DSpace at VNU: On the Performance of Opportunistic Relay Selection in Cognitive Radio Networks with Primary User''s Interference and Direct Channel

DSpace at VNU: On the Performance of Opportunistic Relay Selection in Cognitive Radio Networks with Primary User''''s Inter...

On the Performance of Opportunistic Relay Selection

in Cognitive Radio Networks with Primary User’s

Interference and Direct Channel

Khuong Ho-Van1•Lien Pham-Hong2•Son Vo-Que1•

Tra Luu-Thanh1

 Springer Science+Business Media New York 2016

Abstract This paper analyzes outage performance of opportunistic relay selection incognitive radio networks with primary user’s interference and direct channel over inde-pendent non-identically distributed fading channels and under maximum transmit powerconstraint and interference power constraint Exact analysis is firstly proposed and thenextended to asymptotic analysis to have insights into important performance metrics such

as coding gain and diversity order The proposed analysis can also be applied to sponding analysis for opportunistic relay selection in cognitive radio networks with PU’sinterference and without direct channel to highlight the usefulness of direct channel inrelaying communications without any sacrifice of power and bandwidth A multitude ofresults illustrate an achievable full diversity order, a considerable system performancedeterioration due to primary user’s interference but this deterioration can be drasticallyremedied by increasing the number of involved relays, and the superiority of opportunisticrelay selection with direct channel to that without it

corre-Keywords Opportunistic relay selection Cognitive radio  Interference  Direct channel

1 Introduction

Currently, inefficient traditional spectrum allocation by means of fixed primary users(PUs), emergence of several new wireless applications (e.g., video calling, file transferring,high-definition video streaming, and high-speed internet access), and a severe spectrum

& Khuong Ho-Van

khuong.hovan@yahoo.ca

1

Department of Telecommunications Engineering, HoChiMinh City University of Technology, 268

Ly Thuong Kiet Str., District 10, HoChiMinh City, Vietnam

2

Department of Computer and Communication Engineering, HoChiMinh City University of

Education Technology, 1 Vo Van Ngan Str., Thu Duc District, HoChiMinh City, Vietnam

DOI 10.1007/s11277-016-3464-9

under-utilization as reported in an extensive survey on frequency spectrum utilizationcarried out by the Federal Communications Commission induce radio spectrum to becomemore and more scarce [1] Consequently, devising novel technologies to relieve thepressure of the spectrum scarcity is urgent and essential The cognitive radio technology(e.g., [2]) is one among them, which efficiently resolves this problem by allowing sec-ondary users (SUs) to opportunistically utilize the spectrum inherently allotted to PUs aslong as communications of PUs is not damaged.

Communications of PUs is guaranteed at an acceptable degree as long as the ence from SUs is controlled To this end, SUs usually operates in three modes: interweave,overlay, and underlay [3] Due to its distinct feature of low implementation complexity, theunderlay mode has recently gained much interest, e.g., [4 19] and citations therein Thismode properly allocates the transmit power of SUs to control the interference to PUs ineither short-term or long-term manner According to the long-term mechanism, thetransmit power of SUs is allocated to meet the pre-determined outage probability of PUs[4 10] while according to the short-term mechanism, the transmit power of SUs mustsatisfy either interference power constraint [11–13] or both interference power constraintand maximum transmit power constraint [14–19] It is the limitation of transmit power ofSUs in the underlay mode that significantly shortens the transmission coverage of SUs Toovercome this drawback, relaying communications techniques has recently been integratedinto SUs to exploit short-range point-to-point communications for low path-loss [20] Inrelaying communications, communications between the source and the destination can beassisted by multiple relays operated in either amplify-and-forward (AF) or decode-and-forward (DF) manner [21] for high performance but low bandwidth efficiency due to therequirement of orthogonal channels for different relays in order to avoid mutual interfer-ence Therefore, the relay selection in which a single relay among all potential candidates

interfer-is selected interfer-is preferred to optimize system resource utilization, such as power and width, in comparison with multi-relay assisted transmission while remaining the samediversity order [18,22]

band-Several relay selection schemes in cognitive radio networks1 were proposed in[9 14, 16, 18, 19, 33–41] To be more specific, the opportunistic relay selection wasproposed in [9 11,18,33–35] in which the relay with the maximum end-to-end signal-to-noise ratio (SNR) is selected; the reactive relay selection scheme, which chooses the relayamong all potential candidates (i.e., all relays are presumed to correctly recover sourceinformation) with the largest SNR to the destination, was investigated in[12–14,16,34,36]; the Nth best-relay selection and the Lth-worst relay selection wereproposed in [19] and [37], respectively; the relay selection scheme for maximizing secrecycapacity was studied in [38]; the relay selection scheme with the compromise between thegain for SUs and the loss for PUs was suggested in [39]; the partial relay selection, whichsimply selects the relay with the largest SNR from the source, was analyzed in [40,41].However, several assumptions have been imposed on these works for analysis simplicity:(1) independent partially-identical (i.p.i) [9 11,13,18,31, 33,34, 37,39–41] or inde-pendent identical (i.i.) fading distributions [14,16,19,36]; (2) no interference from PUs;(3) no direct channel; (4) un-correlation among received SNRs

Among relay selection schemes, the opportunistic relay selection is theoretically proved

to be optimal (e.g., [18]), and hence, it is interesting to evaluate its information-theoretic

1

This paper focuses on the DF relays in cooperative cognitive networks and hence, relay selection schemes with the AF relays (e.g., [ 23 – 28 ]) or in dual-hop cognitive networks (e.g., [ 29 – 32 ]) are not necessarily surveyed.

performance limit (i.e., outage probability) under practical conditions such as both ference and maximum transmit power constraints, i.n.i.d fading channels, presence ofPU’s interference and direct channel, correlation among Signal-to-Interference plus NoiseRatios (SINRs)2 This is the objective of this paper To the best of our knowledge, noanalysis accounts for all these practical conditions The current work presents the followingcontributions:

inter-• Propose an exact closed-form outage probability expression for the opportunistic relayselection in cognitive radio networks over i.n.i.d Rayleigh fading channels and underboth maximum transmit power and interference power constraints, the presence ofPU’s interference and direct channel, and correlation among received SINRs Theproposed expression is helpful in fast evaluating the system performance without time-consuming simulations

• Extend the proposed exact analysis to asymptotic analysis to obtain importantperformance metrics (e.g., diversity order and coding gain), which proves that theopportunistic relay selection achieves the full diversity order offered by all involvedrelays and the source

• Propose a corresponding analysis for the opportunistic relay selection with PU’sinterference and without direct channel for the convenience of comparing theopportunistic relay selection with and without direct channel as well as emphasizing theimportance of the direct channel in relaying communications It is recalled that nomatter whether the direct channel is utilized for signal combining at the destination, thesystem resource utilization such as power and bandwidth is almost unchanged As such,

it is essential to investigate how much gain the direct channel can contribute toperformance improvement of the opportunistic relay selection

• Provide numerous results to expose useful insights into the system performance such asdiversity order, coding gain, substantial performance enhancement with respect to theincrease in the number of relays, considerable system performance degradation owing

to the PU’s interference, and superiority of cooperative relaying (i.e., relayingcommunications with direct channel) to its dual-hop counterpart (i.e., relayingcommunications without direct channel)

This paper is structured as follows The next section presents the system model underinvestigation Exact and asymptotic analysis for the opportunistic relay selection with/without direct channel is elaborately discussed in Sect.3 Section4 provides numerousresults to corroborate the proposed analysis and illustrates the outage behavior of theopportunistic relay selection in key system parameters Finally, useful conclusions closethe paper in Sect.5

2 System Model

Figure1 demonstrates a system model for the opportunistic relay selection in cognitiveradio networks with PU’s interference and direct channel In the secondary network, thesource Sscommunicates the destination Sdwith the assistance of the selected relay Sbin thegroup of K relays,S ¼ fS1; S2; ; SKg We assume that secondary transmitters operate inthe underlay mode (e.g., [5,15,17,18]), and hence, the mutual interference between the2

As will be shown in the next section, both PU’s interference and direct channel induce received SINRs to

be correlated, making the analysis more complicated but more general and practical.

primary network and the secondary network is available In other words, Ssand Sbinterferecommunications between the primary transmitter Pt and the primary receiver Pr, and Ptalso causes interference to the received signals at relays and Sd It is recalled that theinterference from the primary network to the secondary network was neglected for analysissimplicity (e.g., [6,8,10,12–19,24,31,33,40,42–47] and citations therein) It is theinterference from PUs that makes the performance analysis complicated but general andpractical Additionally, it is apparent that two stages of the opportunistic relay selection inthe secondary network can take place instantaneously with communications of two dif-ferent primary transmitter-receiver pairs Nevertheless, in order to have a compact figure,Fig.1only illustrates one transmitter-receiver pair However, this paper still reflects thisgeneral case by assuming two different primary transmitter-receiver pairs throughout thefollowing analysis (i.e., there are two different channel coefficients from Ptto Sd for twocorresponding stages, namely htd1 and htd2) Towards this end, channel coefficients areshown in Table1.

Wireless channels are assumed to be independent, frequency-flat, and tributed Therefore, the channel coefficient, hpq, between the transmitter p and the receiver

Rayleigh-dis-q can be modelled as a circular symmetric complex Gaussian random variable with zeromean and 1=kpq-variance, i.e., hpq CN ð0; 1=kpqÞ In contrast to existing works in relayselection where i.p.i.3 or i.i.4 fading distributions are assumed for simplicity of perfor-mance analysis, this paper investigates i.n.i.d fading channels, and so, all kpq’s,8fp; qg arenot necessarily equal, making our work more general and practical

Fig 1 System model

3

That means that k pq ’s are partitioned into groups of equal value For instance, k sk ’s, k kd ’s, k kr ’s, k tk ’s with

k 2 R are assumed to be equal in [ 9 11 , 13 , 18 , 31 , 40 – 43 ].

4 That means that k pq ’s, 8fp; qg are equal in [ 14 , 16 , 19 , 33 ].

As demonstrated in Fig.1, the opportunistic relay selection takes place in two stages Inthe stage 1, Ss broadcasts the signal ws with the power Ps (i.e.,Ps¼ Ew sf wj js2g where

EXfxg denotes the expectation operator) while Ptis concurrently transmitting the signal wt1with the power Pt1¼ Ew t1f wj t1j2g The signals from Ss and Ptcause the mutual interfer-ence between the primary network and the secondary network To this effect, the receivedsignals at Sk and Sd, correspondingly, can be modeled as

where wkis the signal transmitted by Skwith the powerPk ¼ Ew kf wj kj2g and interfered bythe signal wt2 transmitted by Pt with the power Pt2¼ Ew t2f wj t2j2g (i.e., two differentprimary transmitters are assumed for two stages to remain the system model general).This paper considers the opportunistic relay selection (e.g., [18,42]), which selects therelay Sbwith the largest SINR over the relaying channel Ss Sb Sd Mathematically, theSINR generated from this relaying channel can be represented as

csbd¼ max

where ckd is computed from (5) as

Table 1 Notations for channel

h sd  CN 0; 1=k ð sd Þ S s and S d in the stage 1

h sk  CN ð0; 1=k sk Þ S s and S k in the stage 1, k 2 R

h sr  CN ð0; 1=k sr Þ S s and P r in the stage 1

h tk  CN ð0; 1=k tk Þ P t and S k in the stage 1, k 2 R

htd1 CN ð0; 1=ktd1Þ P t and S d in the stage 1

h kr  CN ð0; 1=k kr Þ S k and P r in the stage 2, k 2 R

h kd  CN ð0; 1=k kd Þ S k and S d in the stage 2, k 2 R

h td2  CN ð0; 1=k td2 Þ P t and S d in the stage 2

is assumed for low complexity as compared to the maximum ratio combining [48] To thisend, the end-to-end SINR at Sdis expressed as

In the underlay mode, the secondary transmitter Sp must control its transmit power suchthat the interference induced at PUs does not exceed the maximum interference power, I ,that PUs can tolerate, i.e., Pp I =jhprj2 Additionally, each SU is designed with themaximum transmit power, P As such, in order to meet both the interference powerconstraint and the maximum transmit power constraint as well as to maximize the trans-mission coverage, the transmit power of Sp should be set asPp¼ minð I =jhprj2; PÞ.The system model under consideration is more general and practical than existing works(e.g., [18,42]) by accounting for both direct channel and PU’s interference, and i.n.i.d.fading channels These additional factors also create correlation among received SINRs,which was neglected in the analysis of [18,42], and it is this correlation that makes theanalysis of this paper more complicated Specifically, the proposed system model inducesthe following correlations:

• Since csdand cskhave a common termPs¼ minð I =jhsrj2; PÞ, they are correlated Thisleads to the correlation among quantities min cð sk;ckdÞ in (6), and the correlationbetween csdand csbdin (8) It is noted that both [18] and [42] assumed un-correlationamong quantities min cð sk;ckdÞ

• Correlation among min cð sk;ckdÞ in (6) is also caused by the fact that ckd’s in (7) have acommon term htd2 This correlation is apparently present due to the PU’s interference,which is not available in [18,42]

These correlations can be broken down by using the conditional probability concept, which

is very useful for the analysis of the next section

3 Performance Analysis

The derivation of the exact closed-form outage probability expression at Sd for theopportunistic relay selection in cognitive radio networks with PU’s interference and directchannel is firstly proposed in this section, which is then used for asymptotic analysis toexpose important performance metrics such as diversity order and coding gain Since theproposed analysis framework is relatively general, it is straightforwardly extended tocorresponding analysis for the opportunistic relay selection with PU’s interference andwithout direct channel to illustrate the advantage of utilizing the direct channel in relayingcommunications without exhaustive simulations

3.1 Exact Analysis

The outage probability is defined as the probability that ce2eis below a threshold c0, i.e.,

PCC

o ¼ Pr cf e2e c0g where c0¼ 22s 1 with s being the required transmission rate and

Pr Xf g is the probability of the event X Since ce2e contains two common quantities,

x¼ jhsrj2and y¼ hj td2j2, which cause correlation among received SINRs as discussed inSect.2, PCC

o must be evaluated in terms of conditional probabilities, i.e.,

j j 2 e

 Pt1 htd1 j j 2 þN0

ð Þksd c0 Ps

e

 Pt1zþN0

ð Þ ksd c0

Ps fhtd1

j j 2ð Þdzz

¼

Z1 0

e

 Pt1zþN0

Similarly, the j term in (9) can be written as

1CA:

ekkd ðPt2yþN0I  Þc0y kfh

kr

j j 2ð Þdyyk kþ

Zl 0

ekkd ðPt2yþN0I  Þc0y kkkrekkr y kdykþ

Zl 0

s 2 ¼s 1 þ1

   XK

s u ¼s u1 þ1

Yk2A

akþ 1ð ÞKY

k2R

ak; ð19ÞwhereA ¼ R sf ½ ; R s1 ½ ; ; R s2 ½ ug,5to expand the product in (18), one obtains

s 2 ¼s 1 þ1

   XK

s u ¼s u1 þ1

YAGAþ 1ð ÞKYRGR; ð20ÞwhereB ¼ ;; A; Rf g with ; denoting the empty set, and

Theorem 1 The exact closed-form representation ofYB is given by

mkn l; Mð L; lkÞ þ As

Yk2L

ktkPeksk c0P

Pt1kskc0þ ktkP; ð24Þwith As¼ 1  ek sr l being defined in (17) and

Tk

 Ex Td

Yk2B

Tk

By inserting (31) into (30), we see that (30) perfectly matches (23) Consequently, in order

to complete the proof, we should prove that (31) is represented in closed-form as (24).Towards this end, we firstly plug (14) into (31), and then perform some basic manipula-tions to simplify (31) as

ksreksr xYk2L

eML xYk2L

1

xþ lk

dxþ AsYk2L

Finally, using the partial fraction expansion to decompose theQ

k2L xþl1kproduct in (32),one obtains

mk

Z1 l

eML x

xþ lk

dxþ AsYk2L

ktkPeksk c0P

Pt1kskc0þ ktkP; ð33Þwhere mk is defined in (27)

The last integral in (33) are represented in closed-form as (28) by firstly changing theintegral variable and then using the definition of EiðÞ Given (28), (33) matches (24),

Theorem 2 GB can be represented in closed-form as

XB

j jcþ1

j 1 ¼1

XB

vkeCk H BEiðCkHBÞ; ð35Þwith

vk¼ Yj2Dnk

andjBj denoting the cardinality of the set B

Proof Inserting (16) into (22) and after some algebraic manipulations, one obtains

D kYk2B

D kYk2D

k2D yþC1k product in (38), one obtains