DSpace at VNU: Outage Analysis of Opportunistic Relay Selection in Underlay Cooperative Cognitive Networks Under General Operation Conditions

Outage Analysis of Opportunistic Relay Selectionin Underlay Cooperative Cognitive Networks under General Operation Conditions Khuong Ho-Van Abstract—This paper investigates the impact of

Outage Analysis of Opportunistic Relay Selection

in Underlay Cooperative Cognitive Networks under

General Operation Conditions

Khuong Ho-Van

Abstract—This paper investigates the impact of practical

operation conditions such as channel information imperfection

(CII), independent non-identical (i.n.i) fading distributions, strict

power constraints (i.e., peak transmit power constraint and

primary outage constraint), and primary interference on outage

performance of opportunistic relay selection (ORS) in underlay

cooperative cognitive networks (UCCNs) Towards this end, the

power of secondary transmitters is firstly established to meet

strict power constraints and account for primary interference

and CII Then, exact closed-form outage probability expressions

for the secondary destination employing the maximum ratio

combining (MRC) and the selection combining (SC) are

pro-posed to promptly evaluate the effect of these conditions and

provide useful insights into performance limits Numerous results

illustrate significant system performance deterioration due to

pri-mary interference and CII, performance saturation phenomenon

in the secondary network, performance compromise between

the secondary network and the primary network, significant

performance improvement with respect to the increase in the

number of involved relays, a large gap between the lower outage

bound (MRC’s outage performance) and the upper outage bound

(SC’s outage performance), and the advantage of utilizing direct

channel between the source and the destination.

Index Terms—Opportunistic relay selection, primary

interfer-ence, channel information imperfection, cognitive radio.

NOWADAYS, the development of new wireless

commu-nication applications demands more and more radio

spectrum, which conflicts with the current circumstance of

available spectrum resource utilization as reported by Federal

Communication Commission [1] The feasible solution to

this conflict comes from the cognitive radio (CR) technology

in which secondary users (SUs) can temporarily utilize the

licensed spectrum allocated to primary users (PUs) without

causing any significant harm to the performance of PUs

[2]–[4] Therefore, the spectrum utilization efficiency can be

substantially improved Conversely, the interference from SUs

on PUs is a remarkable challenge to the CR technology

Three modes in which SUs can operate, namely interweave,

overlay and underlay, can efficiently manage this interference

Manuscript received June 29, 2015; revised August 29, 2015, October 6,

2015, October 27, 2015; accepted November 6, 2015 The associate editor

approving this paper for publication is Dr Edward Au.

Engi-neering, HoChiMinh City University of Technology, Vietnam (e-mail:

khuong.hovan@yahoo.ca).

This research is funded by Vietnam National Foundation for Science and

Technology Development (NAFOSTED) under grant number 102.04-2014.42

Digital Object Identifier 10.1109/TVT.2008.2007644

Among these modes, the underlay one is preferred due to its low implementation complexity According to this mode, SUs intelligently adjust their transmit power to ensure that the induced interference at PUs remains below a controllable level, which can be tolerated by PUs SUs can implement power adjustment in short-term or long-term manner According to the former, the power of secondary transmitters is constrained

by either interference power constraint [2] or both interference power constraint and peak transmit power constraint [3] while according to the latter, the power of secondary transmitters is constrained by the outage probability of PUs [4]

In either short-term or long-term power adjustment scheme, the transmit power of SUs is limited, ultimately shortening their radio coverage To extend the radio coverage for SUs, relaying communications technique should be exploited [5] This technique makes use of relays, which play a role as intermediate users to relay information from a transmitter to a receiver Obviously, it can improve reliability of point-to-point communications due to low path-loss effects In other words,

it can increase the radio coverage without degrading sys-tem performance In relaying communications, relay selection strategy plays a very important role in improving system per-formance in terms of spectral efficiency, power consumption, and transmission reliability This can be attributed to the fact that selecting a single relay among a set of possible candidates requires less system resources (e.g., bandwidth and power) than multi-relay assisted transmission while maintaining the same diversity gain as the latter [3], [6]

Several relay selection strategies in UCCNs were proposed (e.g., [2], [3], [7]–[11]) To be more specific, the ORS was proposed in [2], [3], [7], which adopts the relay with the maximum end-to-end signal-to-noise ratio (SNR); the authors

in [7] considered the reactive relay selection (RRS) strategy, which selects the relay among all possible candidates (i.e., all relays are assumed to successfully decode source information) with the largest SNR to the destination; the Nth best-relay selection strategy was proposed in [8]; the maximum secrecy capacity based relay selection strategy was investigated in [9]; the authors in [10] studied the relay selection strategy with the good compromise between the gain for SUs and the loss for PUs; the work in [11] selects the first relay whose instantaneous reward (short-term effective bit rate) is

at least the same as the expected reward (long-term expected throughput) However, several assumptions have been imposed

on these works for analysis tractability: i) perfect channel

information;ii) no primary outage constraint; iii) independent

partially-identical (i.p.i) [2], [3], [10] or independent identical

(i.i) fading distributions [7]–[9], [11]

Channel state information (CSI) plays an important role

in system design optimization such as optimum coherent

detection However, it is inevitable that this information is

imperfect, inducing the study on the effect of CII on the

outage behavior of relay selection strategies in UCCNs to be

essential The impact of CII on the ORS and RRS strategies

was studied in [12] and [13], respectively The partial relay

selection strategy, which chooses the relay with the largest

SNR from the source, under CII was also analyzed in [14]

The common ground of works in [12]–[14] is the assumptions

on i.p.i fading distributions, no primary interference, and no

primary outage constraint In [15], we analyzed the outage

performance of the RRS strategy under consideration of CII,

i.n.i fading distributions, primary outage constraint, and the

MRC at the secondary destination However, [15] did not take

into account primary interference and the SC at the secondary

destination

Briefly, the ORS strategy is proved to be outage-optimal

(e.g., [3]) Together with remarkable features that any relay

selection strategy can bring such as high bandwidth utilization

efficiency, wide radio range, and low transmit power,

out-age performance evaluation of the ORS strategy in UCCNs

before practical deployment/implementation under practical

operation conditions such as CII, i.n.i fading distributions,

primary outage constraint, peak transmit power constraint,

and primary interference is necessary and essential to expose

performance limits without the need of time-consuming

sim-ulations This paper aims at such an objective1 To the best

of the author’s knowledge, no analysis accounts for all these

practical operation conditions Moreover, the SC and the MRC

represent two extremes among signal combining techniques

for space diversity in terms of implementation complexity

and outage performance, where the MRC obtains the lowest

outage probability (lower outage bound) but requires the most

complicated implementation while the SC achieves the highest

outage probability (upper outage bound) but requires the least

complicated implementation [16] Therefore, when the direct

channel between the source and the destination is considered

in this paper, it is useful to analyze their performance to have

insights into performance extremes of the ORS strategy in

UCCNs as well as to expose their performance gap for

appro-priate choice of signal combining techniques in system design

process to better trade-off with implementation complexity

The contributions of the current work are summarized below:

• Exactly analyze the impact of practical operation

con-ditions such as primary interference, CII, peak transmit

power constraint, primary outage constraint, and i.n.i

multi-path fading channels on the outage performance of

the ORS strategy in UCCNs

1 The current paper is not a trivial extension of our previous work in [15] as

follows First of all, they investigate two different relay selection strategies:

the ORS strategy in the former while the RRS strategy in the latter Secondly,

the former considers more general operation conditions than the latter More

specifically, operation conditions in the former include all operation conditions

in the latter together with primary interference and the SC at the secondary

destination.

hop 1

Secondary network Primary network

hop 2

transmission interference

k=1,2, ,K

SD

SR1

SRK

SRb

SS

h=1,2

{gLLh}

{g LDh}

g SL1

g SD1

Fig 1 System model

TABLE I

N OTATIONS FOR CHANNEL COEFFICIENTS

g LLh ∼ CN (0, β LLh ) PT and PR in the hop h, h ∈ {1, 2}

g Lk1 ∼ CN (0, β Lk1 ) PT and SRk, k ∈ K = {1, , K}

g LDh ∼ CN (0, β LDh ) PT and SD in the hop h, h ∈ {1, 2}

g SL1 ∼ CN (0, β SL1 ) SS and PR

g Sk1 ∼ CN (0, β Sk1 ) SS and SR k , k ∈ K = {1, , K}

g kD2 ∼ CN (0, β kD2 ) SR k and SD , k ∈ K = {1, , K}

g SD1 ∼ CN (0, β SD1 ) SS and SD

g kL2 ∼ CN (0, β kL2 ) SR k and PR , k ∈ K = {1, , K}

• Propose a power allocation condition for SUs to satisfy strict power constraints and account for primary interfer-ence and CII

• Derive exact closed-form outage probability expressions for the secondary destination employing the MRC and the

SC to promptly assess the outage performance without exhaustive simulations

• Analytically prove the advantage of utilizing direct chan-nel between the source and the destination

• Provide numerous results to demonstrate useful insights into the system performance

II SYSTEMMODEL

A system model for the ORS in UCCNs under consideration

is illustrated in Fig 1 where the secondary source SS com-municates the secondary destinationSDwith the assistance of the best secondary relay SRb in the group of K secondary

relays,R = {SR1,SR2, ,SRK} We assume that secondary

transmitters operate in the underlay mode, and hence, there exists mutual interference between the primary network and the secondary network To be more specific, SS and SRb

interfere communications between the primary transmitterPT

and the primary receiverPR, andPTalso causes interference

to the received signals atSDandSRk,k ∈ K = {1, 2, , K}

It is recalled that the primary interference caused by PUs to SUs was ignored for analysis simplicity in [3], [4], [12], [13] and references therein However, this interference cannot be omitted in a general set-up due to concurrent communication

of PUs and SUs in the underlay mode It is the interference from PUs that makes the performance analysis complicated but general and practical Furthermore, it is obvious that two hops

of the relay selection process in the secondary network can take place simultaneously with communication of two different

primary transmitter-receiver pairs Nevertheless, in order to

have a compact figure, Fig 1 only illustrates a

transmitter-receiver pair However, to reflect this general case, two

differ-ent channel coefficidiffer-ents,gLL1andgLL2, corresponding to two

different primary transmitter-receiver pairs are assumed in the

following analysis2

We consider independent, frequency-flat, and

Rayleigh-distributed fading channels Consequently, the channel

coef-ficient, gklh, between the transmitter k and the receiver l in

the hop h can be modelled as a circular symmetric complex

Gaussian random variable with zero mean and βklh-variance,

i.e gklh ∼ CN (0, βklh), as illustrated in Table I In contrast

to existing works in relay selection where i.p.i3 or i.i4 fading

distributions are assumed for simplicity of performance

anal-ysis, the current paper investigates i.n.i fading distributions,

and hence, all βklh’s, ∀{k, l, h} are not necessarily equal

Therefore, our work is more general and practical

It is inevitable that channel estimation algorithms cannot

obtain perfect CSI Hence, channel estimation error (CEE)

should be modeled in order to support performance analysis

In this paper, we resort to the well-known CEE model used

in [12], [13] To this effect, the real channel coefficient,gklh,

is related to the estimated one,ˆklh, as follows

ˆklh= µklhgklh+

q

1 − µ2 klhξklh, (1) whereξklh is the CEE andµklh is the correlation coefficient,

0 ≤ µklh ≤ 1, characterizing the average quality of

chan-nel estimation As elaborately addressed in [12], all random

variables{ˆgklh,gklh,ξklh} are modelled as CN (0, βklh)

As illustrated in Fig 1, the ORS takes place in two hops

In the first hop, SS broadcasts the signal uS with transmit

power PS (i.e., PS = EuS{|uS|2} where EX{x} denotes

statistical expectation over random variable X) while PT is

concurrently transmitting the signaluL1 with transmit power

PL The signals fromSSandPTcause the mutual interference

between the primary network and the secondary network To

this effect, the received signals at the primary receiverPRand

the secondary receivers (i.e., SRk, and SD), correspondingly,

can be expressed as

vLL1= gLL1uL1+ gSL1uS+ nL1 (2)

vSl1= gSl1uS+ gLl1uL1+ nl1, l ∈ {D, K} (3)

wherenlh∼ CN (0, N0) is the additive white Gaussian noise

(AWGN) at the corresponding receivers

Using (1) to rewrite (2) and (3) as

vLL1=ˆLL1

µLL1uL1−

p 1−µ2 LL1

µLL1 ξLL1uL1+gSL1uS+nL1 (4)

2 The case that multiple primary transmitter-receiver pairs co-exist in single

orthogonal channel may make the system model more general However, for

tractable analysis, the current paper considers only one primary

transmitter-receiver pair This is suitable to several practical and popular multiple

access techniques such as time division multiple access (TDMA), frequency

division multiple access (FDMA), orthogonal frequency division multiple

access (OFDMA), code division multiple access (CDMA).

3 This means that β klh ’s are partitioned into groups of equal value For

example, β Lkh = α 1 , β kDh = α 2 , β kLh = α 3 , β Skh = α 4 with ∀ SR k ∈

R and α 1 6= α 2 6= α 3 6= α 4 are assumed (e.g., [2], [3], [10], [12], [13]).

4 This means that β klh ’s, ∀{k, l, h} are equal (e.g., [7]–[9], [11]).

vSl1=ˆSl1

µSl1

uS−

p

1 − µ2 Sl1

µSl1

ξSl1uS+ gLl1uL1+ nl1 (5)

From (4) and (5), one can express the signal-to-interference plus noise ratio (SINR) at the primary receiver and the secondary receivers in the first hop as

2

PL

(1−µ2 LL1) βLL1PL+|gSL1|2µ2

LL1PS+µ2

LL1N0

(6)

2

PS

(1 − µ2 Sl1) βSl1PS+ µ2

Sl1|gLl1|2PL+ µ2

Sl1N0

(7)

This paper applies the ORS strategy (e.g., [3]) to remedy the effect of CII and primary interference in UCCNs This strategy selects the relay SRb that obtains the largest end-to-end SINR5, i.e

b = arg max

k∈Kmin (γSk1, γkD2) , (8) where γkD2 is the SINR of the signal received at SD from

SRk in the second hop This signal can be represented in the same form as (5), i.e

vkD2=ˆkD2

µkD2

uk−

p 1−µ2 kD2

µkD2

ξkD2uk+gLD2uL2+nD2, (9)

where k ∈ K, uL2 is the signal transmitted by PT with the power PL, and uk is the signal transmitted by SRk with the power Pk Therefore, γkD2 can be computed in the same manner as (7), i.e

2

Pk

(1−µ2 kD2)βkD2Pk+µ2

kD2|gLD2|2PL+µ2

kD2N0

(10)

In the second hop, PR also receives the desired signal fromPTand the interference signal fromSRb By exchanging notations, the SINR atPRin the second hop can be expressed

in the same form as (6), i.e

2

PL

(1−µ2 LL2)βLL2PL+|gbL2|2µ2

LL2Pb+µ2

LL2N0

(11)

This paper takes advantage of the direct channel between

SS andSD for further performance improvement Therefore,

at SD, both signals received from SS and SRb should be combined in a wise manner to restore the source information The MRC and the SC are two popular combining techniques where the MRC is better but more complicated than the SC [16] Therefore, their outage performance should be analyzed

to expose the performance extremes of the ORS in UCCNs

To this effect, the total SINRs atSDfor the MRC and the SC, respectively, are represented as

γSC = max



γSD1, max

k∈Kmin (γSk1, γkD2)



γMRC= γSD1+ max

k∈Kmin (γSk1, γkD2) , (13) wheremax

k∈Kmin (γSk1, γkD2) is the SINR of theSS−SRb−SD

relaying channel

5 The ORS can be implemented in a distributed manner using the timer method in [6] where each relay SRk sets its timer with the value that is inversely proportional to min (γ Sk1 , γ kD2 ) and the relay with the timer that

runs out first is selected.

It is noted that for the compact figure, the system model

in Fig 1 only shows one primary transmitter-receiver pair

Generally, it is possible that communication of two different

primary transmitter-receiver pairs takes place in two different

hops In such a case, we assume all primary transmitters

have the same transmit power of PL The case of different

transmit powers designed for different primary transmitters can

be straightforwardly extended

III POWERCONSTRAINTS FORSECONDARYUSERS

In the underlay mode, the transmit power of SUs must

be properly allocated to satisfy the primary outage constraint

for guaranteeing reliable communication for PUs (e.g [4])

This constraint forces the outage probability of PUs to be

below a pre-defined thresholdθ Therefore, the smaller θ, the

more reliable communication of PUs Towards this end, the

transmit powers ofSSandSRbmust be controlled to meet the

following two primary outage constraints, correspondingly:

Pr {γLL1< ηL} = Fγ LL1(ηL) ≤ θ (14)

Pr {γLL2< ηL} = Fγ LL2(ηL) ≤ θ, (15) where Pr{W } denotes the probability of the event W ,

ηL = 2T L− 1 with TL being the required spectral efficiency

in the primary network, and FX(x) denotes the cumulative

distribution function (cdf) ofX

In addition, secondary transmitters (i.e., SS and SRb) are

constrained by their designed peak transmit powers (i.e.,PSm

and Pbm) As such, the transmit powers of SS and SRb are

also upper-bounded byPSmandPbm, respectively, i.e

Lemma 1 For maximizing the radio coverage and meeting

both primary outage constraint in (14) and peak transmit

power constraint in (16), the transmit power of SS must be

established as

PS= min



PLβLL1

ηLµ2 LL1βSL1

maxe−η L κ LL1

1 − θ −1,0

 , PSm

 , (18)

where

κLLh= 1 − µ2LLh+µ

2 LLhN0

PLβLLh

, h ∈ {1, 2} (19)

Proof Please see Appendix A.

By following Lemma 1, one immediately infers that the

transmit power of SRb that meets both primary outage

con-straint in (15) and peak transmit power concon-straint in (17) as

well as maximizes the radio coverage can be expressed as

Pb= min

 PLβLL2

ηLµ2 LL2βbL2

maxe−η L κ LL2

1 − θ −1,0

 , Pbm

 (20)

It is noted that even though the power allocation for SUs to

satisfy the primary outage constraint was carried out (e.g [4]),

CII has not been accounted yet Consequently, (18) and (20)

include the existing works (e.g [4]) as special cases when

µklh = 1, ∀{k, l, h}; for example, when µLLh = 1, (18)

reduces to [4, eq (8)]

Generality: To meet both peak transmit power constraint and

primary outage constraint, the powers of secondary transmit-ters in (18) and (20) can be uniquely represented as

Pu= min















PLβLLh

ηLµ2 LLhβuLhmax







e−ηL

 1−µ 2 LLh +µ 2 LLh N0 PLβLLh



1 − θ

D

−1,0







Y

,Pum















(21) where the first hop corresponds to (u, h) = (S, 1) while the

second hop corresponds to (u, h) = (b, 2)

The following are comments on how the degree of reliable communication (DoRC) in the primary network (i.e.,θ) affects

the performance trend of the secondary network:

• For high DoRC requirement in the primary network (i.e., small θ), no power is allocated to SUs (i.e., Pu = 0)

This can be attributed to the fact that D is proportional

toθ Therefore, the small θ can cause D < 1, resulting

inPu= 0 In such a scenario, the secondary network is

always in outage

• For moderate DoRC requirement in the primary network (i.e., moderate θ), Pu is completely controlled by Y

Since Y is proportional to θ, the power of secondary

transmitter increases with respect to θ, enhancing the

performance of the secondary network

• For low DoRC requirement in the primary network (i.e., large θ), Pu is totally determined by Pum, independent

ofθ Consequently, the secondary network suffers

perfor-mance saturation

The above comments show that there exists a performance compromise between the primary network and the secondary network: higher DoRC in the primary network results in lower performance in the secondary network and vice versa These comments will be excellently supported by simulation results

in Section V

IV PERFORMANCEANALYSIS The outage probability is an important metric for system performance evaluation In this section, we derive two exact closed-form outage probability expressions atSDfor the MRC and the SC, which are then applied to investigate the outage performance of the ORS in UCCNs without time-consuming simulations in the next section The outage probability is defined as the probability that the total SINR is below a pre-defined thresholdηS Due to the two-hop nature of the ORS,

ηS is related to the required spectral efficiency, TS, in the secondary network as ηS = 22T S − 1

A Selection Combining

For the SC, the outage probability can be expressed as

OPSC = Pr {γSC ≤ ηS}

= Pr{γSD1≤ ηS}

W 1

Pr

 max

k∈Kmin(γSk1, γkD2) ≤ ηS



W 2

(22)

Before computing W1 andW2 for completing the analytic

evaluation of (22), we introduce the cdf of γSl1 where l =

{D, K} By following the same derivation procedure as (58)

in the appendix A, one immediately obtains the cdf ofγSl1as

Fγ Sl1(x) = 1 − HSl1

x + HSl1

e−κSl1 x, x ≥ 0, (23)

where

HSl1= PSβSl1

µ2 Sl1PLβLl1,

κSl1= 1 − µ2

Sl1+µ

2 Sl1N0

PSβSl1

(24)

It is apparent thatW1 is the cdf ofγSD1 evaluated atηS:

W1= Fγ SD1(ηS) (25)

To analytically evaluateW2in (22), it is recalled thatγkD2’s

in (10) are correlated since they contain a common termgLD2

Thus, min (γSk1, γkD2)’s are also correlated Consequently,

we must resort to the conditional probability to computeW2

In other words,W2 in (22) should be rewritten as

W2=E|gLD2|2

 Pr

 max

k∈Kmin(γSk1,γkD2) ≤ ηS

|gLD2|2



=E|gLD2|2

nY

k∈K(1 − IkJk)o,

(26)

where

Ik = Pr {γSk1 ≥ ηS} = 1 − Fγ Sk1(ηS) , (27)

Jk = PrnγkD2≥ ηS| |gLD2|2o (28) Using (10) to evaluateJk in (28) as (29) wherePk has the

same form as (20) with changingb to k and

κkD2= 1 − µ2kD2+µ

2 kD2N0

βkD2Pk

Applying the fact that

Y

k∈K(1 − tk) = 1 + (−1)KY

k∈Ktk+

K−1

X

i=1

(−1)i

K−i+1

X

w 1 =1

K−i+2

X

w 2 =w 1 +1

· · ·

K

X

w i =w i−1 +1

Y

k∈G

tk, (31)

whereG = {K [w1] , K [w2] , , K [wi]}6, to expand the

prod-uct in (26), one obtains

W2= φ∅+ (−1)KφK+

K−1

X

i=1

(−1)i

K−i+1

X

w 1 =1

K−i+2

X

w 2 =w 1 +1

· · ·

K

X

w i =w i−1 +1

φG, (32)

where

φB =E|g

LD2 | 2

nY

k∈BIkJk

o

(33)

In (34), ∅ denotes the empty set Obviously, the derivation

of the exact closed-form representation of W2 is completed

6 K [j] is the value of the j th

element in the K set.

after analytically evaluating (33) Towards this end, we firstly substitute (29) into (33):

φB=E|g

LD2 | 2

(

e−|gLD2|

2

η S P LP k∈B

µ2kD2 βkD2Pk

) Y

k∈B

Ike−η S κ kD2 (35)

Then using the fact that the pdf of|gLD2|2isf|gLD2|2(x) =

e−x/β LD2/βLD2,x ≥ 0 since gLD2∼ CN (0, βLD2), in (35),

one obtains

φB=

∞

Z

0

e−xηSPL

P k∈B

µ2kD2 βkD2Pk

f|gLD2|2(x)dxY

k∈B

Ike−ηS κ kD2

=

Q

k∈BIke−η S κkD2

1 + ηSβLD2PLP

k∈B

µ 2 kD2

β kD2 P k

(36)

B Maximum Ratio Combining

For the MRC, the outage probability is expressed as

OPMRC = Pr {γMRC ≤ ηS}

= Pr

 max

k∈Kmin (γSk1, γkD2) ≤ ηS− γSD1

 (37)

Since min (γSk1, γkD2)’s are correlated, (37) should be

rewritten in terms of the conditional probability as (38) where

Pk= Pr { γSk1 ≥ ηS− γSD1| γSD1} , (39)

Qk= PrnγkD2≥ ηS− γSD1| γSD1, |gLD2|2o (40) Using (23), one can representPk in (39) as

Pk= 1 − Fγ Sk1( ηS− γSD1| γSD1)

ηS− γSD1+ HSk1

e−κSk1 (η S −γ SD1 ) (41)

Using (10) to evaluate Qk in (40) as (42) Then applying (31) to expand the product in (38), one obtains

OPMRC = Φ∅+ (−1)KΦK+

K−1

X

i=1

(−1)i

K−i+1

X

w 1 =1

K−i+2

X

w 2 =w 1 +1

· · ·

K

X

w i =w i−1 +1

ΦG, (43)

where

ΦB=EγSD1,|gLD2|2

nY

k∈BPkQk

o

Obviously, the derivation of the exact closed-form represen-tation of OPMRC is completed after analytically evaluating (44), which is given in the following theorem

Theorem 1. ΦB is represented in the exact closed form as

ΦB= e−ηS G BMB

Y

k∈B(−HSk1), (45)

where

GB=X

k∈B(κSk1+ κkD2), (46)

MB= CB AΥ(GB,ηS−CB)+X

k∈B

BkΥ(GB,ηS+HSk1)

! , (47)

CB= −



βLD2PL

X

k∈B

µ2 kD2

βkD2Pk

−1

Jk = Pr







|ˆgkD2|2≥ηS

h 1−µ2 kD2

βkD2Pk+µ2

kD2|gLD2|2PL+µ2

kD2N0

i

Pk

|gLD2|2







= e−ηS



κ kD2 +µ 2 kD2 PL βkD2Pk |g LD2 | 2



, (29)

OPMRC =EγSD1,|gLD2|2

 Pr

 max

k∈Kmin (γSk1, γkD2) ≤ ηS− γSD1

γSD1, |gLD2|2



=EγSD1,|gLD2|2

nY

k∈K(1 − PkQk)o, γSD1≤ ηS

(38)

Qk= Pr







|ˆgkD2|2≥ (ηS− γSD1)

h

1 − µ2 kD2

βkD2Pk+ µ2

kD2|gLD2|2PL+ µ2

kD2N0

i

Pk

γSD1, |gLD2|2







= e−(ηS−γSD1)



κ kD2 +µ 2 kD2 PL βkD2Pk |g LD2 | 2

(42)

A =Y

k∈B(−CB− HSk1)−1, (49)

Bk =



(HSk1+ CB)Y

j∈B\k(HSk1− HSj1)

−1

, (50)

Υ(a,b) = HSD1[(κSD1+C)C{T (a−κSD1,−b, ηS)

−T(a−κSD1, HSD1, ηS)}−CV(a−κSD1, HSD1, ηS)] (51)

C = (b+ HSD1)−1, (52)

T (a,b,c) = [Ei(ab+ac) − Ei(ab)] e−ab

, (53)

V (a,b,c) = 1/b− eac

/(b+c) +aT (a,b,c) (54)

with Ei(x) being the exponential integral function defined

in [17, eq (8.211.1)], which is a built-in function in most

computation software (e.g., Matlab).

Proof Please see Appendix B.

It is worth emphasizing that although the ORS was

inves-tigated in open literature (e.g., [3], [12]), the derivation of its

exact closed-form outage probability expressions in (22) and

(43) are more complicated and general than existing works7

for the following reasons: i) i.n.i fading distributions are

considered;ii) primary interference from PUs exists; iii) CII,

primary outage constraint, and direct channel are taken into

account To the best of the author’s knowledge, (22) and (43)

are completely novel and represented in a very convenient and

compact form for the analytical evaluation as demonstrated

in the next section Moreover, it is straightforwardly seen

from (22) that the outage probability of the ORS in underlay

dual-hop cognitive networks (i.e., without accounting for the

direct channel) is just OPDH = W2 Since W1 < 1 and

OPMRC < OPSC, the utilization of the direct channel is

always beneficial in terms of low outage probability (i.e.,

OPMRC < OPSC < OPDH) for both MRC and SC

TABLE II

F ADING POWERS

{β kD2 } 5 k=1 {4.1869, 3.9739, 6.1132, 6.1170, 3.1688}

{β LDh } 2 h=1 0.5727 {β LLh } 2

h=1 11.1803 {β kL2 } 5

k=1 {3.8879, 1.7570, 2.7599, 3.8838, 4.5439}

β SD1 1.0000

β SL1 1.2761 {β Lk1 } 5

k=1 {1.8055, 0.9608, 1.2328, 1.5706, 2.3124}

{β Sk1 } 5 k=1 {15.5592, 17.0076, 10.7495, 9.8886, 19.4494}

This section presents numerous results to validate the pro-posed analytical expressions as well as to demonstrate the outage performance of the ORS in UCCNs with respect to key system parameters such as peak transmit powers of primary and secondary transmitters, severe degree of CII, the number

of relays, and the DoRC requirement of PUs For illustration purpose, we only investigate a primary transmitter-receiver pair and select arbitrary fading powers which generate i.n.i fading distributions as shown in Table II To limit case-studies, we assume: i) peak transmit powers of all SUs

are equal, i.e., Pum = Pm, ∀u ∈ {S, K}; ii) the required

spectral efficiencies in the primary network and the secondary network are TL = 0.7 bits/s/Hz and TS = 0.4 bits/s/Hz,

correspondingly;iii) all correlation coefficients for different

channels are identical, i.e.,µklh= µ, ∀{k, l, h} In the sequel,

three different relay sets ({SR1}, {SRk}3

k=1, {SRk}5

k=1) are

illustrated forK = 1, 3, 5, respectively Common remarks are

withdrawn from all results in Figures 2–5 as follows:

• The analysis perfectly matches the simulation, verifying the accuracy of the proposed expressions

7 For example, [12] studied the ORS under assumptions: i.p.i fading distributions, no primary interference from PUs, no primary outage constraint, and no direct channel.

0.7 0.75 0.8 0.85 0.9 0.95 1

10−4

10−3

10−2

10−1

100

µ

Sim.: K=1 & SC Ana.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC

Fig 2 Outage probability versus µ ‘Sim.’ and ‘Ana.’ denote ‘Simulation’

and ‘Analysis’, respectively.

• The outage performance is significantly enhanced with

respect to the increase in the number of relays This

is attributed to the fact that the larger K, the higher

probability to choose the best relay, and so, the smaller

the outage probability As a result, the relay selection

plays a key role in UCCNs, not only because of the

reduced requirement of the total transmit power and

the transmission bandwidth, but also because of the

dramatically improved performance

• The MRC is significantly better than the SC, as expected

in Section II Notably, the outage performance gap

be-tween the MRC and the SC substantially increases with

respect to the increase inK This result again emphasizes

the importance of the relay selection in improving the

performance extremes (i.e., the lower and upper outage

bounds) of UCCNs Moreover, the exposure of this large

gap can provide a flexible choice of signal combining

techniques in system design process to better trade-off

with implementation complexity

It is recalled that µ characterizes the quality of the

chan-nel estimator Therefore, in order to evaluate the impact of

CII on the outage performance of the ORS in UCCNs, we

should investigate the outage probability with respect to µ

Fig 2 shows the outage probability as a function of µ for

Pm/N0 = 15 dB, PL/N0 = 17 dB, θ = 0.2 It is seen

that the secondary network stops working for a wide range

of µ To be more specific, the secondary network is always

in outage for µ < 0.8 (i.e., only small estimation error is

enough to cease the secondary network) When the channel

estimation is better (e.g., µ ≥ 0.8), the outage performance

of the secondary network is considerably improved In other

words, the channel estimation becomes a decisive factor for

the performance of the ORS in UCCNs, and any inefficient

channel estimation can lead to a unfavorable consequence to

the system performance We can interpret this performance

trend as follows Conditioned on parameters (PL, βLLh, ηL,

βuLh, N0,Pum,θ), Y in (21) is proportional to µLLh = µ

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

10−3

10−2

10−1

100

θ

Sim.: K=1 & SC Ana.: K=1 & SC Asym.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Asym.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Asym.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Asym.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Asym.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC Asym.: K=5 & MRC

Fig 3 Outage probability versus DoRC of PUs (i.e., θ) ‘Asym.’ denotes

‘Asymptotic analysis’.

for large values ofµ (e.g., µ ≥ 0.8 in Fig 2) Therefore, the

powers of secondary transmitters are also increased with the better channel estimation (i.e., larger values of µLLh = µ),

eventually improving the outage performance However, small values ofµ (e.g., µ < 0.8 in Fig 2) causes D in (21) to be less

than1, resulting in Y = 0 Therefore, no power is allocated to

SUs and hence, the secondary network is complete in outage Fig 3 illustrates the effect of the DoRC requirement of PUs on the outage performance of SUs for Pm/N0 = 15

dB,PL/N0= 17 dB, µ = 0.96 This DoRC is managed by θ,

which represents how many percentage the primary network is

in outage Results show some interesting comments as follows:

• The high DoRC (e.g.,θ ≤ 0.05 in Fig 3) requirement in

the primary network causes the secondary network to be always in outage Consequently, the secondary network cannot operate concurrently with the primary network

In other words, conditioned on the operation parameters, SUs cannot adjust their transmit powers to meet the primary outage constraint, i.e (18) and (20) results in

PS= Pb= 0

• When the primary network requires the moderate DoRC (e.g.,0.05 < θ ≤ 0.16 in Fig 3), the outage performance

of the secondary network is drastically enhanced with the increase in θ This is attributed to the fact that the

largerθ enables the primary network to tolerate the more

interference from the secondary network, and thus, the secondary network can utilize more power for transmis-sion, ultimately improving its outage performance

• When the primary network is not stringent in the DoRC (i.e., low DoRC requirement), the secondary network experiences the performance saturation phenomenon for large values of θ (e.g., θ > 0.16 in Fig 3) This

0 5 10 15 20 25 30 35 40

10−3

10−2

10−1

100

P

L /N

0 (dB)

Sim.: K=1 & SC Ana.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC

Fig 4 Outage probability versus P L /N 0

comes from the fact that8 since the power of secondary

transmitters is completely controlled by Pm,

irrespec-tive of the increase in θ, according to (21), fixing Pm

(e.g Pm/N0 = 15 dB) makes the outage probability

unchanged The performance saturation implicitly means

that the ORS in UCCNs gets zero diversity gain in the

presence of imperfect channel information

All above comments can be mathematically interpreted and

mentioned in Section III Also, the results show that better

performance of the primary network (i.e., lower θ) induces

worse performance of the secondary network (i.e., larger

outage probability) and vice versa As such, the performance

compromise between the secondary network and the primary

network should be accounted when designing UCCNs

Fig 4 demonstrates the outage performance of the ORS in

UCCNs with respect to the variation ofPL/N0forPm/N0=

15 dB, θ = 0.1, and µ = 0.96 Some interesting comments

are exposed as follows:

• For small values ofPL (e.g.,PL/N0≤ 15 dB in Fig 4),

the increase inPLdrastically improves the outage

perfor-mance This is attributed to the fact that according to (21),

PL is proportional to Y while the power of secondary

transmitters is controlled by the minimum of Y and Pm,

and thus at small values ofPLand the fixed value ofPm,

the power of secondary transmitters is proportional toPL,

ultimately enhancing the performance of the secondary

network as PL increases and the interference caused by

the primary network to the secondary network is not

significant (due to smallPL)

• For large values ofPL (e.g.,PL/N0> 15 dB in Fig 4),

theY term in (21) is larger than Pmand thus, the power

of secondary transmitters is fixed at the value of Pm

(e.g., Pm/N0 = 15 dB in Fig 4) Meanwhile, as PL

8 It is recalled from (21) that Y → ∞ as θ → 1 Consequently, for low

DoRC requirement (i.e., θ → 1), the power of secondary transmitters P u in

(21) becomes P m = P um By plugging this result of P u = P m into (22)

and (43), the performance saturation levels (or asymptotic performance) in

Fig 3 for the SC and the MRC are straightforwardly computed.

10−3

10−2

10−1

100

P

m /N

0 (dB)

Sim.: K=1 & SC Ana.: K=1 & SC Asym.: K=1 & SC Sim.: K=3 & SC Ana.: K=3 & SC Asym.: K=3 & SC Sim.: K=5 & SC Ana.: K=5 & SC Asym.: K=5 & SC Sim.: K=1 & MRC Ana.: K=1 & MRC Asym.: K=1 & MRC Sim.: K=3 & MRC Ana.: K=3 & MRC Asym.: K=3 & MRC Sim.: K=5 & MRC Ana.: K=5 & MRC Asym.: K=5 & MRC

Fig 5 Outage probability versus P m /N 0

is large and increases, the interference that the primary network imposes on the secondary network considerably increases, ultimately degrading the outage performance of the secondary network (i.e., increasing the outage proba-bility) At the very large values ofPL(e.g.,PL/N0≥ 35

dB in Fig 4), the secondary network is complete in outage

Fig 5 illustrates the outage performance of the ORS in UCCNs with respect to the variation ofPm/N0 forθ = 0.1,

PL/N0 = 17 dB, and µ = 0.96 It is observed that the

system performance is drastically enhanced with the increase

inPm This makes sense sincePm upper bounds the power

of secondary transmitters (e.g., (21)) and thus, the larger

Pm, the larger the transmit power, ultimately mitigating the corresponding outage probability However, the secondary network experiences the performance saturation at large values

ofPm/N0 (e.g.,Pm/N0≥ 16.5 dB in Fig 5) We can

inter-pret this phenomenon as follows9 The power of secondary transmitters in (21) is controlled by the minimum of Pm

and PL Consequently, as Pm is larger than a certain level (e.g.,Pm/N0 ≥ 16.5 dB in Fig 5), the power of secondary

transmitters is totally determined by PL, making the outage performance unchanged irrespective of any increase in Pm Nevertheless, the performance saturation level is significantly reduced with respect to the increase in K; for example, the

performance saturation level reduces more than fifteen times when K increases from 1 to 3 for the secondary destination

9 It is recalled from (21) that for large values of P m = P um (i.e., P m →

∞), the power of secondary transmitters P u in (21) becomes Y By plugging

this result of P u = Y into (22) and (43), the performance saturation levels

(or asymptotic performance) in Fig 5 for the SC and the MRC, respectively are immediately computed.

with the MRC The performance saturation again shows no

diversity gain achievable in the presence of imperfect channel

information

VI CONCLUSIONS This paper proposes an outage analysis framework for the

ORS in UCCNs under general practical operation conditions:

CII, i.n.i fading channels, primary interference, and both

peak transmit power constraint and primary outage constraint

Firstly, the power allocation for SUs was proposed to satisfy

these power constraints and account for primary interference

and CII Then, exact closed-form outage probability

expres-sions for the secondary destination with the MRC and the SC

were derived to analytically evaluate the system performance

in key operation parameters without time-consuming

simula-tions Numerous results illustrate thati) the secondary network

experiences performance saturation, vanishing diversity gain;

ii) CII significantly deteriorates system performance; iii)

the underlay mode causes mutual interference between the

primary network and the secondary network, which

repre-sents the performance compromise between them; iv) the

relay selection is essential in UCCNs for outage performance

improvement, and transmission bandwidth and total transmit

power reduction; v) two performance extremes (the outage

performance of the MRC and the SC) of the ORS in UCCNs

are far away from each other, especially at large number

of relays; vi) the utilization of the direct channel is always

beneficial

Let X = |ˆgLL1|2PL and Y = 1 − µ2

LL1

βLL1PL +

|gSL1|2µ2

LL1PS+ µ2

LL1N0 Since ˆLL1 ∼ CN (0, βLL1) and

gSL1 ∼ CN (0, βSL1), it is straightforward to infer that the

probability density function (pdf) of X and the pdf of Y ,

respectively are expressed as

fX(x) = (PLβLL1)−1e−PLβLL1x , x ≥ 0 (55)

fY (x) = µ2

LL1PSβSL1
−1

e−

x−r

µ 2

wherer = 1 − µ2

LL1

βLL1PL+ µ2

LL1N0 Given γLL1= X/Y in (6), one can express Fγ LL1(ηL) as

Fγ LL1(ηL) =

∞

Z

r





η L y

Z

0

fX(x) dx



fY (y) dy (57)

Substituting (55) and (56) into (57) and after some algebraic

manipulations, one obtains the closed-form expression of

Fγ LL1(ηL) as

Fγ LL1(ηL) = 1 − PLβLL1e

−η L κ LL1

PLβLL1+ ηLµ2

LL1PSβSL1

, (58)

whereκLL1is defined in (19)

Using (58), one deducesPS that meets (14) as

PS ≤ PLβLL1

ηLµ2 LL1βSL1

 e−η L κ LL1

1 − θ − 1



The right-hand side of (59) becomes negative when

e−η L κ LL1+ θ < 1 In such a case, no power is allocated toSS

(i.e., PS = 0), implying the primary channel unavailable for

the secondary transmission Because the power is nonnegative, the constraint in (14) is equivalently rewritten as

PS ≤ PLβLL1

ηLµ2 LL1βSL1

max e−η L κ LL1

1 − θ − 1, 0

 (60) Finally, combining (60) with (16) results in

PS≤ min

 PLβLL1

ηLµ2 LL1βSL1

maxe−η L κ LL1

1 − θ −1, 0

 , PSm

 (61)

To maximize the radio coverage, the equality in (61) must hold, and thus,PS is reduced to (18), completing the proof

Inserting (41) and (42) into (44), one obtains (62) whereGB

andCB are defined in (46) and (48), respectively Apparently, (62) coincides with (45) Therefore, in order to complete the proof, we must prove that MB in (62) coincides with (47) Towards this end, we firstly evaluate theLB term in (62) as

LB=

∞

Z

0

eηS −γSD1βLD2CB x

f|gLD2|2(x) dx

=

∞

Z

0

eηS −γSD1βLD2CB x 1

βLD2e−βLD2x dx

= CB/ (γSD1− ηS+ CB)

(63)

Substituting the above into (62) and then performing the partial fraction expansion, one obtains

MB= CBEγSD1

(

eG B γ SD1A

γSD1−ηS+CB

k∈B

eG B γ SD1Bk

γSD1−ηS−HSk1

)

(64) whereA and Bk are defined in (49) and (50), respectively

By denoting

Υ (a,b) =EγSD1{ea γ SD1/ (γSD1−b)} , (65)

we can infer that (64) coincides with (47) As such, the last step in this proof is to prove that (65) matches (51) To this end, we should firstly compute the pdf of γSD1 Given

Fγ SD1(x) in (23), the pdf of γSD1is immediately deduced as the derivative ofFγ SD1(x):

fγ SD1(x) = HSD1

(

κSD1

x+HSD1

(x+HSD1)2

)

e−κSD1 x (66)

Inserting (66) into (65) and then applying the partial fraction expansion, one obtains

Υ(a,b) =

η S

Z

0

ea x

x −bfγ SD1(x) dx

= HSD1

η S

Z

0

 (κSD1+ C) C e( a −κ SD1 )x

x −b

− e

( a −κ SD1 )x

x + HSD1



− C e

( a −κ SD1 )x

(x + HSD1)2

) dx,

(67)

ΦB= e−ηS G BEγSD1







LD2 | 2

n

eηS −γSD1βLD2CB |g LD2 | 2o

L B

eG B γ SD1 Y

k∈B

1

γSD1− ηS− HSk1







M B

Y

k∈B

(−HSk1) (62)

whereC is defined in (52) By defining two special functions,

T (a,b,c) =R0c e a x

x+ bdx and V (a,b,c) =R0c e a x

(x+ b ) 2dx, one

can infer that (67) exactly agrees with (51) Consequently, in

order to complete the proof, it is imperative to derive their

exact closed-form expressions T (a,b,c) is represented in

closed-form as (53) by firstly changing variables and then

using [17, eq (2.325.1)] while V (a,b,c) is expressed in

closed-form as (54) by applying the integral by part Therefore,

the proof is completed

[1] FCC, Spectrum policy task force report, ET Docket 02−135, Nov 2002.

[2] J Si, Z Li, H Huang, J Chen, and R Gao, “Capacity analysis of

cognitive relay networks with the PU’s interference,” IEEE Commun Lett.,

vol 16, no 12, pp 2020 −2023, Dec 2012.

[3] J Lee, H Wang, J G Andrews, and D Hong, “Outage probability

of cognitive relay networks with interference constraints,” IEEE Trans.

Wireless Commun., vol 10, no 2, pp 390−395, Feb 2011.

[4] L Sibomana, H Tran, H J Zepernick, and C Kabiri, “On non-zero

secrecy capacity and outage probability of cognitive radio networks,” in

Proc WPMC, New Jersey, USA, Jun 2013, pp 1−6.

[5] A Nosratinia, T E Hunter, and A Hedayat, “Cooperative communication

in wireless networks”, IEEE Commun Mag., vol 42, no 10, pp 74−80,

Oct 2004.

[6] A Bletsas, A Khisti, D P Reed, and A Lippman, “Simple cooperative

diversity method based on network path selection,” IEEE J Sel Areas

Commun., vol 24, no 3, pp 659−672, Mar 2006.

[7] M Xia and S Aissa, “Fundamental relations between reactive and

proactive relay-selection strategies,” IEEE Commun Lett., vol 19, no 7,

pp 1249 −1252, Jul 2015.

[8] Z Xing, Z Yan, Y Zhi, X Jia, and W Wenbo, “Performance analysis

of cognitive relay networks over Nakagami-m fading channels,” IEEE J.

Sel Areas Commun., vol 33, no 5, pp 865−877, May 2015.

[9] H Sakran, M Shokair, O Nasr, S El-Rabaie, and A.A El-Azm,

“Proposed relay selection scheme for physical layer security in cognitive

radio networks,” IET Commun., vol 6, no 16, pp 2676−2687, 2012.

[10] C W Chang, P H Lin, and S L Su, “A low-interference relay selection

for decode-and-forward cooperative network in underlay cognitive radio,”

in Proc IEEE CROWNCOM, Osaka, Japan, Jun 2011, pp 306−310.

[11] T Jing, S Zhu, H Li, X Xing, X Cheng, Y Huo, R Bie, and T Znati,

“Cooperative relay selection in cognitive radio networks,” IEEE Trans Veh.

Technol., vol 64, no 5, pp 1872−1881, May 2015.

[12] H Ding, J Ge, D B da Costa, and Z Jiang, “Asymptotic analysis of

cooperative diversity systems with relay selection in a spectrum-sharing

scenario,” IEEE Trans Veh Technol., vol 60, no 2, pp 457−472, Feb.

2011.

[13] X Zhang, J Xing, Z Yan, Y Gao, and W Wang, “Outage performance

study of cognitive relay networks with imperfect channel knowledge,”

IEEE Commun Lett., vol 17, no 1, pp 27−30, Jan 2013.

[14] H Haiyan, L Zan, S Jiangbo, and G Lei, “Underlay cognitive relay

networks with imperfect channel state information and multiple primary

receivers,” IET Commun., vol 9, no 4, pp 460−467, 2015.

[15] K Ho-Van, “On the performance of underlay cooperative cognitive

networks with relay selection under imperfect channel information,” in

Proc IEEE ICCE, DaNang, Vietnam, Aug 2014, pp 144−149.

[16] B Vucetic and J Yuan, Space-time coding, John Wiley & Sons, Inc.,

2003.

[17] I S Gradshteyn and I M Ryzhik, Table of Integrals, Series and

Products, 6th ed San Diego, CA: Academic, 2000.

Khuong Ho-Van received the B.E (with the

first-rank honor) and the M.S degrees in Telecommunica-tions Engineering from HoChiMinh City University

of Technology (HCMUT), Vietnam, in 2001 and

2003, respectively, and the Ph.D degree in Electrical Engineering from University of Ulsan, Korea in

2006 During 2007-2011, he joined McGill Uni-versity, Canada as a postdoctoral fellow Currently,

he is an associate professor at HCMUT His major research interests are modulation and coding tech-niques, diversity techtech-niques, and cognitive radio.

[15] K Ho-Van, “On the performance of underlay cooperative cognitive< /small>

networks with relay selection under imperfect channel information,” in< /small>

Proc IEEE...

that the ORS in UCCNs gets zero diversity gain in the

presence of imperfect channel information

All above comments can be mathematically interpreted and

mentioned in Section... Chang, P H Lin, and S L Su, “A low-interference relay selection< /small>

for decode-and-forward cooperative network in underlay cognitive radio,”

in Proc IEEE