2. To 1 √1 ε
s
guarantee Po(uTt) ≤ εt and Po(uSt) ≤ εs based on the proposed m≤ πd02+− 1 −πd02 ω
2HR-(r,k) protocol, the number of eavesdroppers m the −
network can tolerate must satisfy the following condition. here (cid:0) (cid:1)
8
a distributed routing algorithm that performs dynamic load-
balance by constructs a load-balanced backbone tree [5]. J.
ω =(cid:18)1+γE1ψd0α(cid:19)vuut−(n−1)logγR"k(ϕ2√1+νϕ122)+(40(.251ν+−2rε)tα)ν2−k2ν1# Gbsoaarloanneecttewa[ol6.r]ke.sxI,tnleonpadader-tdbicatuhlaleanrcs,ehfooisrrtseeisngtenprigfiaytchacnrootnuismttirnpagoinrtetoadnswtu,iaprnpedloerastslloostaedno-f-
transmission schemes were proposed for load-balance among
relaysand prolongingthe networklifetime [7][8][9]. Lifetime
Remark 5: The parameter r determines the relay selection
optimization and security of multi-hop wireless networks was
region.Whenparameterr tendsto0,fewsystemnodeslocate
further considered and the secure transmission scheme with
in relayselection region,andthe relayselection processtends
load-balance is proposed in [10][11].
to optimal from the view of relay selection region with less
load-balance capacity. With increasing of parameter r, the Recently, attention is turning to achieve physical layer
more relays are in relay selection region, which can ensure secrecyandsecuretransmissionschemeviacooperativerelays
better load-balance. is considered in large wireless networks. Some transmission
Remark 6: The SINR at the receiver depends on channel protocols are proposed to select the optimal relay in terms of
state informationandthedistancebetweenthetransmitter and themaximumsecrecycapacityorminimumtransmitpower.In
receiver.TheRemark4andRemark5showthattheparameter case that eavesdropper channels or locations is known, node
r and k in 2HR-(r,k) protocol can be flexibly set to control cooperation is used to improve the performance of secure
the tradeoff the load-balance and the transmission efficiency wireless communications and a few cooperative transmission
intermsofchannelstateinformationandthedistancebetween protocols were proposed to jam eavesdroppers [17][18]. In
the transmitter and receiver respectively. case that eavesdropper channels or locations is unknown, D.
Remark7:Inordertogetthebetterload-balance,setalarger Goeckel et al. proposed a transmission protocol based on
r and k which will result in a lower transmission efficiency. optimalrelayselection[19][20].Forbothone-dimensionaland
The Theorem 1 and Theorem 3 show that the number of two-dimensional networks, a secure transmission protocol is
eavesdroppers one network can tolerant is decreasing as the proposed in [21]. Z. Ding et al. considered the opportunistic
useofrelaysandproposedtwosecrecytransmissionprotocols
increasing r and k.
[22]. The ”two-way secrecy scheme” was studied in [23]
Remark 8: In the initial stage of the network operation, the
[24] and M. Dehghan et al. explored the energy efficiency
parameter r and k can be set small values to ensure the high
ofcooperativejammingscheme[25]. A. Sheikholeslamietal.
efficiency, since all relays are energetic which load-balance
proposed a protocol, where the signal of a given transmitter
among the relays is not first considered. With the passage of
is protected by the aggregate interference produced by the
time of the network operation, the parameter r and k can be
other transmitters [26]. A secure transmission protocol are
gradually set higher values for better load-balance among the
presented in case where the eavesdroppers collude [27]. J. Li
relays to extend the network lifetime.
etal. proposedtwo securetransmission protocolsto confound
Based on the above analysis, by simple derivation, we can
the eavesdroppers[28]. The aboveworks mainly focuson the
get the follow corollary to show our proposal is a general
maximum the secrecy capacity, in which the system nodes
protocol.
with best link condition is always selected as information
Corollary 2. Consider the network scenario of Fig 2, the
relay.Such,theseprotocolshavelessload-balancecapacity.In
analysis results of the proposed protocol with r and
→ ∞ order to address this problem, Y. Shen et al. further proposed
k =n is identical to that of Protocol 3 with a=0 and b=0
a protocol with random relay selection in [29][30]. This
(the parameters a and b determine the relay selection region)
protocolcanprovidegoodload-balancecapacityandbalanced
proposed in [30], and the analysis results of the proposed
energy consumption among the relays, whereas it has low
protocolwith r 0 andk =n isidenticalto thatofProtocol
→ transmission efficiency.
3 with a 0.5 and b 0.5 proposed in [30].
→ →
Remark 9: The protocol proposed in [30] have the ability
to control load-balance among the relays by only control on VI. CONCLUSION
the relay selection region. Whereas, 2HR-(r,k) protocol can
Thispaperproposedageneral2HR-(r,k)protocoltoensure
realizeload-balancebycontrolonbothrelayselectionset and
secure and reliable informationtransmission through multiple
relay selection region.
cooperativesystemnodesfortwo-hoprelaywirelessnetworks
withouttheknowledgeofeavesdropperchannelsandlocations.
V. RELATEDWORKS We proved that the 2HR-(r,k) protocol has the capability of
Alotofresearchworkshavebeendedicatedtoload-balance flexible control over the tradeoff between the load-balance
transmissionschemeforbalancedenergyconsumptionamong capacity and the transmission efficiency by a proper setting
system nodes to prolong the network lifetime in wireless net- of the radius r of relay selection region and the size k of
works. A few dynamic load balancing strategies and schemes candidaterelayset.Such,in generalitispossibleforusto set
were proposed in [2][3] for distributed systems. For wireless proper value of parameters according to network scenario to
mesh network, a multi-hop transmission scheme is proposed supportvariousapplications.Theresultsinthis paperindicate
in [4], in which information relay is selected based on the that the parameters r and k of the 2HR-(r,k) protocol do
currentload of the relay nodes. For wireless access networks, also affect the number of eavesdroppers one networks can
9
tolerant under the premise of specified secure and reliable Employing the same method, we can get
requirements.
k n
1 n
PROAOPFPOEFNDLIEXMAMA1 P (cid:16)OR(Tj)∗→D(cid:17)≤ k Xj=1(cid:20)i=nX−j+1(cid:18)i(cid:19)[1−Ψ]iΨn−i(cid:21) (19)
Substitutingformula(18)and(19)intoformula(1),wehave
Proof:
Based on the definition of transmission outage probability,
k n
we have 1 n
P(T) 2 [1 Ψ]iΨn i
out ≤ k i − − 
j=1(cid:20)i=n j+1(cid:18) (cid:19) (cid:21)
X X−
P OS(T→)Rj∗  1 k n n [1 Ψ]iΨn i 2
(cid:16) =P C(cid:17)S,Rj∗ ≤γR −k j=1(cid:20)i=n j+1(cid:18)i(cid:19) − − (cid:21)
=P (cid:0) Rj∈R1EEss(cid:1)··||hhRS,jR,Rj∗j∗|2|2+N0/2 ≤γR! weAkcncoowrditnhgattothe dXefinitioXn−of secrecy outage probability,
=. PP PPHRj∈|hRS1,Rγ|hRj∗R|j2,Rj∗|2 ≤γR! P(cid:16)OS(S→)Rj∗(cid:17)=P i[=m1{CS,Ei ≥γE}!
≤ τ ≤
(cid:18)|R1| (cid:19) Thus, we have
=P (H γ τ)
R 1
≤ |R |
m
(S)
P O P (C γ ) (20)
Here, H = min |hS,Rj∗|2,|hD,Rj∗|2 . Compared to the (cid:16) S→Rj∗(cid:17)≤Xi=1 S,Ei ≥ E
noise generated by multiple system nodes, the environment Based on the Markov inequality,
(cid:0) (cid:1)
noise is negligible and thus is omitted here to simply the
analysis. Notice that = j =j : h 2 <τ .
R1 6 ∗ | Rj,Rj∗| P(C γ )
Employing Appendix C, (cid:8)we should have (cid:9) S,Ei ≥ E
E h 2
P s·| S,Ei| γ
P (cid:16)OS(T→)Rj∗(cid:17)≤F1Hk(γR|R1n|τ) n ≤=E{ hRPj,ERij,∈j=R01,1E,··s·,·n|+hmRjp,,Ej6=i|j2∗}≥,R1E!
=
k i ·
Xj=1(cid:20)i=nX−j+1(cid:18) (cid:19) P|hS,Ei|2 >γE · |hRj,Ei|2
1 e−2γR|R1|τ i e−2γR|R1|τ n−i RXj∈R1
−   
h i h i (cid:21) ≤ER1 EhRj,Ei e−γE|hRj,Ei|2 
RjY∈R1 h i
nuSmibnecreotfhenroeisaer-egenn−era1tiootnhenrordeelsayissgeixvceenpbtyRj∗,1th=e e(xnpec1te)d =E  1 |R1| 
P |hRj,Rj∗|2 <τ =(n−1)(1−e−τ). The|nRw|e have− · R1"(cid:18)1+γE(cid:19) #
Substituting into formula (20), we have
(cid:0) (cid:1)
k n
1 n
P O(T)
1(cid:16)−Se→−2RγjR∗((cid:17)n−≤1)(k1−Xj=e−1τ(cid:20))τi=inX−ej−+21γ(cid:18)R(in(cid:19)−·1)(1−e−τ)τ n−i P (cid:16)OS(S→)Rj∗(cid:17)≤Xi=m1(cid:18)1+1γE(cid:19)|R1| =m·(cid:18)1+1γE(cid:19)|R1(2|1)
h i h i (cid:21)
employing the same method, we can get
For convenience of the description, let Ψ =
e−2γR(n−1)·(1−e−τ)τ, and we have P O(S) m 1 |R2| (22)
(cid:16) Rj∗→D(cid:17)≤ ·(cid:18)1+γE(cid:19)
Since the expected number of noise-generation nodes is
k n
1 n
P (cid:16)OS(T→)Rj∗(cid:17)≤ k Xj=1(cid:20)i=nX−j+1(cid:18)i(cid:19)[1−Ψ]iΨn−i(cid:21) (18) gfoivrmenulbay(2|R1)1|an=d|(R222|)=int(onf−orm1)u(l1a−(2)e,−wτe),ctahnusg,estubstituting
10
Po(uSt) ≤2m· 1+1γ (n−1)(1−e−τ) P(cid:18)OS(T→)Rj∗(cid:12)Al(cid:19)
(cid:18) E(cid:19) (cid:12)
1 (n−1)(1−e−τ) 2 =P C(cid:12)(cid:12)S,Rj∗ ≤γR Al
m (cid:18) (cid:12) (cid:19)
−" ·(cid:18)1+γE(cid:19) # =P Rj∈R1EEss·(cid:12)(cid:12)(cid:12)·|h|dhSαSd,R,αRRRjjj,j∗,R∗R|j2j∗∗|2 + N20 ≤γR(cid:12)(cid:12)(cid:12)Al
Proof: PROAOPFPOEFNLDIEXMBMA3 =. PPRj∈|hRdSαS1,,RR|jhjd∗∗RαR|j2j,,RRjj∗∗|2 ≤γR(cid:12)(cid:12)(cid:12)Al (cid:12) 
Noticethattwo waysleadingto transmissionoutageare:1) P (cid:12) 
there are no candidate relays in the relay selection region; 2)
the SINR at the selected relay or the destination is less than Compared to the noise generated by multiple system
γ . We also notice that if the numberof the eligible relays in nodes, the environment noise is negligible and thus is
R
candidate relay region less than or equal to k, the relay will omitted here to simply the analysis. Notice that =
1
be random selected from candidate relay set R. j =j : h 2 <τ , then R
6 ∗ | Rj,Rj∗|
Let A , l = 0,1, ,n, be the event that there are just l
l
··· (cid:8) (cid:9)
system nodes in the relay selection region. We have
n P(cid:18)OS(T→)Rj∗(cid:12)(cid:12)Al(cid:19)≤P |hRSj,∈RRj∗1|τ2dd−S−R,αjαR,Rj∗j∗ ≤γR(cid:12)(cid:12)Al!
Po(uTt) = Po(uTt)|Al ·P(Al) (23) (cid:12)(cid:12) P (cid:12)(cid:12)
l=0
X
Without loss of generality, Let (x,y) be the coordinate of
Sincetherelayisuniformlydistributed,thenumberofrelays R , shown in Fig 2. The number of noise generation nodes
j
in candidate relay region is a binomial distribution n,πr2 . in square [x,x+dx] [y,y+dy] is (n 1)(1 e τ)dxdy.
−
We have Then, we have × − −
(cid:0) (cid:1)
P(Al)=(cid:18)nl(cid:19)(cid:0)πr2(cid:1)l(cid:0)1−πr2(cid:1)n−l (24) RXj∈R1 dαRjτ,Rj∗
1 1 τ(n 1)(1 e τ)
P(T) is discussed from the following three aspects. = − − − dxdy
1)oult|=Al0 Z0 Z0 x−xRj∗ 2+ y−yRj∗ 2 α2
Inthiscase,therearenorelaysintherelayselectionregion, h(cid:0) (cid:1) (cid:0) (cid:1) i
then, we have
where x ,y is the coordinate of the selected relay
Rj∗ Rj∗
R which locates in the relay selection region. Because the
P(T) =1 (25) rejla∗ys are(cid:0) uniformly(cid:1)distributed, it is the worst case that
out|Al
the selected relay R is located on the point (0,0), where
j
2) 1 l k the interference at R∗ from the noise generation nodes is
Since≤the≤number of candidate relay nodes is less than largest, and the best cja∗se with the selected relay R located
j
or equal to k. The relay selection process is to select relay in the edge of the circular relay selection region, w∗here the
randomlyin the candidaterelay set R which consists of these interferenceat R fromthe noisegenerationnodesislowest.
j
l relays located in the relay selection region. Then, we conside∗r the worst case and have
Notice P(T) is determined as
out|Al
Po(uTt)|Al =P(cid:18)OS(T→)Rj∗(cid:12)Al(cid:19)+P (cid:18)OR(Tj)∗→D(cid:12)Al(cid:19) (26) P (cid:18)OS(T→)Rj∗(cid:12)(cid:12)(cid:12)Al(cid:19)≤P τ(n|h−S,1R)j∗(1|2−d−Se,αR−jτ∗)ϕ1 ≤γR(cid:12)(cid:12)(cid:12)Al!
Based on the−dePfin(cid:18)itOioS(nT→)oRf(cid:12)(cid:12)(cid:12)j∗tr(cid:12)(cid:12)(cid:12)(cid:12)aAnsl(cid:19)mi·sPsio(cid:18)nOoR(uTjta∗)g→eD(cid:12)(cid:12)(cid:12)p(cid:12)(cid:12)(cid:12)(cid:12)rAobl(cid:19)ability, here, ϕ(cid:12)1 =Z−00..55Z−00..55 (x2+1y2)α2 dxdy (cid:12)
we have Due to 0.5 r d 0.5+r, then,
− ≤ S,Rj∗ ≤