1

Improving the Performance of Cell-Edge Users inMISO-NOMA Systems Using TAS and

SWIPT-based Cooperative TransmissionsTri Nhu Do, Student Member, IEEE, Daniel Benevides da Costa, Senior Member, IEEE,

Trung Q. Duong, Senior Member, IEEE, and Beongku An, Member, IEEE.

Abstract—In this paper, we study the performance of acell-edge user in a two-user multiple-input single-output non-orthogonal multiple access (MISO-NOMA) system. Since theoutage performance and fairness data rate of cell-edge usersare essential issues in NOMA systems, we focus on how toresolve such problems. To this end, we propose three cooperativedownlink transmission schemes utilizing hybrid simultaneouswireless information and power transfer (SWIPT) and transmitantenna selection (TAS) protocols. Particularly, in each scheme, acell-center user acts as a relay to assist the cell-edge user and itsrelaying operation is powered by a hybrid time-switching/power-splitting (TS/PS) SWIPT protocol. Additionally, each schemeemploys a different TAS criterion to exploit the spatial diversitygain of a multiple antennas base station. In particular, we derivetight closed-form approximate expressions for the outage proba-bilities (OPs) and the corresponding asymptotic OPs to providesignificant insights into the impact of our proposed schemes onthe system performance. Our numerical results demonstrate theachievable performance improvements of the proposed schemesin comparison to that of the orthogonal multiple access (OMA)and non-cooperative NOMA systems. In addition, the proposedschemes achieve various level of diversity gains accompanyingwith different complexity requirements.

Index Terms—Cooperative relaying transmissions, multiple-input single-output (MISO), non-orthogonal multiple access(NOMA), outage performance, simultaneous wireless informationand power transfer (SWIPT), transmit antenna selection (TAS)

The work of T. N. Do and B. An was supported by the Basic ScienceResearch Program through the National Research Foundation of Korea (NRF)funded by the Ministry of Education (Grant No. 2016R1D1A1B03934898)and by the Leading Human Resource Training Program of RegionalNeo industry Through the National Research Foundation of Korea (NRF)funded by the Ministry of Science, ICT and future planning (Grant No.2016H1D5A1910577). The work of T. Q. Duong was supported in part bythe U.K. Royal Academy of Engineering Research Fellowship under GrantRF1415\14\22 and by the U.K. Engineering and Physical Sciences ResearchCouncil (EPSRC) under Grant EP/P019374/1. The work of D. B. da Costa wassupported by the National Council of Scientic and Technological Development(CNPq) under Grant 304301/2014-0. This paper was presented in part at theIEEE International Conference on Communications, Paris, France, May 2017.

T. N. Do is with the Department of Electronics and Computer Engineeringin Graduate School, Hongik University, Sejong 30016, Republic of Korea(email: dotrinhu@gmail.com).

D. B. da Costa is with the Department of Computer Engineering, Fed-eral University of Ceara, Sobral, CE 62010-560, Brazil (email: danielb-costa@ieee.org).

T. Q. Duong is with the Department of Electronics, Electrical Engineeringand Computer Science, Queen’s University Belfast, Belfast BT7 1NN, U.K.(e-mail: trung.q.duong@qub.ac.uk).

B. An is with the Department of Computer and Information Communi-cations Engineering, Hongik University, Sejong 30016, Republic of Korea(email: beongku@hongik.ac.kr).

I. INTRODUCTION

Non-orthogonal multiple access (NOMA) has been emerg-ing as a promising solution to improving spectral efficiency forthe next generation of wireless communication systems [1]–[4]. The underlying concept of NOMA is that user multiplex-ing is conducted in the power domain [1], which is differentfrom conventional orthogonal multiple access (OMA) tech-niques (e.g., time/frequency/code division multiple access).For example, in a two-user NOMA system, a base station(BS) communicates concurrently with the two users, one ofwhich has a stronger channel condition (which is often locatednear the BS or at the cell-center) and the other has muchweaker channel condition (which is often a cell-edge user). Atthe BS, information signals of the two users are superposedwith different power allocations, where the power allocationcoefficient of the cell-edge user is higher than that of thecell-center user. At the receiver side, the superposed signalis separated using a successive interference cancellation (SIC)technique [1]. As reported in [4], NOMA can achieve a gainover OMA, and improve cell-edge user throughput by 34.2%under a specific setting.

A. Motivation and Related Works

By using NOMA, the spectral efficiency can be significantlyimproved since both cell-center and cell-edge users are sched-uled together and benefit from being assigned more bandwidth[2]. However, recent works in the literature have reportedthat the operation of NOMA raises the user fairness issue ofdata rate between the cell-center and cell-edge users. Indeed,the user throughput fairness is a critical issue as the rate ofthe cell-edge users is often lower than that of the cell-centerusers [5]. Additionally, as reported in [6], the power allocationcoefficient of the cell-center user has to be close to zero if thecell-edge user needs a data rate comparable to that of the cell-center user. Hence, it may harm the quality-of-service (QoS)of the cell-center users since a major part of the power budgetis allocated to cell-edge users, otherwise, it may compromisethe reception reliability of the cell-edge users [7].

Thus, how to not only resolving the user throughput fairnessbut also improving the reception reliability of the cell-edgeuser is an important issue in NOMA context. One possiblesolution to avoid such fairness issue, yet guarantee the per-formance and reliability of the cell-edge user is to use coop-erative relaying transmissions. The authors in [8] proposed a

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cooperative NOMA transmission scheme, in which cell-centerusers (with better channel conditions) exploit prior informationavailable in NOMA system to help improve the receptionreliability of cell-edge users (with poor connections to aBS). The results from [8] also demonstrated that cooperativeNOMA transmissions provide superior performance in termsof outage probability (OP) than conventional OMA and non-cooperative NOMA systems. In [9], the authors showed thatusing cooperative relaying transmissions where the cell-centeruser acts as a relay, the sum-rate of NOMA networks can besignificantly improved. However the performance gap betweencell-center and cell-edge users is still remaining large. In [10],the authors considered a two-user NOMA network, where thebest cell-center user is selected to serve as a relay to helpimprove the outage performance of a selected cell-edge user.

While cooperative relaying transmissions is a sustainablesolution to resolve the mentioned issues in NOMA systems,the raised question is how the cell-center users fairly con-sume their energy since they need to process their own dataand forward the cell-edge users’ data. Simultaneous wirelessinformation and power transfer (SWIPT) is an appropriateanswer since cell-center users can scavenge energy from aBS’s signal and use this harvested energy to power theirrelaying operation. In [11], the authors combined the coop-erative NOMA with SWIPT to propose a new spectral andenergy efficient wireless multiple access protocol, namely,the cooperative SWIPT NOMA protocol. Specifically, theauthors in [11] showed that the use of SWIPT not only isable to self-power the cell-center users but also does notjeopardize the diversity gain of the cell-edge users comparedto the conventional cooperative NOMA. In [12], the authorsinvestigated the performance of SWIPT networks where thedownlink scenario employs two communication protocols, i.e.,time division multiple access (TDMA) and NOMA, while theuplink scenario considers NOMA with time-sharing.

Applications of NOMA to multiple-input single-output(MISO) systems have also been studied in the literature [13],[14]. The authors in [13] investigated the impact of the con-cept of quasi-degradation on MISO-NOMA downlink trans-mission. In addition, considering a two-user MISO-NOMAsystem given a pair of target interference levels, a quality-of-service (QoS) optimization problem was studied in [14]. Itis noteworthy that transmit antenna selection (TAS) has beendemonstrated as a low-complexity and power-efficient commu-nication scheme for the BS with multiple antennas [15], [16].More specifically, TAS schemes can be considered as a goodtradeoff between the diversity gain and the implementationcost [17]. In [18], the authors developed antenna selectionand user scheduling algorithms to maximize the sum-rateof multiple-input multiple-output (MIMO)-NOMA networks,in which different selected antennas sever different pairs ofusers. Recently, in [19], a TAS scheme for NOMA downlinkenergy harvesting (EH) multiple-antenna relaying networkswas studied. Specifically, the authors assumed that direct linksbetween a source and destinations are unavailable; thus, thereis a dedicated EH amplify-and-forward (AF) relay to assistthe communication from the source to the destination whereNOMA is performed at the relay.

B. Contributions

In this paper, we consider a two-user cooperative MISO-NOMA system, where a cell-center user acts as a relay to assistthe communication from a BS to a cell-edge user. Our methodsnot only improve the performance of the cell-edge user but alsoachieve energy efficiency1 for the cell-center user. To this end,we propose three cooperative transmission schemes in which,different TAS criteria are employed at the BS, SWIPT anddecode-and-forward (DF) relaying strategy are employed atthe cell-center user, and selection combining (SC) is employedat the cell-edge user. The main contributions of the paper canbe summarized as follows.• Three proposed schemes, namely Schemes I, II, and III,

employ three different TAS criteria. Specifically, SchemeI aims to achieve an optimal outage performance at thecell-edge user while requires a high complexity TAScriterion. In contrast, Schemes II and III provide sub-optimal outage performance at the cell-edge user whilereduce the complexity of the TAS criteria. In particular,the TAS criterion adopted in Scheme II maximizes theperformance of the direct link from the BS to the cell-edge user; while that in Scheme III tries to achievemaximum amount of harvested energy, which will beused to power the relaying operation, at the cell-centeruser.

• For a comprehensive investigation on SWIPT protocol,we consider a generalized SWIPT architecture, i.e., thehybrid time-switching/power-splitting (TS/PS) EH re-ceiver. We derive tight closed-form approximate expres-sions for the OPs of the cell-edge user and the corre-sponding asymptotic OPs achieved by the three proposedschemes.

• We show that the proposed schemes significantly im-prove the cell-edge outage performance compared tothe conventional OMA and the non-cooperative NOMAsystems. In particular, Scheme I is superior than theothers but requires highest complexity order. Scheme IIIoutperforms Scheme II at low signal-to-noise ratio (SNR)regime and vice versa at high SNR regime. Interestingly,Scheme I and Scheme II achieve the same diversity gain,i.e., K + 1, while that achieved by Scheme III is always2, where K denotes the number of antennas at the BS.

C. Structure

The rest of the paper is arranged as follows. Section II intro-duces the system model and describes in detail the proposedschemes. Section III presents the performance investigationsin terms of the OP for the considered scenarios, and the proofs

1The meaning of energy efficiency considered in this paper can be explainedas follows. In order to assist a cell-edge user, a cell-center user needs to spendits own energy to transmit not-its-own-data, i.e., the message of the cell-edgeuser. To deal with this energy consumption fairness issue at the cell-centeruser, we implement simultaneous information and power transfer (SWIPT) sothat the cell-center user can harvest energy from the source’s signal and thenuses this harvested energy to forward the message of the cell-edge user. Byusing SWIPT, we imply that the energy efficiency has been achieved since thecell-center user does not need to spend its own energy to relay the messageof the cell-edge user.

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of the analytical expressions are provided in the appendixes.Section IV presents the asymptotic analysis of the derivedoutage performance. Section V presents some illustrativenumerical results, based on which insightful discussions areprovided. Monte Carlo simulations are shown to corroboratethe proposed analysis. Finally, Section VI concludes the paper.

II. SYSTEM MODEL

As shown in Fig. 1, we consider a MISO-NOMA down-link transmission where a BS, denoted by S, simultaneouslycommunicates with a cell-center user, named User N, and acell-edge user, called User F, by employing a two-user NOMAscheme. The BS is equipped with K antennas while each useris equipped with single antenna.

Let hiT denote the fading coefficient of a channel from anantenna i, i = 1, . . . ,K to a User T, where T ∈ N,F. As-suming all wireless channels in the network exhibit Rayleighblock flat fading, hiT can be modeled as independent andidentically distributed (i.i.d.) complex Gaussian random vari-ables with zero-mean and variance λST. Additionally, let naTand ncT denote the additive white Gaussian noise (AWGN)at the receiving antenna and the down-converter at UserT, respectively, with zero-mean and variance σ2

aT and σ2cT,

respectively. Thus, the channel gain |hXY|2, where X ∈ i,Nand Y ∈ N,F, is an exponential random variable with proba-bility density function (PDF), f|hXY|2(z) = 1

λXYe− zλXY ,∀z ≥ 0,

otherwise, i.e., z < 0, f|hXY|2(z) = 0, where λXY denotes themean of |hXY|2. Additionally, the average channel gain can bewritten as E[|hXY|2] = L

(dXY/d0)ε [20], where dXY representsthe distance between two nodes (in meters), ε stands for path-loss exponent, d0 denotes the reference distance, and L is theaverage signal power attenuation at d0.

In the proposed network, let User N play the role of ahybrid time-switching/power-splitting (TS/PS) EH relay (formore details related to the time-switching receiver, power-slitting receiver, and hybrid TS/PS receiver, please refer to[21], [22], and references therein). In particular, a block timeT is divided into three sub-blocks. In the first sub-blockwith αT duration time, User N first harvests energy from itsreceived observation, where 0 ≤ α < 1 denotes the fraction ofblock time for energy harvesting. In the second sub-block with(1 − α)T/2 duration time, User N simultaneously utilizes afraction ρ of the received power for energy harvesting and theremaining fraction (1 − ρ) for information decoding, where0 ≤ ρ < 1 denotes the power-splitting ratio. In the thirdsub-block with (1 − α)T/2 duration time, User N employsall harvested energy to power its relaying operation. Fig. 2shows an illustration of the time structure of the hybrid TS/PSSWIPT-based cooperative relaying transmission.

Note that we consider the hybrid TS/PS SWIPT to providea comprehensive investigation and develop a general analyticalframework for SWIPT architecture. Also, the hybrid receiverprovides a flexible choice for system designing. For example,in the case of TS (or PS) is not necessary, α (or ρ) is simplyset to zero. The order of which module, i.e., TS or PS, isperformed first may not be important since their roles are equal[21]. Additionally, by considering TS first, the time structure

Base-station S

:

:

a selected antenna

decodexF thensubtract

decodexN

User N with SIC receiver(acts as an EH relay)

directlydecodexF

User F

√pNxN +

√pFxF

xF

broadcasting signal

relaying signal

Fig. 1. An illustration of a hybrid time-switching/power-splitting (TS/PS)SWIPT-based cooperative relaying transmission with TAS for a two-userMISO-NOMA system.

αT (1− α)T/2 (1− α)T/2

T

1−ρ

ρ

EHusingTS Information

decoding

EH using PS Informationforwardingfrom User Nto User F

Fig. 2. Illustration of a hybrid TS/PS SWIPT-based DF relaying strategy.

as depicted in Fig. 2 is more reasonable since the informationdecoding and relaying processes are consecutive.

According to the time frame of the hybrid TS/PS EH pro-tocol as shown in Fig. 2, the downlink scenario of the MISO-NOMA cooperative relaying transmission is conducted in twophases, namely the energy harvesting and direct informationtransmission phase, which is carried out in the first and secondsub-blocks, and the cooperative relaying transmission phase,which is carried out in the third sub-block. Note that thedurations of the second and third sub-blocks are equal. Inaddition, the BS keeps silent2 while User N transmits to User Fduring the third sub-block, i.e., during the cooperative relayingtransmission phase.

A. The First Phase: Energy Harvesting and Direct Informa-tion Transmission

Suppose that antenna i on the BS has been selected for in-formation transmission. According to the principle of NOMA,the intended transmit messages xN and xF of Users N andF, respectively, are superposed as

√pNxN +

√pFxF and then

broadcasted by the selected antenna at the beginning of the first

2Note that both direct and relaying transmissions are performed on the samefrequency. Thus, if the BS still transmits while User N forwards messagesto User F, the cell-edge user will suffer from co-channel interference (CCI)created by the transmission of the BS. Therefore, in order to avoid such CCI,the direct and relaying transmissions are carried out in two separated sub-blocks. Please note that the use of such two separated sub-blocks, in whichthe BS keeps silent when a relay transmits to a destination, has been well-adopted in the literature, as in [8], [23]

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sub-block time, where pN and pF denote the power allocationcoefficients (PACs) for Users N and F, respectively. Followingthe principle of NOMA, we assume that |hiN|2 > |hiF|2,0 < pN < pF, and pN + pF = 1 [1].

1) At User N: The received observation the antenna of UserN can be written as

yiN =(√

pNPSxN +√pFPSxF

)hiN + naN, (1)

where where hiN ∼ CN(0, λSN), naN ∼ CN(0, σ2aN). Using

the hybrid TS/PS EH protocol, the total harvested energy atUser N associated with antenna i can be expressed as

EiN = ηPS|hiN|2αT + ηρPS|hiN|2(1− α)T/2, (2)

where 0 < η < 1 denotes the energy conversion efficiency,|hiN|2 denotes the channel gain between antenna i and UserN. For information decoding (ID), the received signal at UserN can be written as

yIDiN =√

1− ρ[(√

pNPSxN +√pFPSxF

)hiN + naN

]+ncN,

(3)where ncN ∼ CN(0, σ2

cN).According to the principle of NOMA, the SIC receiver at

User N first decodes xF and then subtracts this componentfrom the received signal to detect its own message, i.e., xN[1]. Thus, the received signal-to-interference-plus-noise ratio(SINR) at User N to decode xF can be expressed as

γxF

iN =(1− ρ)pFPS|hiN|2

(1− ρ)pNPS|hiN|2 + (1− ρ)σ2aN + σ2

cN

, (4)

and the received signal-to-noise ratio (SNR) at User N todecode xN can be written as

γxN

iN =(1− ρ)pNPS|hiN|2(1− ρ)σ2

aN + σ2cN

. (5)

2) At User F: The received observation at User F can beexpressed as3

yiF =(√

pNPSxN +√pFPSxF

)hiF + naF + ncF, (6)

where hiF ∼ CN(0, λSF), naF ∼ CN(0, σ2aF), and ncF ∼

CN(0, σ2cF).

In contrast with User N, User F can directly decode itsinformation signal since User F is allocated with highertransmit power and thus the interference introduced by theinformation signal of User N can be considered as noise [1].Thus, the received SNR at User F to decode xF can be writtenas

γiF =pFPS|hiF|2

pNPS|hiF|2 + σ2aF + σ2

cF

. (7)

B. The Second Phase: Cooperative Relaying TransmissionAssuming that all the energy harvested during the first phase

is employed to power the relaying operation, as in [21], [22],the transmit power of User N in the second phase can beexpressed as

PN =EiN

(1− α)T/2= ηPS|hiN|2

(2α

1− α + ρ

). (8)

3Note that in the first sub-block, User F can perform EH or keep silent,and in the second sub-block, it only performs information decoding.

Considering the DF relaying protocol, the received signalat User F can be written as

yNF =√PNhNFxF + naF + ncF, (9)

where hNF ∼ CN(0, λNF), and xF denotes the re-encodedversion of xF.

From (8) and (9), the received SNR at User F to detect xFtransmitted by User N can be written as

γNF =ηPS|hiN|2|hNF|2

(2α

1−α + ρ)

σ2aF + σ2

cF

. (10)

Finally, User F combines two signals, i.e., the direct signalfrom the BS and the relaying signal from User N by employinga selection combining (SC) technique. Thus, the achievableSNR of the combination of two received signals at User Fcan be expressed as

γSCF = maxγiF, γNF. (11)

C. The Proposed Transmit Antenna Selection (TAS) Criteria

The proposed TAS schemes are conducted before datatransmission through the signaling and channel state infor-mation (CSI) estimation/calculation system. We assume thatthe required CSI of each scheme is available [8], [11]. Let i∗

denote the selected antenna, the three proposed TAS schemesare described as follows.

1) The TAS Criterion Adopted in Scheme I: It can beobserved that the cooperative relaying operation depends onwhether xF can be decoded at User N or not. Thus, the end-to-end SNR at User F can be written as

γe2eF = minγxF

iN , γSCF . (12)

The instantaneous transmission rate achieved by User F asso-ciating with antenna i can be expressed as

RiF =1− α

2log2(1 + γe2eF ). (13)

The TAS criterion adopted in Scheme I aims to select anantenna that maximizes the instantaneous transmission rateof User F. Mathematically, the selection Scheme I can beexpressed as

i∗ =1− α

2log2(1 + γe2eF )

= arg max1≤i≤K

minγxF

iN ,maxγiF, γNF. (14)

2) The TAS Criterion Adopted in Scheme II: As can beobserved, with Scheme I, User F can achieve optimal outageperformance. However, Scheme I requires a high complex-ity operation, i.e., CSI of three kinds of channels, namelyS → N,S → F, and N → F channels is needed. In orderto reduce the complexity of Scheme I but also achieve acomparable outage performance, we propose Scheme II byfocusing on the performance of User F during the first phase,i.e., the broadcasting phase.

Note that, during the broadcasting phase, the message xF ofUser F needs to be decoded not only at User F but also at theSIC receiver of User N. Thus, the instantaneous transmission

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R(1)iF = min

1− α

2log2(1 + γxF

iN),1− α

2log2(1 + γiF)

=

1− α2

log2

(1 + min

(1− ρ)pFPS|hiN|2

(1− ρ)pNPS|hiN|2 + (1− ρ)σ2aN + σ2

cN

,pFPS|hiF|2

pNPS|hiF|2 + σ2aF + σ2

cF

)(15)

rate achieved by User F associating with antenna i can beexpressed as on the top of the next page, where the superscript(1) indicates the first phase. Since User N is located nearer theBS than User F, thus, |hiN|2 |hiF|2. Also, the conversionnoise power is significantly less than the received power.Hence, RiF can be written as

R(1)iF =

1− α2

log2

(1 +

pFPS|hiF|2pNPS|hiF|2 + σ2

aF + σ2cF

). (16)

The TAS criterion adopted in Scheme II aims to select anantenna that maximizes R(1)

iF , but offers relatively low com-putational complexity, which can be mathematically expressedas

i∗ = arg max1≤i≤K

1− α2

log2

(1 +

pFPS|hiF|2pNPS|hiF|2 + σ2

aF + σ2cF

)= arg max

1≤i≤K

pFPS|hiF|2pNPS|hiF|2 + σ2

aF + σ2cF

= arg max1≤i≤K

|hiF|2. (17)

3) The TAS Criterion Adopted in Scheme III: We nowturn our attention into the amount of harvested energy at thecell-center user, i.e., EiN in (2). Note that all the harvestedenergy will be used by User N to transmit xF to User F. TheTAS criterion adopted in Scheme III selects an antenna thatprovides a maximum instantaneous harvested energy at UserN. Mathematically, the selection Scheme III can be expressedas

i∗ = arg max1≤i≤K

ηPS|hiN|2αT + ηρPS|hiN|2(1− α)T/2

= arg max

1≤i≤K|hiN|2. (18)

The performance investigation of the three proposedschemes in terms of OP and asymptotic OP will be presentedin the next section.

III. OUTAGE PERFORMANCE ANALYSIS

The OP of a user can be defined as the probability that theinstantaneous data rate of the user falls below a predefinedtarget data rate [24].

Let Rth,N and Rth,F (bits/s/Hz) denote the target datarates of Users N and F, respectively; a1 , (1−ρ)pFPS

(1−ρ)σ2aN+σ2

cN,

a2 , (1−ρ)pNPS

(1−ρ)σ2aN+σ2

cN, b1 , pFPS

σ2aF+σ2

cF, b2 , pNPS

σ2aF+σ2

cF, and c ,

ηPS

(2α

1−α + ρ)/(σ2

aF + σ2cF), µa , γ2

a1−a2γ2 , µb , γ2b1−b2γ2 ,

and θ , pFpN

. Function Ω(µ, χ, ξ) is defined in (21). For thesake of notational convenience, let Xi , |hiN|2, Y , |hNF|2,and Zi , |hiF|2.

A. Outage Performance Analysis of Scheme I

The OP of User F in Scheme I can be expressed as

P(I)out,F = Pr(RiF < Rth,F)

= Pr

(max

1≤i≤KminγxF

iN ,maxγiF, γNF < γ2

)= Pr

(max

1≤i≤Kmin

a1Xi

a2Xi + 1,

max

b1Zi

b2Zi + 1, cXiY

< γ2

), (19)

where γ2 , 22Rth,F/(1−α) − 1 denotes the SNR threshold forcorrectly decoding the message xF.

Theorem 1: The closed-form approximate expression for theOP of User F in Scheme I can be attained as

P(I)out,F =

K=i+j+k∑i,j,k

(K

i, j, k

)(1− e−

µaλSN− µbλSF

)i(−1)j

× e−kµbλSF

1

λNF

[√4(j + k)λNFγ2

λSNcK1

(√4(j + k)γ2

λSNλNFc

)− Ω

(γ2

cµa,

1

λNF,

(j + k)γ2

λSNc

)]+(

1− e−µaλSN

)Ke− γ2λNFcµa , (20)

where

Ω(µ, χ, ξ)

=e−µχ

χ− ξΓ(0, µχ) +

∞∑u=2

(−1)uξu

u!

×[e−µχ

u−1∑v=1

(v − 1)!(−χ)u−v−1

(u− 1)!µv− (−χ)u−1

(u− 1)!Ei(−µχ)

],

(21)

where Γ(·, ·) is the upper incomplete Gamma function [25,Eq. (8.350.2)], Ei(·) is the exponential integral function [25,Eq. (8.211.1)].

Proof: See Appendix A.

B. Outage Performance Analysis of Scheme II

The achievable end-to-end transmission rate at User F canbe expressed in another form as [26]

Re2eiF =

1− α

2log2(1 + γiF), if RxF

iN < Rth,F,

1− α2

log2(1 + γSCF ), if RxF

iN ≥ Rth,F,(22)

where RxF

iN = 1−α2 log2(1 + γxF

iN). The factor 1−α2 appears

because the direct information transmission or the cooperative

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relaying transmission is conducted during (1−α)T2 duration

time [21], [26].Theorem 2: The closed-form approximate expression for the

OP of User F in Scheme II can be written as

P(II)out,F =

K∑k=0

(K

k

)(−1)ke

− kµbλSF

[1− 1

λSNΩ

(µa,

1

λSN,γ2

λNFc

)],

(23)

if γ2 < θ, o.w., P (II)out,F = 1.

Proof: See Appendix B.

C. Outage Performance Analysis of Scheme III

Theorem 3: The closed-form approximate expression for theOP of User F in Scheme III can be written as

P(III)out,F

=(

1− e−µbλSF

)[ K∑k=0

(K

k

)(−1)ke

− kµaλSN

+

K∑l=1

(K

l

)(−1)l+1

(e− lµaλSN − l

λSNΩ

(µa,

l

λSN,γ2

λNFc

))],

(24)

if γ2 < θ, o.w., P (III)out,F = 1.

Proof: By following the similar calculation steps as pre-sented in Appendix B, P (III)

out,F can be obtained. This completesthe proof of Theorem 3.

IV. ASYMPTOTIC OUTAGE PERFORMANCE ANALYSIS

For the sake of notational convenience, let γN =PS

(1−ρ)σ2aN+σ2

cN, and γF = PS

σ2aF+σ2

cF. It can be seen that γN ≈ γF

when PS → ∞, therefore, let γ represent both γN and γFat the high SNR regime. Thus, µa = µa

γ , µb = µbγ , and

c = γc, where µa = γ2(1−ρ)(pF−pNγ2) , µb = γ2

pF−pNγ2 , and

c = η(

2α1−α + ρ

), respectively.

A. The Asymptotic OP of User F in Scheme I

Using the fact that e−a/x ≈ 1 − a/x when x → ∞, theasymptotic OP of User F in Scheme I, P (I)

asym,F, can be writtenas

P(I)asym,F =

∫ tcµa

0

[1

γ

(µaλSN

+µbλSF

)− 1

γ2

µaµbλSNλSF

− 1

γ

µbλSF

e− tλSNcy

]K1

λYe− yλY dy

+1

γK

(µaλSN

)Ke− γ2λNF cµa . (25)

Relying on trinomial coefficient, the integral in P(I)asym,F,

named I(I)asym,F, can be further expressed as

I(I)asym,F =

K=i+j+k∑i,j,k

(K

i, j, k

)(−1)j+k

1

γi+2j+k

×(µaλSN

+µbλSF

)i(µaλSN

)j(µbλSF

)j+k× 1

λNF

∫ γ2cµa

0

(e− yλNF − e−

kγ2λSNcy

)dy. (26)

Using similar calculation steps as done in Appendix A, I(I)asym,F

in (26) can be further expressed as in (27), which presentedon the top of the next page. Relying on the approximationxK1(x) ≈ 1 + x2

2 ln x2 [11], and then substituting I(I)

asym,F into(27), P (I)

asym,F can be attained as in (28), which presented onthe top of the next page.

B. The Asymptotic OP of User F in Scheme II

Using the fact that e−a/x ≈ 1− a/x when x→∞, Λ1A in(57) and Λ1B in (60) can be asymptotically approximated as

Λasym1A =

1

γ

µaλSN

, Λasym1B =

1

γK

(µbλSF

)K. (29)

By applying the following identities to (66), i.e., Γ(0, x) =−Ei(−x) [25, 8.359.1] and Ei(−x) ≈ CE + ln(x) [25, Eq.(8.214.1)], where CE denotes the Euler’s constant [25, Eq.(8.367.1)], Λ2B can be asymptotically approximated by

Λasym2B = −

(γ2

λSNλNFcγ+

γ22

2λ2SNλ

2NFc

2γ2

)×[CE + ln

(µaλSNγ

)]γ2

2

2λSNλ2NFc

2µaγ

(1− µa

λSNγ

).

(30)

Hence, by combining (29) and (30), the asymptotic OP of UserF can be obtained as

P(II)asym,F = Λasym

1B (Λasym1A + Λasym

2B ) . (31)

C. The Asymptotic OP of User F in Scheme III

Following the similar derivation steps as done in SubsectionIV-B, the asymptotic OP of User F can be expressed as in (32),which presented on the top of the next page.

V. NUMERICAL RESULTS AND DISCUSSIONS

In this section, representative numerical results are pre-sented to illustrate the outage performance of the threeproposed schemes of the system under study. Additionally,insightful comparisons related to the achievable diversity gainare provided.

7

I(I)asym,F =

K=i+j+k∑i,j,k

(K

i, j, k

)(−1)j+k

1

γi+2j+k

(µaλSN

+µbλSF

)i(µaλSN

)j(µbλSF

)j+k

×[√

4kγ2

λSNλNFcγK1

(√4kγ2

λSNλNFcγ

)− e−

γ2λNF cµa +

kγ2

λSNλNFcγΓ

(0,

γ2

λNFcµa

)− k2γ2

2

2λNFλ2SNc

2γ2

(cµaγ2

e− γ2λNF cµa +

1

λNFEi

(− γ2

λNFcµa

))](27)

P(I)asym,F =

K=i+j+k∑i,j,k

(K

i, j, k

)(−1)j+k

1

γi+2j+k

(µaλSN

+µbλSF

)i(µaλSN

)j(µbλSF

)j+k

×[1 +

2kγ2

λSNλNFcγln

(√kγ2

λSNλNFcγ

)− e−

γ2λNF cµa +

kγ2

λSNλNFcγΓ

(0,

γ2

λNFcµa

)− k2γ2

2

2λNFλ2SNc

2γ2

(cµaγ2

e− γ2λNF cµa +

1

λNFEi

(− γ2

λNFcµa

))]+

1

γK

(µaλSN

)Ke− γ2λNF cµa (28)

P(III)asym,F =

1

γ

µbλSF

[1

γK

(µaλSN

)K+

K∑k=1

(K

k

)(−1)k+1k

[γ2

λSNλNFcγ

(− CE − ln

(kµaλSNγ

))− γ2

2

2λSNλ2NFc

2γ2

[(1− kµa

λSNγ

)γ

µa+

k

λSN

(CE + ln

(kµaλSNγ

))]]](32)

A. Determination of the Power Allocation Coefficients andSimulation Settings

In order to select the appropriate PACs for our plots, letus briefly introduce how the PACs have been determined inthe literature. Indeed, there are few methods to determine thePACs in NOMA, such as fixed PACs, where the coefficientscan be randomly chosen provided that the principle of NOMAis satisfied, i.e., pN < pF and pN+pF = 1 as in [10], [27], [28],or dynamic PACs, where the coefficients can be determinedbased on the QoS of users, e.g., the target data rate of users[29] or beamforming design [23].

In this paper, we dynamically determine the power alloca-tion coefficients, based on the target data rates of both thecell-center and cell-edge users, as recently done in [29]. Fora fair comparison with the non-cooperative NOMA system,the PACs are determined based on the QoS of the cell-centeruser, i.e., User N, before it performs energy harvesting4. Thereason of choosing User N is that the SIC process at the cell-center user involves decoding both xF and xN. For the sakeof notational convenience, let γN = PS

σ2aN+σ2

cN. Thus, the SINR

at User N to decode xF in (4) can be now re-expressed as

γxF

iN =pFγN|hiN|2

pNγN|hiN|2 + 1, (33)

4In [29], only power-splitting was considered so that one could determinePACs independently with ρ. On the other hand, in this paper, we consider ahybrid TS/PS architecture, therefore, it is hard to determine pN, pF indepen-dently with both α and ρ. For example, we cannot eliminate α from the term22Rth,F/(1−α).

and the SNR at User N to decode xN in (5) can be rewrittenas

γxN

iN = pNγN|hiN|2. (34)

The achievable rates for User N to detect the message ofUser F, xF, can be expressed as

RxF

N =1

2log2 (1 + γxF

iN) , (35)

and achievable rates for User N to detect its own message, xN,can be expressed as

RxN

N =1

2log2 (1 + γxN

iN ) . (36)

The factor 12 appears in (35) and (36) because α is assumed

to be zero. In order to ensure that User N correctly decodesfirst xF and then xN, we impose that RxF

N = Rth,F and RxN

N =Rth,N, where Rth,F and Rth,N (bits/s/Hz) denote the targetdata for decoding xF and xN, respectively. Thus, we have

1

2log2

(1 +

pFγN|hiN|2pNγN|hiN|2 + 1

)= Rth,F,

1

2log2

(1 + pNγN|hiN|2

)= Rth,N,

pF + pN = 1,

(37)

and after some manipulations, (37) can be rewritten as (1− pN22Rth,F

)γN|hiN|2 = 22Rth,F − 1,

pNγN|hiN|2 = 22Rth,N − 1,(38)

8

and after some algebraic steps, the power allocation coeffi-cients of Users N and F can be determined as pN =

22Rth,N − 1

22Rth,N+2Rth,F − 1,

pF = 1− pN.(39)

In the simulation setting, we assume that the source, UsersN and F form a line network, where User N is located on thethe direct line between the BS and User F. It is noteworthythat this setting has been a well-known assumption not onlyin conventional cooperative networks [16], [30] but also incooperative NOMA networks [9], [28]. There are few reasonsof using this setting. For instance, it can be used to discussthe influence of User N’s position on the performance of thetwo-hop cooperative NOMA systems, where User N is movingalong the S→ F line as presented in Fig. 6.

In addition, we assume that the path loss exponent equals3 for all wireless channels, this assumption has been widelyadopted in the literature [31]–[33]. It is noteworthy that thepath loss exponent for urban microcells varies typically from2.7 to 3.5 [34].

Unless otherwise stated, the simulation parameters are pre-sented in Table. I.

TABLE ISIMULATION PARAMETERS

Parameters Value

Bandwidth 1 MHzAntenna noise power density, naN = naF −100 dBm/HzInformation processing noise power density, ncN = ncF −90 dBm/HzTarget data rates of Users N and F, Rth,N = Rth,F 0.1 bits/s/HzThe distance between S and User F, dSF 10 metersThe distance between S and User N, dSN 3 metersThe distance between User N and User F, dNF dSF − dSNPath-loss exponent, ε 3Path-loss at reference distance, (L at d0 = 1 m) −30 dBEnergy conversion efficiency of the EH process, η 0.7

B. Outage Performance

For demonstration purpose, Fig. 3 presents the OP ofScheme I at User F as a function of the fraction of time for EH,α, and the power-splitting ratio, ρ. As can be observed, theresults generated using the obtained closed-form approximateexpressions for the OP are well corroborated with the simu-lation results, which validates our developed analysis. Sincesimilar observations are obtained for Schemes II and III, theirnumerical examples are omitted to present here. The impactsof α and ρ on the OPs will be elaborated next.

In Figs. 4a and 4b, we plot the OPs of three schemes asfunctions of α and ρ, respectively. As can be seen, α hasstronger impact than ρ on the OPs of the proposed schemes.Indeed, for a given value of ρ, OP significantly changes withdifferent values of α. In contrast, for a given value of ρ, suchchange of OP is not much considerable. It can be explainedthat from the standpoint of the performance of the cell-edgeuser, fixing ρ and varying α affects the performance of both thedirect and relaying transmissions, while fixing α and varying ρjust affects only the performance of the relaying transmission.

Fig. 3. Outage probability of User F in Scheme I as a function of the fractionof time for EH, α, and the power splitting ratio, ρ, with K = 3, PS = 30dBm.

0.1 0.3 0.5 0.7 0.9

Fraction of time for EH,

10-4

10-3

10-2

10-1

Ou

tag

e P

rob

ab

ility

Scheme I (ana.)

Scheme II (ana.)

Scheme III (ana.)

(a)

0.1 0.3 0.5 0.7 0.9

Power-splitting ratio,

10-4

10-3

10-2

10-1

Ou

tag

e P

rob

ab

ility

Scheme I (ana.)

Scheme II (ana.)

Scheme III (ana.)

(b)

Fig. 4. Outage probability of User F as a function of (a) the fraction of timefor EH, α, with ρ = 0 and (b) the power-splitting ratio, ρ, with α = 0, wherein both (a) and (b) we set K = 3 and PS = 30 dBm.

Fig. 5 presents a comparison of the OPs of the three pro-posed schemes while the performance of the random antenna

9

10 20 30 40

SNR (dBm)

10-6

10-5

10-4

10-3

10-2

10-1

100

Ou

tag

e P

rob

ab

ility

Random selection (sim.)

Scheme I (sim.)

Scheme II (sim.)

Scheme III (sim.)

Analysis

Fig. 5. Comparison of the outage probability of User F in Schemes I, II, III,and the random antenna selection scheme with K = 3.

1 2 3 4 5 6 7 8 9

dSN

(meters)

10-5

10-4

10-3

10-2

10-1

100

Ou

tag

e P

rob

ab

ility

Random selection (sim.)

Scheme I (sim.)

Scheme II (sim.)

Scheme III (sim.)

Fig. 6. Outage probability of User F as a function of the distance betweenS and User N, with K = 3, α = 0.3, ρ = 0.3, and PS = 30 (dBm).

Fig. 7. Cell-edge outage performance comparison of between hybrid SWIPT-based cooperative NOMA, conventional OMA, and non-cooperative NOMAsystems, where the random antenna selection is performed with K = 3 andPS = 30 dBm.

selection is used as a benchmark. We can see that with the

user of the proposed TAS criteria, Schemes I, II, III achievebetter outage performance compared to that of the randomantenna selection. Among the proposed schemes, Scheme Iindeed provides the best outage performance. Additionally,Fig. 5 shows that Scheme II outperforms Criterion III at thehigh SNR regime, and vice-versa at the low SNR regime.

Next, the distance between the BS and User N, dSN, isdiscussed more deeply. Fig. 6 plots OP of User F in Schemes I,II, III, and the random antenna selection scheme as a functionof dSN. As can be observed, the OP of the TAS schemesincreases as dSN increases. One possible reason is that whenUser N is located more far away from the BS, the amount ofharvested energy becomes smaller, and thus, the less powerfor User N to relay the message of User F. In addition, oneof the principles of NOMA is to make use of the differencein the channel conditions of the channels from the BS to thecell-center and cell-edge users, so that the SIC receiver at thecell-center user is able to work better. However, when UserN is closer to User F, their channel conditions become moresimilar, which leads to the decreasing of the performance ofNOMA system.

In Fig. 7, we provide a performance comparison between thehybrid SWIPT-based cooperative MISO-NOMA, conventionalMISO-OMA, and non-cooperative MISO-NOMA systems. Fora fair comparison, the random antenna selection is considered.In the OMA system, the block time T is divided into equalsub-blocks, each one is used to serve one user. In the non-cooperative NOMA system, the source simultaneously servesthe two users in the whole block time. As can be seen fromFig. 7, conventional NOMA actually improves the cell-edgeperformance compared to that of the conventional OMA. Con-sidering the hybrid SWIPT-based cooperative NOMA system,it is obvious that the cell-edge performance becomes worseas α and/or ρ are set too high, i.e., near 1. Since in suchscenario, the users do not have sufficient received power tocorrectly decoded their information.

C. Diversity Gain

We now turn our attention to the achievable diversity gain ofthe proposed schemes. The physical meaning of the diversitygain can be explained as follows. In wireless communications,diversity technique uses the fact that independent users havea low probability of experiencing deep effects of fadingsimultaneously [24]. Diversity gain is used as a performancemetric of a diversity technique. The diversity gain, D, ismathematically formulated as [35]

D = − limγ→∞

logPe(γ)

log γ, (40)

where γ denotes SNR and Pe denotes bit error rate asa function of SNR. When the outage probability Pout isconsidered instead of the bit error rate, the diversity gain, D,can be written as [11]

D = − limγ→∞

logPout(γ)

log γ. (41)

Consequently, as the slope of an OP curve of a scheme isparallel to the curve that is proportional to 1

γDat high SNR

10

regime, we can conclude that the diversity gain achieved bythat scheme is D [28].

Fig. 8 shows the diversity gain achieved by three proposedschemes. Recall that diversity behavior can be indicated by theslope at the high SNR regime of the outage performance curve[8], [28]. As shown in Fig. 8, the slope of the performancecurves of User F in Schemes I and II are parallel to the linesfor 1

γK+1 = 1γ4 , while that of User F in Scheme III is parallel

to the line for 1γ2 .

Similar trends are observed in Fig. 9, where we plot theOPs of User F with different numbers of antennas. As canbe seen, for a given number of antenna, the slope of theperformance curves of Schemes I and II are parallel, whichconfirms that the diversity gains achieved by Schemes I andII are the same. In addition, by substituting the asymptoticOP of Scheme II into (41), and relying on the fact thatlimx→∞

log[c1/x

K+2 + (c2/xK+1) ln

(c3x

)]/ log x = −K − 1,

where c1, c2, c3 are constants, it can be concluded that thediversity gain achieved by Scheme II at User F is K + 1.5

On the other hand, the slopes of the performance curves ofScheme III are always parallel to each other irrespective ofthe number of antennas, K. Thus, the diversity gain achievedby Scheme III does not increase as K increases. By carryingout similar diversity analysis as done with Scheme II, we canconclude that the diversity gain achieved by scheme III at thecell-edge user is always 2.

Finally, in order to discuss the complexity of the proposedschemes, we introduce a definition for the complexity order.Specifically, the complexity order of a scheme will be definedin terms of the number of channels that require CSI estimation.Its unit concerns to the number of channels. Note that the BSconducts CSI estimation of the considered channels in orderto select an appropriate antenna before transmitting data.

TABLE IIACHIEVABLE DIVERSITY GAINS AND COMPLEXITY ORDER OF THE

PROPOSED SCHEMES

Schemes Achievable diversity gain Complexity order

Scheme I K + 1 2K + 1Scheme II K + 1 KScheme III 2 K

The achievable diversity gain and complexity order of eachscheme are summarized in Table. II. As can be observed, theTAS criterion in Scheme I requires the highest complexityorder, i.e., 2K + 1. While Schemes II and III needs thesame number of CSI estimation and is indeed lower than thatrequired by Scheme I, i.e., K.

VI. CONCLUSIONS

In this paper, aiming to improve the performance of cell-edge users in two-user MISO-NOMA cooperative downlinktransmissions, we have proposed three cooperative schemeswhere the SWIPT is employed at the cell-center user to power

5Note that this analytical proof cannot be applied for Scheme I since whensubstituting the asymptotic OP of Scheme I into (41), the limit becomesintricate and cannot be obtained.

20 30 40 50

SNR (dBm)

10-10

10-8

10-6

10-4

10-2

100

Ou

tag

e P

rob

ab

ility

Scheme I (ana.)

Scheme II (ana.)

Scheme III (ana.)

Asymptotic

Fig. 8. Illustrations of the diversity gain achieved by the proposed schemeswith K = 3, α = 0.3, and ρ = 0.3.

20 30 40 50

SNR (dBm)

10-20

10-15

10-10

10-5

100

Ou

tag

e P

rob

ab

ility

Scheme I (ana.)

Scheme II (ana.)

Scheme III (ana.)

Dashed lines are for the case of K = 3

Solid lines are for the case of K = 6

Fig. 9. Illustrations of the diversity gain achieved by the proposed schemesunder different numbers of antennas with α = 0.3 and ρ = 0.3.

the DF relaying operation. Additionally, each scheme adoptsdifferent TAS criterion to provide flexible choices for systemdesigning. Considering the hybrid TS/PS SWIPT architec-ture, we have investigated the performance of the cell-edgeuser in terms of outage probability and diversity gain. Morespecifically, the tight closed-form approximate expressions forthe OPs and the corresponding asymptotic OPs achieved bythe three schemes have been derived and validated throughMonte-Carlo simulations. Numerical results have showed thatthe proposed schemes provide essential cell-edge performanceimprovements compared to the conventional OMA and non-cooperative NOMA systems. Particularly, Scheme I obtainsthe optimal outage performance with the diversity gain ofK+1, where K is the number of antennas. Scheme II achieveslower performance compared to that of Scheme I but the samediversity gain. Scheme III outperforms Scheme II at low SNRregime and vice versa at high SNR regime while it gives thelowest diversity gain, i.e., always 2.

11

APPENDIX APROOF OF THEOREM 1

From (19), the OP of User F in Scheme I can be written as

P(I)out,F = Pr

(max

1≤i≤Kmin

a1Xi

a2Xi + 1,

max

b1Zi

b2Zi + 1, cXiY

< γ2

). (42)

As we can observe, the events of the probability in (42) arenot mutually exclusive because they include the same randomvariable Y . Therefore, conditioning on Y = y, P (I)

out,F can bere-expressed as

P(I)out,F =

∫ ∞0

Pr

(max

1≤i≤Kmin

a1Xi

a2Xi + 1,

max

b1Zi

b2Zi + 1, cXiy

< γ2

)fY (y)dy. (43)

Next, conditioning on Xi = x, P (I)out,F can be further expressed

as

P(I)out,F =

∫ ∞0

K∏i=1

∫ ∞0

Pr

(min

a1x

a2x+ 1,

max

b1Zi

b2Zi + 1, cxy

< γ2

)fX(x)dxfY (y)dy

=

∫ ∞0

K∏i=1

[1−

∫ ∞0

Pr

(a1x

a2x+ 1≥ γ2

)× Pr

(max

b1Zi

b2Zi + 1, cxy

≥ γ2

)fX(x)dx

]× fY (y)dy. (44)

As can be observed, if γ2 ≥ θ then P (I)out,F = 1. For the case

γ2 < θ, let µa = γ2a1−a2γ2 , P (I)

out,F can be expressed as

P(I)out,F

=

∫ ∞0

K∏i=1

[1−

∫ ∞µa

[1

− Pr

(max

b1Zi

b2Zi + 1, cxy

< γ2

)]fX(x)dx

]fY (y)dy

=

∫ ∞0

K∏i=1

[1− e−

µaλX +

∫ ∞µa

Pr

(b1Zi

b2Zi + 1< γ2

)× Pr

(x <

γ2

cy

)fx(x)dx

]fY (y)dy. (45)

Since µa ≤ x < γ2cy , we first consider the case y < γ2

cµa, let

µb = γ2b1−b2γ2 , and after some algebraic steps, P (I)

out,F can be

written as

P(I)out,F = Ξ1 ,

∫ γ2cµa

0

K∏i=1

[1− e−

µaλX

+

∫ γ2cy

µa

(1− e−

µbλZ

) 1

λXe− xλX dx

]fY (y)dy

=

∫ γ2cµa

0

[1− e−

µaλX +

(1− e−

µbλZ

)×(e− µaλX − e−

γ2λXcy

)]K 1

λYe− yλY dy. (46)

In order to further simplify the above integral, we relyon the trinomial coefficient, i.e., (α + β + γ)K =∑K=i+j+ki,j,k

(Ki,j,k

)αiβjγk [36]. Thus, Ξ1 can be expressed as

Ξ1 =

K=i+j+k∑i,j,k

(K

i, j, k

)(1− e−

µaλX− µbλZ

)i(−1)je

− kµbλZ

× 1

λY

∫ tcµa

0

e− yλY− (j+k)γ2

λXcy dy︸ ︷︷ ︸I1

. (47)

The integral I1 in (47) can be expressed as

I1 =

∫ ∞0

e− yλY− (j+k)γ2

λXcy dy −∫ ∞γ2cµa

e− yλY− (j+k)γ2

λXcy dy. (48)

By making use of the relationship∫∞

0e−χx−

ξ4x =√

ξχK1(

√ξχ) [25, Eq. (3.324.1)], where K1(·) is the first-

order modified Bessel function of the second kind [25, Eq.(8.407.1)], and relying on a result in our previous work [37],i.e.

∫∞µe−χx−

ξx dx ≈ Ω(µ, χ, ξ), where Ω(µ, χ, ξ) is defined

in (21), I1 can be obtained as

I1 =

√4ξ

χK1(

√4ξχ)− Ω

(γ2

cµa,

1

λSN,

(j + k)γ2

λXc

). (49)

Next, considering the case y ≥ γ2cµa

, P (I)out,F can be obtained

as

P(I)out,F = Ξ2 =

∫ ∞γ2cµa

K∏i=1

(1− e−

µaλX

)fY (y)dy

=

∫ ∞γ2cµa

(1− e−

µaλX

)K 1

λYe− yλY

=(

1− e−µaλX

)Ke− γ2λY cµa . (50)

Combining Ξ1 and Ξ2, the OP of User F in Scheme I canbe obtained as presented in (20). This completes the proof ofTheorem 1.

APPENDIX BPROOF OF THEOREM 2

From (22), the OP of User F can be expressed as

P(II)out,F = Pr(γxF

i∗N < γ2, γi∗F < γ2)︸ ︷︷ ︸Λ1

+ Pr(γxF

i∗N ≥ γ2,maxγi∗F, γNF < γ2)︸ ︷︷ ︸Λ2

, (51)

12

where the superscript (II) represents a notation for Scheme II.From (4), (7) and (17), Λ1 in (51) can be rewritten as

Λ1 = Pr

(a1|hi∗N|2

a2|hi∗N|2 + 1< γ2,

b1|hi∗F|2b2|hi∗F|2 + 1

< γ2

), (52)

Since Users N and F are assumed to be independent, Λ1 canbe further expressed as

Λ1 = Pr

(|hi∗N|2<

γ2

a1 − a2γ2

)︸ ︷︷ ︸

Λ1A

Pr

(|hi∗F|2<

γ2

b1 − b2γ2

)︸ ︷︷ ︸

Λ1B

,

(53)if γ2 < θ, otherwise, Λ1 = 1. It can be explained that whena1 − a2γ2 ≤ 0 and b1 − b2γ2 ≤ 0, respectively, which turnsout γ2 ≥ pF

pN, Λ1A and Λ1B always equal to 1.

In Scheme II, the antenna that has the largest channel gainof the channel from the BS to User F will be selected. Inthis case, the statistical characteristics of the channel from theselected antenna at the BS to User N can be determined asfollows. Using the total probability theory [38], the cumulativedistribution function (CDF) of |hi∗N|2 can be expressed as

F|hi∗N|2(x) = Pr(|hi∗N|2 < x)

=

K∑i=1

Pr(i∗ = i) Pr(|hiN|2 < x), (54)

where Pr(i∗ = i) in this case, i.e., Scheme II, can be obtainedas

Pr(i∗ = i) = Pr

( K⋂j=1,j 6=i

|hjF|2 < |hiF|2)

=

∫ ∞0

K∏j=1,j 6=i

[1− Pr(|hjF|2 < x)

]f|hiF|2(x)dx

= 1/K. (55)

Consequently, the CDF and the probability density function(PDF) of |hi∗N|2 can be, respectively, written by

F|hi∗N|2(x) = 1− e−xλSN , f|hi∗N|2(x) =

1

λSNe− xλSN . (56)

Thus, Λ1A can be obtained as

Λ1A = 1− e−γ2

λSN(a1−a2γ2) , (57)

if γ2 <pFpN

, otherwise, Λ1A = 1.Following the TAS criterion adopted in Scheme II, with the

aid of order statistics [38], and [25, Eq. (1.111)], the CDF andPDF of |hi∗F|2 can be written, respectively, as

F|hi∗F|2(y) =

K∑k=0

(K

k

)(−1)ke

− kxλSF , (58)

f|hi∗F|2(x) =

K∑k=1

(K

k

)(−1)k+1 k

λXe− kxλSF . (59)

Thus, Λ1B can be obtained as

Λ1B =

K∑k=0

(K

k

)(−1)ke

− kγ2λSF(b1−b2γ2) , (60)

if γ2 < θ, otherwise, Λ1B = 1.Next, since Users N and F are assumed to be independent,

Λ2 in (51) can be rewritten as

Λ2 = Pr(γi∗F < γ2)︸ ︷︷ ︸Λ2A

Pr(γxF

i∗N ≥ γ2, γNF < γ2)︸ ︷︷ ︸Λ2B

, (61)

where Λ2A = Λ1B , and Λ2B can be re-expressed as

Λ2B = Pr

(a1|hi∗N|2

a2|hi∗N|2 + 1≥ γ2, c|hi∗N|2|hNF|2 < γ2

).

(62)Note that |hNF|2 follows exponential distribution with mean

λNF. Conditioning on |hi∗N|2 = x, (62) becomes

Λ2B =

∫ ∞0

Pr

(x ≥ µa, |hNF|2 <

γ2

cx

)f|hi∗N|2(x)dx, (63)

where µa , γ2/(a1 − a2γ2), and can be further expressed as

Λ2B =

∫ ∞µa

Pr

(|hNF|2 <

γ2

cx

)f|hi∗N|2(x)dx (64)

= e− µaλSN − 1

λSN

∫ ∞µa

e− γ2λNFcx

− xλSN dx︸ ︷︷ ︸

I2

. (65)

I2 can be obtained as done in Appendix A. Thus, Λ2B canbe obtained as

Λ2B = e− γ2λSN(a1−a2γ2) − 1

λSNΩ

(γ2

a1 − a2γ2,

1

λSN,γ2

λNFc

).

(66)By substituting Λ1A,Λ1B and Λ2B into (51), the closed-formapproximate expression for the OP of Use F in Scheme II canbe obtained. This completes the proof of Theorem 2.

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Tri Nhu Do (S’16) was born and raised in Da Nang,Vietnam. He received the B.S. degree in electronicsand telecommunications engineering from the Postsand Telecommunications Institute of Technology,Vietnam, in 2012, and the M.S. degree in electronicsand computer engineering from Hongik University,Sejong Campus, South Korea, in 2015. He is cur-rently pursuing the Ph.D. degree in electronics andcomputer engineering with Hongik University.

His main research topics are wireless communi-cations and cooperative relaying transmissions.

Daniel Benevides da Costa (S’04–M’08–SM’14)was born in Fortaleza, Ceara, Brazil, in 1981. Hereceived the B.Sc. degree in Telecommunicationsfrom the Military Institute of Engineering (IME),Rio de Janeiro, Brazil, in 2003, and the M.Sc.and Ph.D. degrees in Electrical Engineering, Area:Telecommunications, from the University of Camp-inas, SP, Brazil, in 2006 and 2008, respectively.His Ph.D thesis was awarded the Best Ph.D. Thesisin Electrical Engineering by the Brazilian Ministryof Education (CAPES) at the 2009 CAPES Thesis

Contest. From 2008 to 2009, he was a Postdoctoral Research Fellow withINRS-EMT, University of Quebec, Montreal, QC, Canada. Since 2010, he hasbeen with the Federal University of Ceara, where he is currently an AssistantProfessor.

Prof. da Costa is currently Editor of the IEEE COMMUNICATIONSSURVEYS AND TUTORIALS, IEEE ACCESS, IEEE TRANSACTIONS ONCOMMUNICATIONS, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORK-ING, and KSII TRANSACTIONS ON INTERNET AND INFORMATION SYS-TEMS. He has also served as Associate Technical Editor of the IEEECOMMUNICATIONS MAGAZINE. From 2012 to 2017, he was Editor of theIEEE COMMUNICATIONS LETTERS. He has served as Guest Editor of severalJournal Special Issues. He has been involved on the Organizing Commit-tee of several conferences. He is currently the Latin American ChaptersCoordinator of the IEEE Vehicular Technology Society. Also, he acts as aScientific Consultant of the National Council of Scientific and TechnologicalDevelopment (CNPq), Brazil and he is a Productivity Research Fellow ofCNPq. From 2012 to 2017, he was Member of the Advisory Board of theCeara Council of Scientific and Technological Development (FUNCAP), Area:Telecommunications.

Prof. da Costa is the recipient of three conference paper awards. He receivedthe Exemplary Reviewer Certificate of the IEEE WIRELESS COMMUNICA-TIONS LETTERS in 2013, the Exemplary Reviewer Certificate of the IEEECOMMUNICATIONS LETTERS in 2016, the Certificate of Appreciation of TopAssociate Editor for outstanding contributions to IEEE TRANSACTIONS ONVEHICULAR TECHNOLOGY in 2013, 2015 and 2016, and the ExemplaryEditor Award of IEEE COMMUNICATIONS LETTERS in 2016. He is aDistinguished Lecturer of the IEEE Vehicular Technology Society. He is aSenior Member of IEEE, Member of IEEE Communications Society and IEEEVehicular Technology Society.

14

Trung Q. Duong (S’05, M’12, SM’13) received hisPh.D. degree in Telecommunications Systems fromBlekinge Institute of Technology (BTH), Sweden in2012. Since 2013, he has joined Queen’s UniversityBelfast, UK as a Lecturer (Assistant Professor).His current research interests include small-cell net-works, ultra-dense networks, physical layer security,energy-harvesting communications, massive MIMO.He is the author or co-author of more than 280technical papers published in scientific journals (156articles) and presented at international conferences

(125 papers).Dr. Duong currently serves as an Editor for the IEEE TRANSACTIONS

ON WIRELESS COMMUNICATIONS, IEEE TRANSACTIONS ON COMMUNI-CATIONS, IET COMMUNICATIONS, and a Senior Editor for IEEE COMMU-NICATIONS LETTERS. He was awarded the Best Paper Award at the IEEEVehicular Technology Conference (VTC-Spring) in 2013, IEEE InternationalConference on Communications (ICC) 2014, and IEEE Global Communi-cations Conference (GLOBECOM) 2016. He is the recipient of prestigiousRoyal Academy of Engineering Research Fellowship (2016-2021) and haswon a prestigious Newton Prize 2017.

Beongku An received the M.S. degree in elec-trical engineering from the New York University(Polytechnic), NY, USA, in 1996 and Ph.D. degreefrom New Jersey Institute of Technology (NJIT),NJ, USA, in 2002, BS degree in electronic engi-neering from Kyungpook National university, Korea,in 1988, respectively. After graduation, he joinedthe Faculty of the Department of Computer andInformation Communications Engineering, HongikUniversity in Korea, where he is currently a Profes-sor. From 1989 to 1993, he was a senior researcher in

RIST, Pohang, Korea. He also was lecturer and RA in NJIT from 1997 to 2002.He was a president of IEIE Computer Society (The Institute of Electronics andInformation Engineers, Computer Society) in 2012. From 2013, he also worksas a General Chair in the International Conference, ICGHIT (InternationalConference on Green and Human Information Technology).

His current research interests include mobile wireless networks and com-munications such as ad-hoc networks, sensor networks, wireless internet,cognitive radio networks, ubiquitous networks, cellular networks, and IoT.In particular, he is interested in cooperative routing, multicast routing, energyharvesting, physical layer security, visible light communication (VLC), cross-layer technology, mobile cloud computing. Professor An was listed in MarquisWho’s Who in Science and Engineering, and Marquis Who’s Who in theWorld, respectively.