en opy
A icle
Sec ecy Pe o mance Enhancemen o Unde lay
Cogni i e Radio Ne wo ks Employing Coope a i e
Mul i-Hop T ansmission wi h and wi hou P esence
o Ha dwa e Impai men s
Phu T an Tin 1,2 , Dang The Hung 3, Tan N. Nguyen 4,* , T an T ung Duy 5
and Mi osla Voznak 1
1VSB—Technical Uni e si y o Os a a, 17. lis opadu 15/2172, 708 33 Os a a, Po uba, Czech Republic;
[email p o ec ed] (P.T.T.); mi osla [email p o ec ed] (M.V.)
2Facul y o Elec onics Technology, Indus ial Uni e si y o Ho Chi Minh Ci y,
Ho Chi Minh Ci y 71408, Vie nam
3Facul y o Radio-Elec onics Enginee ing, Le Quy Don Technical Uni e si y, Hanoi 11917, Vie nam;
[email p o ec ed]
4Wi eless Communica ions Resea ch G oup, Facul y o Elec ical and Elec onics Enginee ing,
Ton Duc Thang Uni e si y, Ho Chi Minh Ci y 72912, Vie nam
5Depa men o Telecommunica ions, Pos s and Telecommunica ions Ins i u e o Technology,
Ho Chi Minh Ci y 71007, Vie nam; [email p o ec ed]
*Co espondence: [email p o ec ed]
Recei ed: 2 Janua y 2019; Accep ed: 20 Feb ua y 2019; Published: 24 Feb ua y 2019


Abs ac :
In his pape , we conside a coope a i e mul i-hop secu ed ansmission p o ocol o
unde lay cogni i e adio ne wo ks. In he p oposed p o ocol, a seconda y sou ce a emp s o ansmi
i s da a o a seconda y des ina ion wi h he assis ance o mul iple seconda y elays. In addi ion,
he e exis s a seconda y ea esd oppe who ies o o e hea he sou ce da a. Unde a maximum
in e e ence le el equi ed by a p ima y use , he seconda y sou ce and elay nodes mus adjus
hei ansmi powe . We i s o mula e e ec i e signal- o-in e e ence-plus-noise a io (SINR) as
well as sec ecy capaci y unde he cons ain s o he maximum ansmi powe , he in e e ence
h eshold and he ha dwa e impai men le el. Fu he mo e, when he ha dwa e impai men le el is
elaxed, we de i e exac and asymp o ic exp essions o end- o-end sec ecy ou age p obabili y o e
Rayleigh ading channels by using he ecu si e me hod. The de i ed exp essions we e e i ied
by simula ions, in which he p oposed scheme ou pe o med he con en ional mul i-hop di ec
ansmission p o ocol.
Keywo ds:
physical-laye secu i y; unde lay cogni i e adio; coope a i e mul i-hop ansmission;
sec ecy ou age p obabili y; ha dwa e impai men s
1. In oduc ion
Secu i y is one o he mos impo an issues in wi eless communica ion because o he b oadcas
na u e o wi eless medium. Con en ionally, enc yp ion/dec yp ion algo i hms ha gene a e
public/p i a e keys a e used o gua an ee he secu i y [
1
,
2
]. Recen ly, a secu i y amewo k o he
physical laye , called he wi e ap channel o physical-laye secu i y (PLS) [
3
–
11
], has been in oduced
as a po en ial solu ion. In PLS, di e ence be ween Shannon capaci y o he da a link and ha o
he ea esd opping link, named sec ecy capaci y, is commonly used o e alua e sec ecy pe o mance
such as a e age sec ecy capaci y (ASC), sec ecy ou age p obabili y (SOP) and p obabili y o non-ze o
sec ecy capaci y (PNSC). Hence, o enhance he sec ecy pe o mance o wi eless sys ems, esea che s
En opy 2019,21, 217; doi:10.3390/e21020217 www.mdpi.com/jou nal/en opy
En opy 2019,21, 217 2 o 16
p oposed e icien communica ion me hods o inc ease channel capaci y o he da a links, and/o
dec ease ha o he ea esd opping links. Indeed, in [
12
–
14
], oppo unis ic elay selec ion p o ocols a e
conside ed o enhance he quali y o he da a channels in one-hop and dual-hop elaying ne wo ks.
In [
15
–
18
], he au ho s conside ed coope a i e jamming app oaches o educe he da a a e ecei ed
a he ea esd oppe s. The au ho s o [
19
–
25
] conside ed he sec ecy pe o mance enhancemen o
unde lay cogni i e adio (UCR) ne wo ks in which ansmi powe o seconda y use s (SUs) is limi ed
by maximum in e e ence le els equi ed by p ima y use s (PUs). The au ho s o [
26
–
29
] p oposed
secu e communica ion p o ocols o wo-way elay ne wo ks. In [
30
–
33
], he end- o-end sec ecy
pe o mance o mul i-hop elaying sys ems is in es iga ed.
Thus a , mos published wo ks ela ed o pe o mance e alua ion assume ha anscei e
ha dwa e o wi eless e minals is pe ec . Howe e , in p ac ice, i su e s om impai men s due o
phase noises, ampli ie –ampli ude non-linea i y and in phase and quad a u e imbalance
(IQI) [34–36],
which signi ican ly deg ade he pe o mance o wi eless communica ion sys ems. In [
37
,
38
], he
au ho s p oposed a ious elay selec ion me hods o compensa e he impac o he ha dwa e
impe ec ion. The au ho s o [
39
] s udied he ou age pe o mance o pa ial elay selec ion and
oppo unis ic elay selec ion schemes in he UCR ne wo ks unde he join o ha dwa e impe ec ion
and in e e ence cons ain .
To he bes o ou knowledge, se e al published wo ks e alua e he sec ecy pe o mance unde
he impac o impe ec anscei e ha dwa e. In [
40
], he au ho s i s s udied he impac o he
ha dwa e impe ec ion on he sec ecy capaci y. In pa icula , he wo k in [
40
] conside s he e ec s o
IQI in one-hop OFDMA communica ion sys ems. The au ho s o [
41
] designed a secu e massi e MIMO
sys em in he p esence o a passi e mul iple-an enna ea esd oppe and he ha dwa e impai men s.
Re e ence [
42
] p o ided a powe -e icien esou ce alloca ion algo i hm o secu e wi eless-powe ed
communica ion ne wo ks wi h he ha dwa e noises. Taking ha dwa e impe ec ion in o accoun , he
au ho s o [
43
] p oposed an op imal powe alloca ion s a egy o maximize he ins an aneous sec ecy
a e o a coope a i e ampli y-and- o wa d (AF) elaying scheme. In [
44
], we calcula ed PNSC o
mul i-hop elay ne wo ks o e Nakagami-
m
ading channels in p esence o he ha dwa e impai men s.
The esul s in [
44
] show ha he ha dwa e impai men s signi ican ly a ec on he PNSC pe o mance.
Howe e , he e is no published wo k ela ed o coope a i e mul i-hop PLS in he UCR ne wo ks.
This mo i a ed us o p opose such a scheme and e alua e i s pe o mance. In he p oposed p o ocol,
named Coope a i e Mul i-Hop T ansmission P o ocol (CMT), a seconda y sou ce sends i s da a
o a seconda y des ina ion ia mul iple seconda y elays. In addi ion, in he seconda y ne wo k,
a seconda y ea esd oppe o e hea s he sou ce da a ansmi ed by he sou ce and elay nodes.
In addi ion, he seconda y ansmi e s mus adjus he ansmi powe o sa is y he in e e ence
cons ain equi ed by a PU and a maximal powe h eshold. The ope a ion o he p oposed scheme can
be ealized ia one o many o hogonal ime slo s. A each ime slo , he cu en ansmi e inds an
in ended ecei e ha is nea es o he des ina ion, and can ecei e he da a secu ely and success ully.
I his ecei e is he des ina ion, he da a ansmission ends. O he wise, he p ocedu e is epea ed wi h
he new selec ed ansmi e . We also design a coope a i e MAC me hod a each ime slo o e e sing
he channel as well as selec ing he po en ial ecei e . Fo pe o mance measu emen , we i s o mula e
he sec ecy capaci y unde join cons ain o he limi ed in e e ence and he ha dwa e impe ec ion.
When he ha dwa e impai men s a e elaxed, we de i e exac and asymp o ic exp essions o he
end- o-end SOP o e Rayleigh ading channels by using a ecu si e exp ession. Compu e simula ions
we e ealized o e i y he heo e ical de i a ions as well as o show he ad an ages o he CMT
me hod. The esul s show ha he p oposed scheme ou pe o med he con en ional mul i-hop di ec
ansmission (MDT) p o ocol, and pa ame e s such as he impe ec CSI es ima ions, he numbe o
in e media e elays, he ha dwa e impai men le el and he posi ion o he ea esd oppe signi ican ly
a ec ed he end- o-end SOP.
The es o his pape is o ganized as ollows. Sys em model o he p oposed scheme is desc ibed
in Sec ion 2. In Sec ion 3, exac and asymp o ic exp essions o he end- o-end SOP o he MDT and
En opy 2019,21, 217 3 o 16
CMT p o ocols a e de i ed. The simula ion esul s a e p esen ed in Sec ion 4. Sec ion 5p esen s
ou conclusions.
2. Sys em Model
As illus a ed in Figu e 1, we conside an
M
-hop seconda y ne wo k, whe e he sou ce
(N0)
communica es wi h he des ina ion
(NM)
ia
M−
1 elay nodes deno ed by
N1
,
N2
, ...,
NM−1
. The
elay nodes a e numbe ed acco ding o hei dis ances o he des ina ion, i.e., he elay
NM−1
is nea es
and he elay
N1
is he u hes . In UCR, he sou ce and he elay nodes mus adap he ansmi powe
so ha he co-channel in e e ence le els caused by hei ansmission a e below a h eshold
(I h)
gi en
by a p ima y use (PU). Mo eo e , he ansmi powe o he seconda y ansmi e s is also limi ed
by a maximum powe (P h). In addi ion, in he seconda y ne wo k, he ea esd oppe (E) a emp s o
o e hea he sou ce da a ansmi ed by he seconda y ansmi e s. Be o e desc ibing he ope a ion o
he p oposed p o ocol, we gi e assump ions used in his pape .
En opy 2019,xx, 5 3 o 16
2. Sys em Model
0
N
PU
E
1
N
1M
N-
M
N
Sou ce
Des ina ion
Figu e 1. Sys em model o he p oposed p o ocol.
As illus a ed in Figu e 1, we conside an
M
-hop seconda y ne wo k, whe e he sou ce
(N0)
communica es wi h he des ina ion
(NM)
ia
M
-1 elay nodes deno ed by
N1
,
N2
, ...,
NM−1
. The elay
nodes a e numbe ed acco ding o hei dis ances o he des ina ion, i.e., he elay
NM−1
is nea es and
he elay
N1
is he u hes . In UCR, he sou ce and he elay nodes mus adap he ansmi powe so
ha he co-channel in e e ence le els caused by hei ansmission a e below a h eshold
(I h)
gi en
by a p ima y use (PU). Mo eo e , he ansmi powe o he seconda y ansmi e s is also limi ed
by a maximum powe (P h). In addi ion, in he seconda y ne wo k, he ea esd oppe (E) a emp s o
o e hea he sou ce da a ansmi ed by he seconda y ansmi e s. Be o e desc ibing he ope a ion o
he p oposed p o ocol, we gi e assump ions used in his pape .
We assume ha all o he elays a e in he adio ange o he sou ce and des ina ion nodes. We
assume ha all o he nodes ha e a single an enna, and he da a ansmission is hence spli in o
o hogonal ime slo s. Fo ease o p esen a ion and analysis, i is assumed ha all o he nodes ha e he
same s uc u e, and he impai men le els a e he same. We also assume ha he ea esd oppe
is an ac i e node, and hence he seconda y nodes can es ima e channel s a e in o ma ion (CSI)
be ween hemsel es and he node E [
45
]. Nex , he da a ansmission be ween wo seconda y nodes
is conside ed o be secu e and success ul i he ob ained sec ecy capaci y is highe han a posi i e
h eshold
(RS)
. O he wise, he da a a e assumed o be in e cep ed, which is e e ed o as a sec ecy
ou age e en .
2.1. Channel and Ha dwa e Impai men Models
Le
dNi,Nj
,
dNi,PU
and
dNi,E
deno e dis ances o he
Ni→Nj
,
Ni→PU
and
Ni→
E links,
espec i ely, whe e
i
,
j∈{0, 1, ..., M−1, M}
. We also deno e
hNi,Nj
,
hNi,PU
and
hNi,E
as channel
coe icien s o
Ni→Nj
,
Ni→PU
and
Ni→
E links, espec i ely. Because he channels expe ience
a Rayleigh ading dis ibu ion, he channel gains such as
γi,j=|hNi,Nj|2
,
γi,P =|hNi,PU|2
and
γi,E =
|hNi,E|2
ollow exponen ial dis ibu ions. To ake pa h-loss in o accoun , we can model he pa ame e s
o he andom a iables (RVs)
γi,j
,
γi,P
and
γi,E
as [
46
]:
λi,j=dβ
Ni,Nj
,
λi,P=dβ
Ni,PU
and
λi,E=dβ
Ni,E
,
whe e βis pa h-loss exponen .
Conside ing he da a ansmission be ween he ansmi e X and he ecei e Y (X
∈
{N0,N1, ..., NM−1}, Y ∈{N1,N2, ..., NM, E, PU}), he ecei ed da a a Y is gi en as in [34–36]:
y=pPXhX,Y (x0+η ,X)+η ,Y +νY, (1)
whe e
x0
is he sou ce da a,
PX
is he ansmi powe o X,
hX,Y
is channel coe icien o he X-Y link,
η ,X and η ,Y a e ha dwa e noises a X and Y, espec i ely, and νYis Gaussian noise a Y.
Figu e 1. Sys em model o he p oposed p o ocol.
We assume ha all o he elays a e in he adio ange o he sou ce and des ina ion nodes.
We assume ha all o he nodes ha e a single an enna, and he da a ansmission is hence spli in o
o hogonal ime slo s. Fo ease o p esen a ion and analysis, i is assumed ha all o he nodes ha e he
same s uc u e, and he impai men le els a e he same. We also assume ha he ea esd oppe
is an ac i e node, and hence he seconda y nodes can es ima e channel s a e in o ma ion (CSI)
be ween hemsel es and he node E [
45
]. Nex , he da a ansmission be ween wo seconda y nodes
is conside ed o be secu e and success ul i he ob ained sec ecy capaci y is highe han a posi i e
h eshold
(RS)
. O he wise, he da a a e assumed o be in e cep ed, which is e e ed o as a sec ecy
ou age e en .
2.1. Channel and Ha dwa e Impai men Models
Le
dNi,Nj
,
dNi,PU
and
dNi,E
deno e dis ances o he
Ni→Nj
,
Ni→PU
and
Ni→
E links,
espec i ely, whe e
i
,
j∈{0, 1, ..., M−1, M}
. We also deno e
hNi,Nj
,
hNi,PU
and
hNi,E
as channel
coe icien s o
Ni→Nj
,
Ni→PU
and
Ni→
E links, espec i ely. Because he channels expe ience
a Rayleigh ading dis ibu ion, he channel gains such as
γi,j=|hNi,Nj|2
,
γi,P =|hNi,PU|2
and
γi,E =
|hNi,E|2
ollow exponen ial dis ibu ions. To ake pa h-loss in o accoun , we can model he pa ame e s
o he andom a iables (RVs)
γi,j
,
γi,P
and
γi,E
as [
46
]:
λi,j=dβ
Ni,Nj
,
λi,P=dβ
Ni,PU
and
λi,E=dβ
Ni,E
,
whe e βis pa h-loss exponen .
Conside ing he da a ansmission be ween he ansmi e X and he ecei e Y (X
∈
{N0,N1, ..., NM−1}, Y ∈{N1,N2, ..., NM, E, PU}), he ecei ed da a a Y is gi en as in [34–36]:
y=pPXhX,Y (x0+η ,X)+η ,Y +νY, (1)
whe e
x0
is he sou ce da a,
PX
is he ansmi powe o X,
hX,Y
is channel coe icien o he X-Y link,
η ,X and η ,Y a e ha dwa e noises a X and Y, espec i ely, and νYis Gaussian noise a Y.
En opy 2019,21, 217 4 o 16
Simila o he wo k in [
34
–
36
],
η ,X
,
η ,Y
and
νY
a e modeled as Gaussian andom a iables (RVs)
wi h ze o-mean and hei a iances a e gi en, espec i ely, as
a {η ,X}=τ2
, a {η ,Y}=τ2
PX|hX,Y|2, a {νY}=σ2
0, (2)
whe e τ2
and τ2
a e le els o he ha dwa e impai men s a X and Y, espec i ely.
F om Equa ions
(1)
and
(2)
, he ins an aneous signal- o-in e e ence-plus-noise a io (SINR) is
o mula ed by
ΨX,Y =PX|hX,Y|2
τ2
+τ2
PX|hX,Y|2+σ2
0
=PX|hX,Y|2
κPX|hX,Y|2+σ2
0
, (3)
whe e κ=τ2
+τ2
is he o al ha dwa e impai men le el.
Le us conside he ansmi powe
PX
o he node X in he unde lay CR ne wo k. Fi s ly,
PX
is
below he maximum ansmi powe , i.e.,
PX≤P h
. Secondly, he in e e ence caused a he PU due o
he ansmission o he node X mus be below he in e e ence h eshold I h, i.e.,
PX≤I h
(1+κ)|hX,PU|2. (4)
The e o e, PXcan be gi en as
PX=min P h,I h
(1+κ)|hX,PU|2
=P h min 1, µ
(1+κ)|hX,PU|2, (5)
whe e µ=I h/P h is assumed o be a cons an .
Combining Equa ions (3) and (5) yields
ΨX,Y =
Pmin 1, µ
(1+κ)|hX,PU|2|hX,Y|2
κPmin 1, µ
(1+κ)|hX,PU|2|hX,Y|2+1
, (6)
whe e P=P h/σ2
0.
F om Equa ion
(6)
, we can o mula e he SINR o he
Ni→Nj
and
Ni→
E links, whe e
i,j∈{0, 1, ..., M}, espec i ely, as
Ψi,j=Pmin (1, µ/γi,P)γi,j
κPmin (1, µ/γi,P)γi,j+1,
Ψi,E =Pmin (1, µ/γi,P)γi,E
κPmin (1, µ/γi,P)γi,E +1. (7)
Mo eo e , when he anscei e ha dwa e o all he nodes is pe ec , i.e.,
κ=κ2
=κ2
=
0, we can
ew i e Equa ion (7) as
Ψi,j=Pmin 1, µ
γi,P γi,j,
Ψi,E =Pmin 1, µ
γi,P γi,E. (8)
En opy 2019,21, 217 5 o 16
Hence, he sec ecy capaci y ob ained a Njdue o he ansmission o Niis calcula ed as
Ri,j=max 0, log21+Ψi,j−log2(1+Ψi,E)
=log21+Ψi,j
1+Ψi,E +
, (9)
whe e [x]+=max (0, x).
F om Equa ions
(7)
and
(9)
, because
Ψi,j
P→+∞
≈
1
/κ
and
Ψi,E
P→+∞
≈
1
/κ
, he sec ecy capaci y a
high P egime can be gi en as
Ri,j
P→+∞
≈log21+1/κ
1+1/κ+
=0. (10)
Mo eo e , as κ=0, we ha e
Ri,j=log21+Pmin (1, µ/γi,P)γi,j
1+Pmin (1, µ/γi,P)γi,E +
P→+∞
≈log2γi,j
γi,E +
. (11)
2.2. Ope a ion o he P oposed P o ocol
Nex , we desc ibe he ope a ion o he p oposed p o ocol, in which a MAC laye ope a ion is
designed o e e se he channel. Simila o he CoopMAC p oposed in [
47
], in he i s ime slo , be o e
ansmi ing he da a, he sou ce sends a eques - o-send (RTS) message o he des ina ion and all
o he elays. By ecei ing his message, all o he nodes can es ima e CSI be ween hemsel es and
he sou ce, calcula e he ins an aneous sec ecy capaci y by using Equa ion
(9)
, and compa e wi h
RS
. I is assumed ha he sou ce can exac ly es ima e he channel coe icien s o he in e e ence and
ea esd opping links, and include hese alues in o he RTS message. I he des ina ion can ecei e he
sou ce da a secu ely and success ully, i.e.,
R0,M≥RS
, i will eedback a clea - o-send (CTS) message
o in o m. In his case, he sou ce di ec ly sends he da a o he des ina ion wi hou using he elays.
In he case whe e
R0,M<RS
, he des ina ion has o gene a e a non-CTS message o eques he help
o he elays. Now, le us deno e
U1=nN11,N12, ..., N1 1o
as se o he po en ial elays which can
ecei e he da a secu ely and success ully, i.e.,
R0,1u≥RS
, whe e
u=
1, 2, ...,
1
, 0
≤ 1≤M−
1,
N1u∈{N1,N2, ..., NM−1}
. To selec he elay o he e ansmission, we also p opose a dis ibu ed
elay selec ion me hod. Simila o he wo k in [48], he elay N1uwill se a ime gi en as
ω1u=A
λ1u,M
, (12)
whe e A is a p ede e mined cons an .
Then, he elay whose ime expi es i s will b oadcas he CTS message, and i be selec ed o
e ansmi he da a o he des ina ion. We can obse e om Equa ion
(12)
ha he selec ed elay is
nea es o he des ina ion. I is wo h no ing ha , i he se
U1
is emp y (
1=
0), no elay node can
e ansmi he da a o he des ina ion, and his case is conside eda sec ecy ou age e en . In he case
whe e 1≥1, he ope a ion will be epea ed wi h he new sou ce.
Gene ally, a he
k
h ime slo
(k≥1)
, assume ha he cu en sou ce is
Nik
,
ik∈{0, 1, ..., M−1}
and
i1=
0. Le
Wk=Nik+1,Nik+2, ..., NM
deno e se o elays om he node
Nik+1
o he des ina ion.
Simila ly,
Nik
sends he RTS message o all o he nodes belonging o
Wk
. Then, i
Rik,M≥RS
, he
des ina ion gene a es he CTS message, and
Nik
will di ec ly ansmi he da a o
NM
. O he wise,
he po en ial elay which belongs o
Wk
and is nea es o he des ina ion will become he new sou ce
and epea he p ocess ha
Nik
did. Indeed, we deno e
Uk
as he se o he po en ial elays, i.e.,

En opy 2019,21, 217 6 o 16
Uk=nNk1,Nk2, ..., Nk ko
, whe e
Uk⊂ Wk
, 0
≤ k≤M−ik
. In addi ion, le us deno e
Zk=
nNk k+1,Nk k+2, ..., NM−iko
as se o he nodes ha canno ecei e he da a secu ely, whe e
k k+1<
k k+2<
...
<kM−ik
and
NkM−ik≡NM
. Then, assume ha
k1<k2<
...
<k k
and
k≥
1, using he elay
selec ion me hod desc ibed abo e, he elay
Nk
will become he new sou ce a he
(k+1)
h ime slo .
This p ocess is only s opped when
NM
can secu ely and success ully ecei e he da a o he e is
no elay be ween he cu en sou ce and he des ina ion ha can secu ely and success ully ecei e
he da a. I is no ed ha , o a oid he ea esd oppe and combine he ecei ed da a wi h maximal
a io combining (MRC) echnique, he sou ce and he selec ed elays use andomize-and- o wa d (RF)
me hod [49,50].
In he p oposed p o ocol, o selec he success ul elay a each ime slo co ec ly, he CSI
es ima ions o e he da a, in e e ence and ea esd opping links a e assumed o be pe ec . Howe e ,
in p ac ice, he es ima ions may no be co ec due o he ime a ia ion o he channel, ini e numbe
o pilo symbols and noises. Hence, we will discuss his p oblem in he nex sub-sec ion.
2.3. Impe ec Channel Es ima ion
In his subsec ion, we conside he impe ec channel es ima ion a he ansmi e
Ni
and he
ecei e Nj. F om Equa ion (9), i Njwan s o calcula e he sec ecy capaci y Ri,j, i has o es ima e he
channel coe icien
hNi,Nj
co ec ly. In addi ion,
Ni
has o es ima e he channel coe icien s
hNi,PU
and
hNi,E, which a e hen sen o Nj h ough he RTS message.
Le
he
Ni,Nj
,
he
Ni,PU
and
he
Ni,E
deno e he es ima ed CSIs o
hNi,Nj
,
he
Ni,PU
and
hNi,E
, espec i ely;
he co ela ion be ween
he
Ni,Nj
and
hNi,Nj
;
he
Ni,PU
and
hNi,PU
; and
he
Ni,E
and
hNi,E
can be exp essed,
espec i ely as in [51]:
he
Ni,Nj=φDhNi,Nj+q1−φ2
DεD,
he
Ni,PU =φPhNi,PU +q1−φ2
PεP,
he
Ni,E =φEhNi,E +q1−φ2
EεE, (13)
whe e
φD
,
φP
and
φE
a e channel co ela ion ac o s, and
εD
,
εP
and
εE
a e es ima ion e o s. We can
obse e ha i
φD=φP=φE=
1, all o he channel es ima ions a e pe ec . I
φD<
1,
φP<
1,
φE<
1,
he channel es ima ions ha e e o s, and he es ima ed sec ecy capaci y in Equa ion (9) is w i en by
Re
i,j=

log2


1+Pmin 1, µ
γe
i,P γe
i,j
1+Pmin 1, µ
γe
i,P γe
i,E





+
, (14)
whe e
γe
i,j=|he
Ni,Nj|2
,
γe
i,P =|he
Ni,PU|2
and
γe
i,E =|he
Ni,E|2
. Again, we no e ha he CSI es ima ion e o s
may lead o he inco ec elay selec ion, which would deg ade he sys em pe o mance.
2.4. Mul i-Hop Di ec T ansmission P o ocol
To show he ad an ages o he p oposed p o ocol, we compa ed he sec ecy pe o mance
o he p oposed p o ocol wi h ha o he con en ional mul i-hop di ec ansmission p o ocol
(MDT) [
44
]. In he MDT scheme, he da a a e ansmi ed hop-by-hop om he sou ce o he des ina ion.
Pa icula ly, he da a ansmission is spli in o
M
o hogonal ime slo s. A he
m
h ime slo , whe e
m=
1, 2, ...,
M
, he node
Nm
ansmi s he sou ce da a o he node
Nm+1
. I he communica ion be ween
Nm
and
Nm+1
is secu e and success ul,
Nm+1
will o wa d he da a o he nex hop in he nex ime
slo . O he wise, he da a ansmission is insecu e and he sec ecy ou age e en occu s. Simila o he
MCT p o ocol, he sou ce and elays in he MDT p o ocol use he RF echnique.
En opy 2019,21, 217 7 o 16
3. Pe o mance Analysis
Fi s ly, we can o mula e SOP o he Ni→Njlink as
SOPDT
i,j=P Ri,j<RS
=P 1+Ψi,j
1+Ψi,E
<ρ, (15)
whe e ρ=2RS(ρ>1).
F om Equa ions (9) and (15), i is s aigh o wa d ha , i κ>0, hen
SOPDT
i,j
P→+∞
≈1. (16)
When he anscei e ha dwa e is pe ec
(κ=0)
, we can de i e he exac closed- o m exp ession
o SOPDT
i,j. A i s , se ing x=γi,P, SOPDT
i,jcondi ioned on xcan be gi en by
SOPDT
i,j(x)=P γi,j<ρ−1
Pmin (1, µ/x)+ργi,E. (17)
Due o he independence o γi,jand γi,E, we can w i e
SOPDT
i,j(x)=Z+∞
0 γi,E (y)Fγijρ−1
Pmin (1, µ/x)+ρydy. (18)
Subs i u ing p obabili y densi y unc ion (PDF) o he exponen ial RV
γi,E
 γi,E (y)=λi,E exp (−λi,Ey)
, and he cumula i e dis ibu ion unc ion (CDF) o he exponen ial RV
γi,jγi,E Fγi,j(y)=1−exp −λi,jyin o Equa ion (18), a e some manipula ions, we ob ain
SOPDT
i,j(x)=1−λi,E
λi,E +λi,jρexp −ρ−1
Pmin (1, µ/x). (19)
Then, SOPDT
i,jcan be ob ained om SOPDT
i,j(x)by
SOPDT
i,j=Z+∞
0SOPDT
i,j(x) γi,P (x)dx. (20)
Subs i u ing Equa ion
(19)
and
γi,P (y)=λi,P exp (−λi,Py)
in o Equa ion
(20)
, we ob ain an exac
closed- o m exp ession o SOPDT
i,jas
SOPDT
i,j=Zµ
0 1−λi,E
λi,E +λi,jρexp −ρ−1
P!λi,P exp (−λi,Px)dx
+Z+∞
µ 1−λi,E
λi,E +λi,jρexp −ρ−1
Pµx!λi,P exp (−λi,Px)dx
=1−λi,E
λi,E+λi,jρ"(1−exp(−λi,Pµ)) exp
−λi,j
ρ−1
P+λi,PPµ
λi,PPµ+λi,j(ρ−1)exp
−λi,Pµ−λi,j
ρ−1
P#. (21)
Fu he mo e, using he app oxima ion in Equa ion
(11)
, an asymp o ic closed- o m exp ession o
SOPDT
i,ja high P alues can be p o ided by
SOPDT
i,j
P→+∞
≈P γi,j
γi,E
<ρ=1−λi,E
λi,E +λi,jρ. (22)
En opy 2019,21, 217 8 o 16
3.1. Mul i-hop Di ec T ansmission P o ocol (MDT)
Because he ansmission on each hop is independen , he end- o-end SOP o he MDT p o ocol
can be gi en as
SOPMDT
0,M=1−
M
∏
m=11−SOPDT
m−1,m. (23)
As
κ=
0, subs i u ing Equa ion
(21)
in o Equa ion
(23)
, we ob ain an exac closed- o m exp ession
o he end- o-end SOP o he MDT p o ocol as
SOPMDT
0,M=1−
M
∏
m=1


λm−1,E
λm−1,E +λi,jρ

(1−exp (−λm−1,Pµ)) exp −λm−1,mρ−1
P
+λm−1,PPµ
λm−1,PPµ+λm−1,m(ρ−1)exp −λm−1,Pµ−λm−1,mρ−1
P



. (24)
A high
P
egions, using Equa ion
(22)
, an app oxima e exp ession o Equa ion
(24)
can be
ob ained by
SOPMDT
0,M
P→+∞
≈1−
M
∏
m=1
λm−1,E
λm−1,E +λm−1,mρ. (25)
3.2. Coope a i e Mul i-Hop T ansmission P o ocol (CMT)
In he CMT p o ocol, he end- o-end SOP is exp essed by a ecu si e exp ession as ollows:
SOPCMT
Nik,Uk=∑
Uk
P 


1+Ψik,k1
1+Ψik,E ≥ρ,1+Ψik,k2
1+Ψik,E ≥ρ, ..., 1+Ψik,k k
1+Ψik,E ≥ρ,
1+Ψik,k k+1
1+Ψik,E
<ρ,1+Ψik,k k+2
1+Ψik,E
<ρ, ..., 1+Ψik,kM−ik
1+Ψik,E
<ρ


=∑
Uk
P















1+Pmin1,µ/γik,Pγik,k1
1+Pmin1,µ/γik,Pγik,E
≥ρ,1+Pmin1,µ/γik,Pγik,k2
1+Pmin1,µ/γik,Pγik,E
≥ρ, ...,
1+Pmin1,µ/γik,Pγik,k k
1+Pmin1,µ/γik,Pγik,E
≥ρ,
1+Pmin1,µ/γik,Pγik,k k+1
1+Pmin1,µ/γik,Pγik,E
<ρ,1+Pmin1,µ/γik,Pγik,k k+2
1+Pmin1,µ/γik,Pγik,E
<ρ, ...,
1+Pmin1,µ/γik,Pγik,kM−ik
1+Pmin1,µ/γik,Pγik,E
<ρ















, (26)
whe e
SOPCMT
Nik,Uk
is SOP a
k
h ime slo ,
k=
1, 2, ...,
M
. Then, he end- o-end SOP o he CMT p o ocol
is gi en as
SOPCMT
0,M=SOPCMT
N0,U1. (27)
Be o e calcula ing SOPCMT
Nik,Uk, we gi e an example wi h M=3, whe e SOPCMT
0,3 is exp essed by
SOPCMT
0,3 =SOPCMT
N0,{∅}+SOPCMT
N0,{N1}+SOPCMT
N0,{N2}
+SOPCMT
N0,{N1,N2}. (28)
Equa ion
(28)
shows ha he e a e 04 possible cases o he se
U1
, i.e.,
U1={∅}
,
U1={N1}
,
U1={N2}
,
U1={N1,N2}
. In Equa ion
(28)
, he e ms
SOPCMT
N0,{∅}
and
SOPCMT
N0,{N2}
can be calcula ed as
in (32). Conside ing he e m SOPCMT
N0,{N1}, which can be w i en by
En opy 2019,21, 217 9 o 16
SOPCMT
N0,{N1}=SOPCMT
N1,U2=SOPCMT
N1,{∅}+SOPCMT
N1,{N2}. (29)
In Equa ion
(29)
, he e a e wo possible cases o he se
U2
, i.e.,
U2={∅}
,
U2={N2}
, and
SOPCMT
N1,{∅}
and
SOPCMT
N1,{N2}
a e SOP a he second ime slo s. In addi ion,
SOPCMT
N1,{∅}
is calcula ed by
Equa ion (32), while SOPCMT
N1,{N2}is exp essed by
SOPCMT
N1,{N2}=SOPDT
2,3 , (30)
whe e, because he ansmission be ween
N2
and
N3
is di ec , Equa ion
(21)
is used o calcula e
SOPCMT
N1,{N2}.
Nex , le us conside he e m
SOPCMT
N0,{N1,N2}
in Equa ion
(28)
, whe e he elay
N2
will be selec ed
o e ansmi ing he da a o he des ina ion. Simila o Equa ion (30), we ha e
SOPCMT
N0,{N1,N2}=SOPDT
2,3 . (31)
Now, he ecu si e exp ession o SOPCMT
Nik,Ukis gi en as in Lemma 1.
Lemma 1. When κ=0,SOPCMT
Nik,Ukcan be exp essed as
SOPCMT
Nik,Uk=∑
Uk
λik,E
λik,E +
k
∑
=1
λik,k ρ





exp −
k
∑
=1
λik,k (ρ−1)
P1−exp −λik,Pµ
+λik,PPµ
λik,PPµ+
k
∑
=1
λik,k (ρ−1)
exp −λik,Pµ−
k
∑
=1
λik,k
(ρ−1)
P




+∑
Uk
M−ik− k
∑
=1
(−1) M−ik− k
∑
Nj1,...,Nj ∈Zk
j1<j2<...<j
λik,E
λik,E +
∑
=1
λik,j +
k
∑
=1
λik,k ρ
×





exp −
∑
=1
λik,j +
k
∑
=1
λik,k ρ−1
P1−exp −λik,Pµ
+λik,PPµ
λik,PPµ+ λik,E+
k
∑
=1
λik,k !(ρ−1)
exp −λik,Pµ−
∑
=1
λik,j +
k
∑
=1
λik,k ρ−1
P





. (32)
P oo . A i s , we se x=γik,E and y=γik,P, and SOPCMT
Nik,Ukcondi ioned on xand ycan be gi en by
SOPCMT
Nik,Uk(x,y)
=∑
Uk" k
∏
=1
exp−λik,k ρ−1
Pmin (1, µ/y)+ρxM−ik− k
∏
=11−exp −λik,k ρ−1
Pmin (1, µ/y)+ρx#
=∑
Uk
exp −
k
∑
=1
λik,k ρ−1
Pmin (1, µ/y)+ρx!
+∑
Uk
M−ik− k
∑
=1
(−1) M−ik− k
∑
Nj1,...,Nj ∈Zk
j1<j2<...<j
exp −
∑
=1
λik,j +
k
∑
=1
λik,k !ρ−1
Pmin (1, µ/y)+ρx!. (33)
En opy 2019,21, 217 16 o 16
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c
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