A Tutorial on Nonorthogonal Multiple Access for 5G and Beyond2017/11/23 ·...

Review ArticleA Tutorial on Nonorthogonal Multiple Accessfor 5G and Beyond

Mahmoud Aldababsa1 Mesut Toka12 Selahattin Goumlkccedileli 3

GuumlneG Karabulut Kurt3 and OLuz Kucur 1

1Electronics Engineering Department Gebze Technical University Gebze 41400 Kocaeli Turkey2Electrical and Electronics Engineering Department Omer Halisdemir University 51240 Nigde Turkey3Department of Communications and Electronics Engineering Istanbul Technical University 34469 Istanbul Turkey

Correspondence should be addressed to Oguz Kucur okucurgtuedutr

Received 23 November 2017 Accepted 5 February 2018 Published 28 June 2018

Academic Editor Nathalie Mitton

Copyright copy 2018 Mahmoud Aldababsa et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Todayrsquos wireless networks allocate radio resources to users based on the orthogonal multiple access (OMA) principle Howeveras the number of users increases OMA based approaches may not meet the stringent emerging requirements including very highspectral efficiency very low latency and massive device connectivity Nonorthogonal multiple access (NOMA) principle emergesas a solution to improve the spectral efficiency while allowing some degree of multiple access interference at receivers In thistutorial style paper we target providing a unified model for NOMA including uplink and downlink transmissions along with theextensions tomultiple input multiple output and cooperative communication scenariosThrough numerical examples we comparethe performances of OMA and NOMA networks Implementation aspects and open issues are also detailed

1 Introduction

Wireless mobile communication systems became an indis-pensable part of modern lives However the number andthe variety of devices increase significantly and the sameradio spectrum is required to be reused several times bydifferent applications andor users Additionally the demandfor the Internet of Things (IoT) introduces the necessity toconnect every person and every object [1] However currentcommunication systems have strict limitations restrictingany modifications and improvements on the systems to meetthese demands Recently researchers have been working ondeveloping suitable techniques that may be integrated in nextgeneration wireless communication systems in order to fun-damentally fulfill the emerging requirements including veryhigh spectral efficiency very low latency massive device con-nectivity very high achievable data rate ultrahigh reliabilityexcellent user fairness high throughput supporting diversequality of services (QoS) energy efficiency and a dramaticreduction in the cost [2] Some potential technologies have

been proposed by the academia and the industry in order tosatisfy the aforementioned tight requirements and to addressthe challenges of future generations For example millimeterwave (mmWave) technology was suggested to enlarge thetransmission bandwidth for very high speed communications[3] massive multiple input multiple output (MIMO) conceptwas presented to improve capacity and energy efficiency [4]and ultradense networks were introduced to increase thethroughput and to reduce the energy consumption throughusing a large number of small cells [5]

Besides the aforementioned techniques a new radioaccess technology is also developed by researchers to be usedin communication networks due to its capability in increasingthe system capacity Recently nonorthogonality based systemdesigns are developed to be used in communication networksand have gained significant attention of researchers Hencemultiple access (MA) techniques can now be fundamen-tally categorized as orthogonal multiple access (OMA) andnonorthogonal multiple access (NOMA) In OMA eachuser can exploit orthogonal communication resources within

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 9713450 24 pageshttpsdoiorg10115520189713450

2 Wireless Communications and Mobile Computing

either a specific time slot frequency band or code in order toavoid multiple access interference The previous generationsof networks have employedOMA schemes such as frequencydivision multiple access (FDMA) of first generation (1G)time division multiple access (TDMA) of 2G code divisionmultiple access (CDMA) of 3G and orthogonal frequencydivision multiple access (OFDMA) of 4G In NOMA multi-ple users can utilize nonorthogonal resources concurrently byyielding a high spectral efficiency while allowing some degreeof multiple access interference at receivers [6 7]

In general NOMA schemes can be classified into twotypes power-domain multiplexing and code-domain multi-plexing In power-domain multiplexing different users areallocated different power coefficients according to their chan-nel conditions in order to achieve a high system performanceIn particularmultiple usersrsquo information signals are superim-posed at the transmitter side At the receiver side successiveinterference cancellation (SIC) is applied for decoding thesignals one by one until the desired userrsquos signal is obtained[8] providing a good trade-off between the throughput ofthe system and the user fairness In code-domain multi-plexing different users are allocated different codes andmultiplexed over the same time-frequency resources such asmultiuser shared access (MUSA) [9] sparse code multipleaccess (SCMA) [10] and low-density spreading (LDS) [11]In addition to power-domain multiplexing and code-domainmultiplexing there are other NOMA schemes such as patterndivision multiple access (PDMA) [12] and bit division mul-tiplexing (BDM) [13] Although code-domain multiplexinghas a potential to enhance spectral efficiency it requires ahigh transmission bandwidth and is not easily applicableto the current systems On the other hand power-domainmultiplexing has a simple implementation as considerablechanges are not required on the existing networks Also itdoes not require additional bandwidth in order to improvespectral efficiency [14] In this reviewtutorial paper we willfocus on the power-domain NOMA

Although OMA techniques can achieve a good systemperformance evenwith simple receivers because of nomutualinterference among users in an ideal setting they still donot have the ability to address the emerging challenges dueto the increasing demands in 5G networks and beyond Forexample according to International Mobile Telecommunica-tions (IMT) for 2020 and beyond [15] 5G technology shouldsupport three main categories of scenarios such as enhancedmobile broadband (eMBB) massive machine type commu-nication (mMTC) and ultrareliable and low-latency com-munication (URLLC)Themain challenging requirements ofeMBB scenario are 100Mbps user perceived data rate andmore than 3 times spectrum efficiency improvement overthe former LTE releases to provide services including highdefinition video experience virtual reality and augmentedreality Since a large number of IoT devices will have accessto the network the main challenge of mMTC is to provideconnection density of 1 million devices per square kilometerIn case of URLLC the main requirements include 05msend-to-end latency and reliability above 99999 [16ndash18] Byusing NOMA scheme for mMTC and URLLC applicationsthe number of user connections can be increased by 5 and

9 times respectively [18] Also according to [19] NOMA hasbeen shown to bemore spectral-efficient by 30 for downlinkand 100 for uplink in eMBB when compared to OMATherefore NOMA has been recognized as a strong candidateamong all MA techniques since it has essential features toovercome challenges in counterpart OMA and achieve therequirements of next mobile communication systems [20ndash22] The superiority of NOMA over OMA can be remarkedas follows

(i) Spectral efficiency and throughput in OMA such asin OFDMA a specific frequency resource is assignedto each user even it experiences a good or badchannel condition thus the overall system suffersfrom low spectral efficiency and throughput In thecontrary in NOMA the same frequency resource isassigned to multiple mobile users with good andbad channel conditions at the same time Hence theresource assigned for the weak user is also used bythe strong user and the interference can be mitigatedthrough SIC processes at usersrsquo receivers Thereforethe probability of having improved spectral efficiencyand a high throughput will be considerably increasedas depicted in Figure 1

(ii) User fairness low latency and massive connectivityin OMA for example in OFDMA with schedulingthe user with a good channel condition has a higherpriority to be servedwhile the user with a bad channelcondition has to wait for access which leads to a fair-ness problem and high latencyThis approach can notsupport massive connectivity However NOMA canservemultiple users with different channel conditionssimultaneously therefore it can provide improveduser fairness lower latency and higher massive con-nectivity [20]

(iii) Compatibility NOMA is also compatible with thecurrent and future communication systems since itdoes not require significant modifications on theexisting architecture For example NOMA has beenincluded in third generation partnership project long-term evolution advanced (3GPP LTE Release 13) [23ndash29] More detailed in the standards a downlinkversion of NOMAmultiuser superposition transmis-sion (MUST) has been used [23] MUST utilizesthe superposition coding concept for a multiusertransmission in LTE-A systems In 3GPP radio accessnetwork (RAN) while using MUST the deploymentscenarios evaluation methodologies and candidateNOMA scheme have been investigated in [24ndash26]respectivelyThen system level performance and linklevel performance of NOMA have been evaluated in[27 28] respectively Next 3GPP LTE Release 14 hasbeen proposed [29] in which intracell interferenceis eliminated and hence LTE can support down-link intracell multiuser superposition transmissionAlso NOMA known as layered divisionmultiplexing(LDM) is used in the future digital TV standardATSC 30 [30] Moreover the standardization studyof NOMA schemes for 5GNewRadio (NR) continues

Wireless Communications and Mobile Computing 3

Power PowerNOMA

Frequency Frequency

OMA (OFDMA based)

Figure 1 A pictorial comparison of OMA and NOMA

within 3GPP LTE Release 15 [31] Agreed objectives inRelease 15 can be summarized as follows (1) trans-mitter side signal processing schemes for NOMAsuch as modulation and symbol level processingcoded bit level processing and symbol to resourceelement mapping (2) receivers for NOMA suchas minimum mean-square error (MMSE) receiverSIC andor parallel interference cancellation (PIC)receiver joint detection type receivers and complex-ity of the receivers (3) NOMA procedures such asuplink transmission detection link adaptation MAsynchronous and asynchronous operation and adap-tation betweenOMAandNOMA (4) link and systemlevel performance evaluation or analysis for NOMAsuch as traffic model and deployment scenarios ofeMBB mMTC and URLLC coverage latency andsignaling overhead

In otherwords the insufficient performance ofOMAmakes itinapplicable and unsuitable to provide the features needed tobe met by the future generations of wireless communicationsystems Consequently researchers suggest NOMA as astrong candidate as an MA technique for next generations[32] Although NOMA has many features that may supportnext generations it has some limitations that should beaddressed in order to exploit its full advantage set Thoselimitations can be pointed out as follows In NOMA sinceeach user requires to decode the signals of some users beforedecoding its own signal the receiver computational com-plexity will be increased when compared to OMA leadingto a longer delay Moreover information of channel gainsof all users should be fed back to the base station (BS)but this results in a significant channel state information(CSI) feedback overhead Furthermore if any errors occurduring SIC processes at any user then the error probabilityof successive decoding will be increased As a result thenumber of users should be reduced to avoid such errorpropagation Another reason for restricting the number ofusers is that considerable channel gain differences among

users with different channel conditions are needed to have abetter network performance

This paper written in a tutorial name focuses on NOMAtechnique along with its usage in MIMO and cooperativescenarios Practice implementation aspects are also detailedBesides an overview about the standardizations of NOMA in3GPP LTE and application in the 5G scenarios is provided Inaddition unlike previous studies this paper includes perfor-mance analyses of MIMO-NOMA and cooperative NOMAscenarios to make the NOMA concept more understandableby researchers The remainder of this paper is organized asfollows Basic concepts of NOMA in both downlink anduplink networks are given in Section 2 In Sections 3 and4 MIMO-NOMA and cooperative NOMA are describedrespectively Practical implementation challenges of NOMAare detailed in Section 5The paper is concluded in Section 6

2 Basic Concepts of NOMA

In this section an overview of NOMA in downlinkand uplink networks is introduced through signal-to-interference-and-noise ratio (SINR) and sum rate analysesThen high signal-to-noise ratio (SNR) analysis has beenconducted in order to compare the performances of OMAand NOMA techniques

21 Downlink NOMA Network At the transmitter side ofdownlink NOMA network as shown in Figure 2 the BStransmits the combined signal which is a superposition ofthe desired signals of multiple users with different allocatedpower coefficients to all mobile users At the receiver of eachuser SIC process is assumed to be performed successivelyuntil userrsquos signal is recovered Power coefficients of usersare allocated according to their channel conditions in aninversely proportional manner The user with a bad channelcondition is allocated higher transmission power than the onewhich has a good channel condition Thus since the userwith the highest transmission power considers the signalsof other users as noise it recovers its signal immediately


Base station(BS)

s

Power

Resource signals detection

UL signalSIC for U1 U2 ULminus1

detectionUl signal

signalsSIC for U1 U2 Ulminus1

detectionU2 signal

signalSIC for U1

detectionU1 signal

U1

U1

U2

U2

Ul

Ul

UL

UL

Figure 2 Downlink NOMA network

without performing any SIC process However other usersneed to perform SIC processes In SIC each userrsquos receiverfirst detects the signals that are stronger than its own desiredsignal Next those signals are subtracted from the receivedsignal and this process continues until the related userrsquos ownsignal is determined Finally each user decodes its own signalby treating other users with lower power coefficients as noiseThe transmitted signal at the BS can be written as follows

119904 = 119871sum119894=1

radic119886119894119875119904119909119894 (1)

where 119909119894 is the information of user 119894 (119880119894) with unit energy119875119904 is the transmission power at the BS and 119886119894 is the powercoefficient allocated for user 119894 subjected to sum119871119894=1 119886119894 = 1 and1198861 ge 1198862 ge sdot sdot sdot ge 119886119871 since without loss of generality thechannel gains are assumed to be ordered as |ℎ1|2 le |ℎ2|2 lesdot sdot sdot le |ℎ119871|2 where ℎ119897 is the channel coefficient of 119897th userbased on NOMA concept The received signal at 119897th user canbe expressed as follows

119910119897 = ℎ119897119904 + 119899119897 = ℎ119897 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119897 (2)

where 119899119897 is zero mean complex additive Gaussian noise witha variance of 1205902 that is 119899119897 sim CN(0 1205902)211 SINR Analysis By using (2) the instantaneous SINR ofthe 119897th user to detect the 119895th user 119895 le 119897 with 119895 = 119871 can bewritten as follows

SINR119895rarr119897 = 119886119895120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119895+1 119886119894 + 1 (3)

where 120574 = 1198751199041205902 denotes the SNR In order to find thedesired information of the 119897th user SIC processes will beimplemented for the signal of user 119895 le 119897 Thus the SINR of119897th user can be given by

SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1 (4)

Then the SINR of the 119871th user is expressed as

SINR119871 = 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162 (5)

212 Sum Rate Analysis After finding the SINR expressionsof downlinkNOMA the sum rate analysis can easily be doneThe downlink NOMA achievable data rate of 119897th user can beexpressed as

119877NOMA-d119897 = log2 (1 + SINR119897)

= log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1) (6)

Therefore the sum rate of downlinkNOMA can be written as

119877NOMA-dsum = 119871sum

119897=1

log2 (1 + SINR119897)= 119871minus1sum119897=1

log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162)


rBase station

(BS)signals

U1

U2

Ul

UL

x1

x2

xl

xL

SIC for U1 U2 UL

Figure 3 Uplink NOMA network

= 119871minus1sum119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003816100381610038161003816ℎ11989710038161003816100381610038162)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) (7)

In order to figure out whether NOMA techniques out-perform OMA techniques we conduct a high SNR analysisThus at high SNR that is 120574 rarr infin the sum rate of downlinkNOMA becomes

119877NOMA-dsum asymp 119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) + log2 (120574 1003816100381610038161003816ℎ11987110038161003816100381610038162)asymp log2 (120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) (8)

22 Uplink NOMA Network In uplink NOMA network asdepicted in Figure 3 each mobile user transmits its signal tothe BS At the BS SIC iterations are carried out in order todetect the signals of mobile users By assuming that downlinkand uplink channels are reciprocal and the BS transmitspower allocation coefficients to mobile users the receivedsignal at the BS for synchronous uplink NOMA can beexpressed as

119903 = 119871sum119894=1

ℎ119894radic119886119894119875119909119894 + 119899 (9)

where ℎ119894 is the channel coefficient of the 119894th user 119875 is themaximum transmission power assumed to be common forall users and 119899 is zero mean complex additive Gaussian noisewith a variance of 1205902 that is 119899 sim CN(0 1205902)

221 SINR Analysis The BS decodes the signals of usersorderly according to power coefficients of users and then theSINR for 119897th user 119897 = 1 can be given by [33]

SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574sum119897minus1119894=1 119886119894 1003816100381610038161003816ℎ11989410038161003816100381610038162 + 1 (10)

where 120574 = 1198751205902 Next the SINR for the first user is expressedas

SINR1 = 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162 (11)

222 Sum Rate Analysis The sum rate of uplink NOMA canbe written as

119877NOMA-usum = 119871sum

119897=1

log2 (1 + SINR119897)= log2 (1 + 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162)+ 119871sum119897=2

log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574sum119897minus1119894=1 119886119894 1003816100381610038161003816ℎ11989410038161003816100381610038162 + 1)= log2(1 + 120574 119871sum

119897=1

119886119897 1003816100381610038161003816ℎ11989710038161003816100381610038162)

(12)

When 120574 rarr infin the sum rate of uplink NOMA becomes

119877NOMA-usum asymp log2(120574 119871sum

119897=1

1003816100381610038161003816ℎ11989710038161003816100381610038162) (13)


23 Comparing NOMA and OMA The achievable data rateof the 119897th user of OMA for both uplink and downlink can beexpressed as [33]

119877OMA119897 = 120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (14)

where 120573119897 and 120572119897 are the power coefficient and the parameterrelated to the specific resource of 119880119897 respectively And thenthe sum rate of OMA is written as

119877OMAsum = 119871sum

119897=1

120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (15)

For OMA for example FDMA total bandwidth resourceand power are shared among the users equally then using120572119897 = 120573119897 = 1119871 the sum rate can be written as

119877OMAsum = 119871sum

119897=1

1119871 log2 (1 + 120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (16)

When 120574 rarr infin the sum rate of OMA becomes

119877OMAsum asymp 119871sum

119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (17)

Using |ℎ1|2 le |ℎ2|2 le sdot sdot sdot le |ℎ119871|2119877OMAsum asymp 119871sum

119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) le 119871sum119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11987110038161003816100381610038162)= log2 (120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) asymp 119877NOMA-d

sum (18)

Hence we conclude 119877OMAsum le 119877NOMA-d

sum For the sake of simplicity sum rates of uplinkNOMA and

OMA can be compared for two users Then using (13) and(17) the sum rate of uplink NOMA and OMA at high SNRcan be expressed respectively as

119877NOMA-usum asymp log2 (120574 1003816100381610038161003816ℎ110038161003816100381610038162 + 120574 1003816100381610038161003816ℎ210038161003816100381610038162) (19)

119877OMAsum asymp 12 log2 (120574 1003816100381610038161003816ℎ110038161003816100381610038162) + 12 log2 (120574 1003816100381610038161003816ℎ210038161003816100381610038162)le log2 (120574 1003816100381610038161003816ℎ210038161003816100381610038162) (20)

From (19) and (20) we notice 119877OMAsum le 119877NOMA-u

sum Figure 4 shows that NOMA outperforms OMA in terms

of sum rate in both downlink and uplink of two user networksusing (7) (12) and (16)

3 MIMO-NOMA

MIMO technologies have a significant capability of increas-ing capacity as well as improving error probability of wirelesscommunication systems [34] To take advantage of MIMOschemes researchers have investigated the performance ofNOMA over MIMO networks [35] Many works have been

studying the superiority of MIMO-NOMA over MIMO-OMA in terms of sum rate and ergodic sum rate underdifferent conditions and several constrictions [36ndash39] Specif-ically in [36] the maximization problem of ergodic sumrate for two-userMIMO-NOMAsystemover Rayleigh fadingchannels is discussed With the need of partial CSI at theBS and under some limitations on both total transmissionpower and the minimum rate for the user with bad channelcondition the optimal power allocation algorithm witha lower complexity to maximize the ergodic capacity isproposed However in order to achieve a balance betweenthe maximum number of mobile users and the optimalachievable sum rate in MIMO-NOMA systems sum ratehas been represented through two ways The first approachtargets the optimization of power partition among the userclusters [37] Another approach is to group the users indifferent clusters such that each cluster can be allocated withorthogonal spectrum resources according to the selected usergrouping algorithm [38] Furthermore in [37] performancesof two users per cluster schemes have been studied forbothMIMO-NOMA andMIMO-OMA over Rayleigh fadingchannels In addition in accordance with specified powersplit the dominance of NOMA over OMA has been shownin terms of sum channel and ergodic capacities

On the other side the authors in [38] have examined theperformance of MIMO-NOMA system in which multipleusers are arranged into a cluster An analytical comparisonhas been provided between MIMO-NOMA and MIMO-OMA and then it is shown that NOMA outperforms OMAin terms of sum channel and ergodic capacities in case ofmultiple antennas Moreover since the number of users percluster is inversely proportional to the achievable sum rateand the trade-off between the number of admitted usersand achieved sum rate has to be taken into account (whichrestricts the system performance) a user admission schemewhich maximizes the number of users per cluster based ontheir SINR thresholds is proposed Although the optimumperformance is achieved in terms of the number of admittedusers and the sum rate when the SINR thresholds of allusers are equal even when they are different good resultsare obtained In addition a low complexity of the proposedscheme is linearly proportional to the number of users percluster In [39] the performance of downlinkMIMO-NOMAnetwork for a simple case of two users that is one clusteris introduced In this case MIMO-NOMA provides a betterperformance than MIMO-OMA in terms of both the sumrate and ergodic sum rate Also it is shown that for a morepractical case of multiple users with two users allocated intoa cluster and sharing the same transmit beamforming vectorwhere ZF precoding and signal alignment are employed at theBS and the users of the same cluster respectively the sameresult still holds

Antenna selection techniques have also been recognizedas a powerful solution that can be applied to MIMO systemsin order to avoid the adverse effects of using multipleantennas simultaneously These effects include hardwarecomplexity redundant power consumption and high costMeanwhile diversity advantages that can be achieved fromMIMO systems are still maintained [40] Several works apply


NOMAOMA

NOMAOMA

Downlink network Uplink network

2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)

0 10 15 20 25 30 35 40 45 505Signal to noise ratio (dB)

5 20 35 4525 3010 4015 500Signal to noise ratio (dB)

2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)

Figure 4 Sum rate of NOMA and OMA in both downlink and uplink networks with 1198861 = 06 1198862 = 04 |ℎ1|2 = 0 dB and |ℎ2|2 = 20 dB

antenna selection techniques in MIMO-NOMA as they havealready been developed for MIMO-OMA systems But thegains can not be easily replicated since there is a heavyinteruser interference inMIMO-NOMAnetworks dissimilarfrom those in MIMO-OMA networks in which informationis transmitted in an interference-free manner Consequentlythere are a few works that challenged the antenna selectionproblem [41ndash43] In [41] the sum rate performance for down-link multiple input single output- (MISO-) NOMA system isinvestigatedwith the help of transmit antenna selection (TAS)at the BS where the transmitter of the BS and the receiverof each mobile user are equipped with multiantenna andsingle antenna respectively Basically in TAS-OMA schemethe best antenna at the BS offering the highest SINR isselected However in the proposed TAS-NOMA scheme in[41] the best antenna at the BS providing the maximumsum rate is chosen In addition to using an efficient TASscheme user scheduling algorithm is applied in two usermassive MIMO-NOMA system in order to maximize theachievable sum rate in [42] for two scenarios namely thesingle-band two users and the multiband multiuser In thefirst scenario an efficient search algorithm is suggested Thisalgorithm aims to choose the antennas providing the highestchannel gains in such a way that the desired antennas are onlysearched from specified finite candidate set which are usefulto the concerned users On the other hand in the secondscenario a joint user and antenna contribution algorithmis proposed In particular this algorithm manipulates theratio of channel gain specified by a certain antenna-userpair to the total channel gain and hence antenna-user pairoffering the highest contribution to the total channel gain isselected Moreover an efficient search algorithm provides abetter trade-off between system performance and complexityrather than a joint antenna and user contribution algorithmUnfortunately neither the authors of [41] nor the authors

of [42] have studied the system performance analyticallyIn [43] the maximization of the average sum rate of two-user NOMA system in which the BS and mobile users areequipped with multiantenna is discussed through two com-putationally effective joint antenna selection algorithms themax-min-max and the max-max-max algorithms Howeverthe instantaneous channel gain of the user with a bad channelcondition is improved in max-min-max antenna selectionscheme while max-max-max algorithm is the solution for theuser with a good channel condition Furthermore asymptoticclosed-form expressions of the average sum rates are evalu-ated for both proposed algorithms Moreover it is verifiedthat better user fairness can be achieved by themax-min-maxalgorithm while larger sum rate can be obtained by the max-max-max algorithm

Multicast beamforming can also be introduced as a tech-nique that can be employed in MIMO schemes since it offersa better sum capacity performance even for multiple usersHowever it can be applied in different ways One approachis based on a single beam that can be used by all usershence all users receive this common signal [44] Anotherapproach is to use multiple beams that can be utilized bymany groups of users that is each group receives a differentsignal [45] The following works have studied beamformingin MIMO-NOMA systems In [46] multiuser beamformingin downlinkMIMO-NOMA system is proposed Particularlya pair of users can share the same beam Since the proposedbeam can be only shared by two users with different channelqualities it is probable to easily apply clustering and powerallocation algorithms to maximize the sum capacity and todecrease the intercluster and interuser interferences In [47]performance of multicast beamforming when the beam isused to serve many users per cluster by sharing a commonsignal is investigated with superposition coding for a down-linkMISO-NOMAnetwork in a simple scenario of two users


Principally the transmitter of the BS has multiantenna andits information stream is based on multiresolution broadcastconcept in which only low priority signal is sent to theuser that is far away from the BS that is user with abad channel quality Both signals of high priority and lowpriority are transmitted to the user near to BS that is userwith good channel quality Furthermore with superpositioncoding a minimum power beamforming problem has beendeveloped in order to find the beamforming vectors andthe powers for both users Moreover under the consideredoptimization condition and the given normalized beamform-ing vectors (which are founded by an iterative algorithm)the closed-form expression for optimal power allocation iseasily obtained In [48] random beamforming is carried outat the BS of a downlink MIMO-NOMA network In thesystem model each beam is assumed to be used by all theusers in one cluster and all beams have similar transmissionpower allocations Moreover a spatial filter is suggested tobe used in order to diminish the intercluster and interbeaminterferences Fractional frequency reuse concept in whichusers with different channel conditions can accommodatemany reuse factors is proposed in order to improve the powerallocation among multiple beams In [49] interference mini-mization and capacity maximization for downlink multiuserMIMO-NOMA system are introduced in which the numberof receive antennas of mobile user is larger than the numberof transmit antennas of the BS Zero-forcing beamformingtechnique is suggested to reduce the intercluster interferenceespecially when distinctive channel quality users is assumedIn addition dynamic power allocation and user-cluster algo-rithms have been proposed not only to achieve maximumthroughput but also to minimize the interference

There are many research works investigating resourceallocation problem in terms of maximization of the sumrate in case of perfect CSI [50ndash52] Specifically in [50]sum rate optimization problem of two-user MIMO-NOMAnetwork that is two users in one cluster in which differentprecoders are implemented has been introduced under theconstraint of transmission power at the BS and the minimumtransmission rate limitation of the user with bad channelcondition In [51] the sum rate maximization problem fordownlinkMISO-NOMA system is investigated However thetransmitted signal for each mobile user is weighted witha complex vector Moreover for the sake of avoiding thehigh computational complexity related to nonconvex opti-mization problem minorization-maximization method issuggested as an approximationThe key idea ofminorization-maximization algorithm is to design the complex weightingvectors in such a way that the total throughput of thesystem is maximized for a given order of users that isperfect CSI is assumed In [52] a downlink MIMO-NOMAsystem where perfect CSI available at all nodes is assumedand with different beams BS broadcasts precoded signalsto all mobile users that is each beam serves several usersHowever there are three proposed algorithms combined inorder to maximize the sum rate The first one is whereweighted sum rate maximization proposes to design a specialbeamforming matrix of each beam benefiting from all CSIat the BS The second algorithm is where user scheduling

aims to have super SIC at the receiver of each mobile userThus to take full benefits of SIC differences in channelgains per cluster should be significant and the channelcorrelation between mobile users has to be large The finalone is where fixed power allocation targets optimizationoffering not only a higher sum rate but also convenientperformance for the user with bad channel quality In [53]the optimal power allocation method in order to maximizethe sum rate of two-user MIMO-NOMA with a layeredtransmission scheme under a maximum transmission powerconstraint for each mobile user is investigated Basically byusing the layered transmission each mobile user performssequence by sequence decoding signals throughout SICyielding much lower decoding complexity when comparedto the case with nonlayered transmission Moreover theclosed-form expression for the average sum rate and itsbounds in both cases of perfect CSI and partial CSI areobtained Also it is shown that the average sum rate islinearly proportional to the number of antennas In [54]a comprehensive resource allocation method for multiuserdownlink MIMO-NOMA system including beamformingand user selection is proposed yielding low computationalcomplexity and high performance in cases of full and partialCSI However resource allocation has been expressed interms of the maximum sum rate and the minimum ofmaximum outage probability (OP) for full CSI and partialCSI respectively Outage behavior for both downlink anduplink networks in MIMO-NOMA framework with inte-grated alignment principles is investigated in a single cell[55] and multicell [56 57] respectively Furthermore anappropriate trade-off between fairness and throughput hasbeen achieved by applying two strategies of power alloca-tion methods The fixed power allocation strategy realizesdifferent QoS requirements On the other hand cognitiveradio inspired power allocation strategy verifies that QoSrequirements of the user are achieved immediately In addi-tion exact and asymptotic expressions of the system OPhave been derived In [58] the power minimization problemfor downlink MIMO-NOMA networks under full CSI andchannel distribution information scenarios are studied In[59] linear beamformers that is precoders that provide alarger total sum throughput also improving throughput ofthe user with bad quality channel are designed meanwhileQoS specification requirements are satisfied Also it is shownthat the maximum number of users per cluster that realizes ahigher NOMA performance is achieved at larger distinctivechannel gains

Moreover since massive MIMO technologies can ensurebountiful antenna diversity at a lower cost [4] many workshave discussed performance of NOMA over massive MIMOFor instance in [60] massive MIMO-NOMA system wherethe number of the transmit antennas at the BS is significantlylarger than the number of users is studied with limited feed-back Also the exact expressions of the OP and the diversityorder are obtained for the scenarios of perfect order of usersand one bit feedback respectively In [61] the scheme basedon interleave divisionmultiple access and iterative data-aidedchannel estimation is presented in order to solve the reliabilityproblem of multiuser massive MIMO-NOMA system with


imperfect CSI available at the BS In [62] the achievablerate in massive MIMO-NOMA systems and iterative data-aided channel estimation receiver in which partially decodedinformation is required to get a better channel estimation areinvestigated through applying two pilot schemes orthogonalpilot and superimposed pilot However pilots in the orthog-onal pilot scheme occupy timefrequency slots while they aresuperimposed with information in superimposed pilot oneMoreover it is shown that the greatest part of pilot power insuperimposed pilot scheme seems to be zero in the case whenGaussian signal prohibits overhead power and rate loss thatmay be resulted through using pilot Consequently with codemaximization superimposed scheme has a superior perfor-mance over orthogonal one under higher mobility and largernumber of mobile users Different from massive MIMOin [63] performance of massive access MIMO systems inwhich number of users is larger than the number of antennasemployed at the BS is studied Low-complexity Gaussianmessage specially passing iterative detection algorithm isused and both its mean and variance precisely converge withhigh speed to those concerned with the minimum meansquare error multiuser detection in [64]

In addition NOMA has been proposed as a candidateMA scheme integrated with beamspace MIMO in mmWavecommunication systems satisfying massive connectivitywhere the number of mobile users is much greater than thenumber of radio frequency chains and obtaining a betterperformance in terms of spectrum and energy efficiency[65] Furthermore a precoding scheme designed on zero-forcing (ZF) concept has been suggested in order to reducethe interbeam interference Moreover iterative optimizationalgorithmwith dynamic power allocation scheme is proposedto obtain a higher sum rate and lower complexity In [66]the optimization problem of energy efficiency for MIMO-NOMA systems with imperfect CSI at the BS over Rayleighfading channels is studied under specified limitations ontotal transmission power and minimum sum rate of theuser of bad channel condition However two-user schedulingschemes and power allocation scheme are presented in[67] in order to maximize the energy efficiency The userscheduling schemes depend on the signal space alignmentwhile one of them effectively deals with the multiple interfer-ence the other one maximizes the multicollinearity amongusers On the other hand power allocation scheme usesa sequential convex approximation that roughly equalizesthe nonconvex problem by a set of convex problems iter-atively that is in each iteration nonconvex constraints aremodified into their approximations in inner convex Alsoit is shown that higher energy efficiency is obtained whenlower power is transmitted and a higher sum rate of centerusers is obtained whenmaximummulticollinearity scheme isemployed

Many other problems have been investigated in MIMO-NOMA systems For example in [68 69] QoS optimizationproblem is proposed for two-user MISO-NOMA systemIn particular closed-form expressions of optimal precodingvectors over flat fading channels are achieved by applying theLagrange duality and an iterative method in [68] and [69]respectively

As mentioned before NOMA promises to satisfy theneed of IoT in which many users require to be servedrapidly for small packet transmissions Consequently theliterature tends to study performance of MIMO-NOMA forIoT For instance in [70] aMIMO-NOMAdownlink networkwhere one transmitter sending information to two usersis considered However one user has a low data rate thatis small packet transmission while the second user has ahigher rate Particularly outage performance in case of usingprecoding and power allocationmethod is investigated Alsoit is shown that the potential of NOMA is apparent evenwhenchannel qualities of users are similar

Most current works of MIMO-NOMA focus on sum rateand capacity optimization problems However performanceof symbol error rate (SER) for wireless communicationsystems is also very substantial In [71] SER performanceusing the minimum Euclidean distance precoding scheme inMIMO-NOMA networks is studied For simple transmissioncase two-user 2 times 2 MIMO-NOMA is investigated How-ever to facilitate realization of practical case of multiuserMIMO-NOMA network two-user pairing algorithms areapplied

In order to demonstrate the significant performanceof MIMO-NOMA systems in terms of both OP and sumrate as well as its superiority over MIMO-OMA a specialcase performance of single input multiple output- (SIMO-)NOMA network based on maximal ratio combining (MRC)diversity technique in terms of both OP and ergodic sumrate is investigated in the following sectionMoreover closed-form expression of OP and bounds of ergodic sum rate arederived

31 Performance Analysis of SIMO-NOMA This networkincludes a BS and 119871 mobile users as shown in Figure 5 Thetransmitter of BS is equipped with a single antenna and thereceiver of each mobile user is equipped with 119873119903 antennasThe received signal at the 119897th user after applying MRC can bewritten as follows

119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)

where hl is119873119903 times 1 fading channel coefficient vector betweenthe BS and 119897th user and without loss of generality and dueto NOMA concept they are sorted in ascending way that ish12 le h22 le sdot sdot sdot le hL2 and nl is 119873119903 times 1 zero meancomplex additive Gaussian noise with 119864[nlnH

l ] = I1198731199031205902119897 atthe 119897th user where 119864[sdot] (sdot)119867 and I119903 denote the expectationoperator Hermitian transpose and identitymatrix of order 119903respectively and 1205902119897 = 1205902 is the variance of nl per dimensionFrom (21) instantaneous SINR for 119897th user to detect 119895th user119895 le 119897 with 119895 = 119871 can be expressed as follows

SINR119895rarr119897 = 119886119895120574 1003817100381710038171003817hl10038171003817100381710038172120574 1003817100381710038171003817hl10038171003817100381710038172sum119871119894=119895+1 119886119894 + 1 (22)


Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL

Figure 5 System model of the downlink SIMO-NOMA

Now nonordered channel gains for MRC can be given asfollows

10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)

where ℎ119897119894 denotes the channel coefficient between the BSand 119894th antenna of the 119897th user and are independent andidentically distributed (iid) Nakagami-119898 random variablesBy the help of the series expansion of incomplete Gammafunction [72 eq (83526)] the cumulative distributionfunction (CDF) and probability density function (PDF) ofGamma random variable 119883 square of Nakagami-119898 randomvariable can be defined as follows

119865119883 (119909) = 120574 (119898119898119909Ω)Γ (119898) = 1 minus 119890minus119898119909Ω119898minus1sum119896=0

(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)

where 120574(sdot sdot) and Γ(sdot) are the lower incomplete Gammafunction given by [72 eq (83501)] and the Gamma functiongiven by [72 eq (83101)] respectively 119898 is parameter ofNakagami-119898 distribution and Ω = 119864[|119883|2] With the helpof the highest order statistics [73] we can write CDF ofnonordered hl2 as follows119865hl2 (119909) = 120574 (119898119873119903 119898119909Ω)Γ (119898119873119903)

= 1 minus 119890minus119898119909Ω119898119873119903minus1sum119904=0

(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)

where Ω = 119864[hl2] and 120599119886(119887 119892119888) denotes multinomialcoefficients which can be defined as [72 eq (0314)]

120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)

In (26) 119889120588 = (119892119888Ω)120588120588 1205990(119887 119892119888) = 1 and 120599119886(119887 119892119888) = 0 if120588 gt 119892119888 minus 1 Next CDF of the ordered hl2 can be expressedas [74]

119865hl2 (119909) = 119871(119871 minus 119897) (119897 minus 1)119871minus119897sum119905=0 (minus1)119905119897 + 119905 (119871 minus 119897119905 )

times [119865hl2 (119909)]119897+119905 = 119871(119871 minus 119897) (119897 minus 1)sdot 119871minus119897sum119905=0

119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119905+119903119897 + 119905sdot (119871 minus 119897119905 )(119897 + 119905119903 ) 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω

(27)

311 Outage Probability of SIMO-NOMA The OP of the 119897thuser can be obtained as follows

119875out119897 = Pr (SINR119895rarr119897 lt 120574th119895)= Pr( 119886119895120574 1003817100381710038171003817hl10038171003817100381710038172120574 1003817100381710038171003817hl10038171003817100381710038172sum119871119894=119897+1 119886119894 + 1 lt 120574th119895)= Pr(1003817100381710038171003817hl10038171003817100381710038172 lt 120574th119895120574 (119886119895 minus 120574th119895 sum119871119894=119897+1 119886119894))


= Pr (1003817100381710038171003817hl10038171003817100381710038172 lt 120578lowast119897 ) = 119865hl2 (120578lowast119897 ) = 119871(119871 minus 119897) (119897 minus 1)sdot 119871minus119897sum119905=0

119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119905+119903119897 + 119905sdot (119871 minus 119897119905 )(119897 + 119905119903 ) 120599119904 (119903 119898119873119903) 120578lowast119904119897 119890minus119903119898120578lowast119897 Ω

(28)

where 120578lowast119897 = max[1205781 1205782 120578119897] with 120578119895 = 120574th119895120574(119886119895 minus120574th119895 sum119871119894=119897+1 119886119894) 120574th119895 denotes the threshold SINR of the 119895th userUnder the condition 119886119895 gt 120574th119895 sum119871119894=119895+1 119886119894 the 119897th user candecode the 119895th userrsquos signal successfully irrespective of thechannel SNR

312 Ergodic Sum Rate Analysis of SIMO-NOMA Ergodicsum rate can be expressed as

119877sum = 119871sum119897=1

119864 [12 log2 (1 + SINR119897)]= 119871minus1sum119897=1

119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)

Then 119877119871 can be expressed as

119877119871 = 119871minus1sum119897=1

119864[12 log2(1 + 119886119897120574 1003817100381710038171003817hl10038171003817100381710038172120574 1003817100381710038171003817hl10038171003817100381710038172sum119871119894=119897+1 119886119894 + 1)]= 119871minus1sum119897=1

119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)

Due to computational difficulty of calculating the exactexpression of the ergodic sum rate and for the sake ofsimplicity we will apply high SNR analysis in order to findthe upper and lower bounds related to ergodic sum rateThuswhen 120574 rarr infin in (30) then 119877infin

119871can be given by

119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)

Now by using the identity intinfin0

ln(1 + 119886119910)119891(119910)119889119910 = 119886 intinfin0((1 minus119865(119910))(1 + 119886119910))119889119910 log119887119886 = ln 119886ln 119887 119877119871 can be written as

119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]

= 12 ln 2 intinfin0 ln (1 + 120572119871120574119909) 119891hL2 (119909) 119889119909= 1198861198711205742 ln 2 intinfin0 1 minus 119865hL2 (119909)1 + 119886119871120574119909 119889119909

(32)

Simply by using (27) 119865hL2 can be expressed as

119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)

By substituting (33) into (32)

119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903)sdot intinfin0

119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)

By defining 119906 = 119886119871120574119909 119868 can be written as follows

119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)

Using [74 (eq 11)] as 120574 rarr infin then 119868 can be approximated as

119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)

By substituting (36) into (34) then 119877infin119871 can be given by

119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)

Finally by substituting (37) and (31) into (29) then asymp-totic ergodic sum rate 119877infinsum can be expressed as

119877infinsum= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)

313 Numerical Results of SIMO-NOMA We consider twousers and their average power factors that providesum119871119894=1 119886119894 = 1are selected as 1198861 = 06 and 1198862 = 04 respectively Alsoin order to make a comparison between the performances


(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

Figure 6 Outage probability of MIMO-NOMA system versus SNRfor 119871 = 2 1198861 = 06 1198862 = 04 120574th1 = 1 120574th2 = 2 and 120574th = 5

2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2

Lower bound sum rateUpper bound sum rateConventional OMA

0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)

Figure 7 Ergodic sum rate of MIMO-NOMA system versus SNRfor 119871 = 2 1198861 = 06 1198862 = 04 120574th1 = 1 120574th2 = 2 120574th = 5 and(119898119873119903) = (2 2)of conventional OMA and the proposed NOMA in terms ofOP and ergodic sum rate over Nakagami-119898 fading channelsSNR threshold value of conventional OMA 120574th which verifies(12)sum119871119894=1 log2(1 + 120574th119894) = (12)log2(1 + 120574th) is used

Figure 6 shows the outage probability versus the systemSNR over different Nakagami m parameters In Figure 6 thesimulations verify exact analytical results and a better outageperformance at higher number of antennas is obtained

Figure 7 depicts the ergodic sum rates of mobile usersversus the system SNR It is observed that ergodic rate forthe first user is approximately constant over high SNR Thisis due to high power allocation for the first user such that it

considers the signal of the second user as noise while ergodicrate for the second user proportionally increases with SNRbecause of no interference with the first one Figures 6 and 7show that NOMA outperforms conventional OMA in termsof outage probability and ergodic sum rate respectively

4 Cooperative NOMA

Cooperative communication where the transmission be-tween the source and destination is maintained by the helpof one or multiple relays has received significant attention ofresearchers since it extends the coverage area and increasessystem capacity while reducing the performance deteriorat-ing effects of multipath fading [75 76] In cooperative com-munication systems relays transmit the received informationsignals to the related destinations by applying forwardingprotocols such as amplify-and-forward (AF) and decode-and-forward (DF) In addition in the last decade the relayscan be fundamentally categorized as half-duplex (HD) andfull-duplex (FD) according to relaying operation Differingfrom HD FD relay maintains the data reception and trans-mission process simultaneously in the same frequency bandand time slot [77] Thus FD relay can increase the spectralefficiency compared to its counterpart HD [78] Thereforethe combination of cooperative communication and NOMAhas been considered as a remarkable solution to furtherenhance the system efficiency of NOMA Accordingly in[79] a cooperative transmission schemewhere the userswithstronger channel conditions are considered as relays due totheir ability in the decoding information of other users inorder to assist the users with poor channel conditions hasbeen proposed to be implemented in NOMA In [80] byassuming the same scenario in [79] Kim et al proposed adevice-to-device aided cooperativeNOMAsystemwhere thedirect link is available between the BS and one user andan upper bound related to sum capacity scaling is derivedIn addition a new power allocation scheme is proposedto maximize the sum capacity On the other hand in [81]the authors analyze the performance of NOMA based onuser cooperation in which relaying is realized by one of theusers operating in FD mode to provide high throughput byapplying power allocation

However aforementioned user cooperation schemes aremore appropriate for short-range communications such asultrawideband and Bluetooth Therefore in order to furtherextend the coverage area and to exploit the advantages ofcooperation techniques the concept of cooperative com-munication where dedicated relays are used has also beeninvestigated in NOMA In this context in [82] a coordinatedtransmission protocol where a user communicates with BSdirectly while the other needs the help of a relay to receivethe transmitted information from the BS has been employedin NOMA scheme in order to improve the spectral efficiencyand OP analysis is conducted for frequency-flat block fadingchannels by using DF relaying as shown in Figure 8(a) In[83] the same scenario in [82] is considered and OP andasymptotic expressions are obtained in approximated closedforms for AF relaying networks Differing from [82] and[83] in [84] the authors proposed a cooperative relaying


1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

Figure 8 System model of cooperative NOMA downlink (a) Coordinated direct and relay transmission (b) A cooperative scheme withoutdirect link

system where two symbols transmitted from the BS to theuser by the help of a relay were combined at the BS by apply-ing NOMA concept The exact and asymptotic expressionsrelated to achievable average rate are derived in iid Rayleighfading channels and the results demonstrate that cooperativerelaying based on NOMA outperforms the conventional oneAlso the authors of [85] analyzed the same transmissionscheme in [84] over Rician fading channels In order tofurther improve the achievable rate of the system investigatedin [84] in [86] authors proposed a novel receiver schemewhere the transmitted symbols from the BS are combined atthe destination according toMRC technique and investigatedthe system performance in terms of ergodic sum rate and OPTheir results demonstrate that the proposed scheme achievesbetter performance than the one in [84] In addition Wanet al [87] investigated the same system in [86] by usingtwo DF relays and assuming no direct link for cooperationand analyzed the system performance in terms of achievablesum rate In [88] the authors investigate the performanceof NOMA over iid Rayleigh fading channels by employinga downlink cooperative network in which the BS transmitsthe superimposed information to the mobile users through arelay and also the direct link is consideredTheOP expressionof the related user is obtained in closed form and ergodic sumrate and asymptotic analyses are also maintained as perfor-mance metricsThe results show that the NOMA exhibits thesameperformance in terms of diversity orderwhen comparedto OMA by improving spectral efficiency and providing abetter user fairness Furthermore in [89] performance ofNOMA is investigated in relaying networkswithout the directlink over Nakagami-119898 fading environments for the networkgiven in Figure 8(b) where all nodes and mobile users areassumed to have a single antenna While closed-form OPexpressions and simple bounds are obtained ergodic sum rateand asymptotic analyses are also conducted Under the con-sideration of imperfect CSI the authors of [90] analyze theperformance of NOMA system investigated in [89] in termsof OPThey provide exact OP and lower bound expressions inclosed form and their results show that an error floor comesup due to the imperfect CSI at all SNR region Similar tothe scenario in [89] in [91] performance of NOMA with

fixed gain AF relaying is analyzed over Nakagami-119898 fadingchannels in case when the direct transmission also exists Forperformance criterion new closed-form expressions relatedto the exact and asymptotic OPs are obtained Moreover abuffer-aided cooperative technique where the relay transmitsand receives the information packets when source-relayand relay-destination links are in outage respectively hasbeen taken into account by researchers in order to furtherenhance the reliability of the relaying systems and increasethe system throughput [92] Accordingly in [93] the authorsproposed a cooperative NOMA system with buffer-aidedrelaying technique consisting of one source and two usersin which the stronger user is used as a buffer-aided relayDiffering from [93] Zhang et al [94] proposed a buffer-aidedNOMA relay network in which a dedicated relay was used toforward the information to two users and exact OP of thesystem was obtained in single integral form and lowerupperbounds were derived in closed forms In [95] for the samesystem in [94] an adaptive transmission scheme in whichthe working mode is adaptively chosen in each time slot isproposed to maximize the sum throughput of the consideredNOMA system

As can be seen from the aforementioned studies thepower allocation issue is vital for the performances of userdestinations In this context there are several studies thatfocus on power allocation strategies for cooperative NOMAin the literature [96ndash99] Accordingly in [96] the authorsproposed a novel two-stage power allocation scheme forcooperative NOMAwith direct link consisting of one sourceone relay and one user destination in order to improve sumrate andOP of the system In [97] Gau et al proposed a noveldynamic algorithm that selects the optimal relaying modeand determines the optimal power allocation for cooperativeNOMA where the BS communicates with two users via acouple of dedicated relays For the proposed approach newclosed-form expressions related to optimal power allocationwere derived In [98] the authors investigated a joint sub-carrier pairing and power allocation problem in cooperativeNOMA which consists of one BS and two users (one of theusers acts as a relay) Theoretical expressions related to joint


optimization approach are derived and superiority of the con-sidered algorithms is demonstrated by simulations In [99]in order to optimize the resource allocation for maximizingthe average sum-rate authors studied the performance ofa single-cell NOMA system consisting of multiple source-destination pairs and one OFDM AF relay

As well known from the literature diversity techniquesand using multiantenna strategies improve system perfor-mance significantly Therefore in [100] the same authorsof [88] consider using multiple antennas at the BS andmobile users and analyze the OP behavior of the networkover iid Rayleigh in case when the direct link does notexist They apply TAS and MRC techniques at the BS andmobile users respectively while the relay has single antennaand show that using multiple antennas improves the systemOP performance Additionally it is shown that NOMAprovides a better OP performance than OMA when thedistance between the BS and relay is sufficiently short In[101] OP performance of the same system investigated in[100] was analyzed for Nakagami-119898 channels in case thatfixed gain AF relay was used In [102] performance ofthe same system in [100] was investigated over Nakagami-119898 fading environments in the presence of imperfect CSIThe system OP was obtained in closed form and tightlowerupper bounds were provided for further insights In[103] the authors proposed an Alamouti space-time blockcoding scheme based on two-phase cooperative DF relayingfor NOMA and obtained closed-form expressions for bothOP and ergodic sum-rate In [104] the authors analyzedthe system performance of nonregenerative massive MIMONOMA relay network in case that SIC and maximum meansquare error SIC techniques were adopted at the receivers Inthe systemmultiple users and relays are equipped with singleantennawhile the BS hasmultiple antennas For performancemetrics system capacity and sum rate expressions werederived in closed forms and authors demonstrated that theconsidered system outperforms massive MIMO OMA

In addition to the aforementioned studies using multire-lays andor relay selection techniques in cooperative NOMAconcept are hot issues since using multiple relays improvesthe system performance significantly as already known fromstudies in the literature Therefore in [105] the authorsproposed a novel NOMA relaying system based on hybridrelaying scheme where some of relays adopted DF protocolwhile the others used AF for signal transmission consistingof two sources and one user destination For performancecomparison with the conventional systems channel capacityand average system throughput were investigated and theproposed system was shown to achieve larger sum channelcapacity and average system throughput than the conven-tional systems Gendia et al [106] investigated a cooperativeNOMAwithmultiple relays in which all users except the userto whom the information signal would be transmitted wereconsidered as relays Comparisons with the other equivalentNOMA systems were done in terms of user-average bit errorrate ergodic sum rate and fairness level by simulations In[107] OP performance of a NOMA system where the BStransmits the information signals to two users by using tworelays was analyzed when cooperative and TDMA schemes

were applied for transmission The authors demonstratedthat cooperative scheme outperforms TDMA one in termsof OP Shin et al [108] proposed a novel multiple-relay-aided uplink NOMA scheme for multicell cellular networkswhere the BS was equipped with multiantenna and lim-ited by user numbers in each cell Moreover the feasibil-ity conditions of the considered system were investigatedBesides multirelaying strategies relay selection techniqueswere also investigated Accordingly in [109] the authorsinvestigated the impact of two relay selection techniqueson the performance of cooperative NOMA scheme withoutdirect link According to the results with the relay selectionstrategies significant performance gain in terms of OP hasbeen achieved in NOMA compared to counterpart OMAIn [110] performance of a cooperative NOMA with the bestrelay selection technique was analyzed in terms of averagerate The considered relay network consists of one BS oneuser and multiple relays and the direct link is also availableAuthors demonstrated that the significant performance gaincan be achieved by increasing the number of relays whencompared to OMA one Deng et al [111] investigated thejoint user and relay selection problem in cooperative NOMArelay networks where multiple source users communicatewith two destination users via multiple AF relays In orderto improve the system performance the authors proposed anoptimal relay selection scheme where the best user-relay pairwas selected In [112] performance of cooperative NOMAwith AF relays was analyzed by using partial relay selectiontechnique In the network communication between the BSand two users was realized by selected relay and also directlink between the BS and users was taken into account Whileauthors provided closed-form OP and sum rate expressionsasymptotic analysis at high SNR regionwas also conducted Itis shown that the performance can be improved by increasingthe number of relays but the same performance gain isobtained at high SNR region for more than two relays Inaddition to above studies Yang et al [113] proposed a noveltwo-stage relay selection scheme for NOMA networks whichconsists of one source multiple DFAF relays and two usersThe considered selection strategy relies on satisfying the QoSof one user in the first stage while maximizing the rate of theother user in the second stage

Besides that NOMA improves the system spectral effi-ciency energy harvesting (EH) technology has also gainedmuch attention because of its ability in increasing energyefficiency Therefore simultaneous wireless information andpower transfer (SWIPT) which uses radio-frequency signalsto enable self-sustainable communication was proposedby Varshney [114] and regarded as an efficient solutionover all emerging EH techniques due to the limitation ofenvironmental energy sources In this context many studiescombining cooperative NOMA with EH technologies wereconducted in the literature [115ndash123] In order to exploitthe energy and spectral efficiency features of SWIPT andNOMA Liu et al [115] studied the application of SWIPTto cooperative NOMA where users nearby to the BS act asEH relays In addition different user selection schemes wereproposed in order to determine which nearby user would


cooperate with far user and OP and throughput expressionsrelated to the selection schemes were obtained in closedforms In [116] a transceiver design problem in cooperativeNOMA with SWIPT was studied In the considered systemthe stronger user acting as a relay and BS were equippedwith multiple antennas while the other user had only singleantenna Optimal transmitter beamforming and ZF-basedtransmitter beamforming structures were proposed to maxi-mize the rate of relay node In [117 118] the authors analyzedOP performance of NOMA-SWIPT relay networks over iidRayleigh andNakagami-119898 fading environments respectivelyDiffering from the previous works authors considered thatthe BS and multiple users were equipped with multipleantennas and communication between the BS and users wasestablished only via an EH relay They considered that TASand MRC techniques were employed at the BS and usersrespectively and proved closed-form OP expressions forperformance criterion Similar to [115] in [119] a best-nearbest-far user selection scheme was proposed for a cellularcooperative NOMA-SWIPT system and OP analysis wasconducted to demonstrate the superiority of the proposedscheme In [120] the authors investigated TAS schemes inMISO-NOMA system based on SWIPT technique wherethe BS with multiple antennas communicates with two userswith single antenna and the stronger user is also used as anEH relay in terms of OP and conducted diversity analysisThe impact of power allocation on cooperative NOMA-SWIPT networks was investigated by Yang et al [121] Forperformance comparisons with existing works OP and highSNR analyses were conducted and the proposed system wasshown to improve the OP performance significantly In [122]authors analyzedOPperformance of a downlinkNOMAwithEH technique consisting of one BS and two users Whilethe BS and one of the users which was used as a relay wereequipped with multiple antennas the other user far fromthe BS had only single antenna Closed-form OP expressionswere derived for AF DF and quantize-map-forward relayingprotocols over iid Rayleigh fading channels Xu et al [123]investigated joint beamforming and power splitting controlproblem in NOMA-SWIPT system studied in [120] In orderto maximize the rate of the relay user power splitting ratioand beamforming vectors were optimized Moreover SISO-NOMA system was also studied

While most of the prior works on the cooperative NOMAsystems have focused on the use of HD relaying techniquethere are also some studies that consider using FD relayingtechnique in order to further increase spectral efficiency ofNOMA systems In [124] performance of cooperative SISO-NOMA relaying system consisting of one BS and two userswas investigated The user near BS was considered as anFD relay which employed compress-and-forward protocolfor poor user Authors provided theoretical expressions ofachievable rate region based on the noisy network codingZhong and Zhang [125] proposed using FD relay instead ofHD for the investigated system in [82] where one user cancommunicate with the BS directly while the other needs arelay cooperation In order to demonstrate the superiorityof using FD relay authors provided exact OP and ergodic

sum capacity expressions In [126] OP performance ofcooperative NOMA system in which the strong user helpsthe other by acting as an FD-DF relay was analyzed in termsof OP Moreover an adaptive multiple access scheme thatselects access mode between proposed NOMA conventionalNOMA and OMA was investigated in order to furtherenhance the system OP Differing from [126] authors of[127] investigated optimizing the maximum achievable rateregion of cooperative NOMA system in which the BS alsooperated in FD mode Therefore the authors proposed threeapproaches for maximization problem such as fixed trans-mit power nonfixed transmit power and transmit powercorrupted by error vector magnitude In [128] a hybridhalffull-duplex relaying scheme was proposed to implementin cooperative NOMA and power allocation problem wasinvestigated in terms of achievable rate In addition NOMAwith HD and NOMA with FD systems were separatelyinvestigated by providing closed-form optimal expressionsrelated to powers Hybrid NOMA scheme was shown tooutperform the other NOMA schemes The same hybridNOMA system in [128] was also investigated by Yue et al[129] in terms of OP ergodic rate and energy efficiency Inaddition the authors also investigated the system when thedirect link was not available between the BS and poor user In[130] OP and ergodic sum rate performance of a cooperativeNOMA system with FD relaying was investigated in case thatthe direct link was not availableTheoretical expressions werederived in closed forms Moreover in order to maximize theminimum achievable rate optimization problem for powerallocation was also studied

In the next section we provide an overview of thecooperative NOMA system which is investigated in [89] toprovide an example of cooperative NOMA

41 Performance Analysis of Cooperative NOMA Consider adual hop relay network based on downlinkNOMAas given inFigure 8(b)which consists of one BS (119878) oneAFHDrelay (119877)and 119871 mobile users In the network all nodes are equippedwith a single antenna and direct links between the BS andmobile users can not be established due to the poor channelconditions andor the mobile users are out of the range ofBS We assume that all channel links are subjected to flatNakagami-119898 fading Therefore channel coefficients of 119878-119877and 119877-119880119897 are denoted by ℎ119878119877 and ℎ119877119880119897 with the correspondingsquared means 119864[|ℎ119878119877|2] = Ω119878119877 and 119864[|ℎ119877119880|2] = Ω119877119880respectively where 119897 = 1 119871 In order to process NOMAconcept without loss of generality we consider ordering thechannel gains of 119871 users as |ℎ1198771198801 |2 le |ℎ1198771198802 |2 le sdot sdot sdot le |ℎ119877119880119871 |2In the first phase the superimposed signal 119904 given in (1) istransmitted from the BS to the relay and then the receivedsignal at 119877 can be modeled as

119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)

where 119899119877 is the complex additive Gaussian noise at 119877 anddistributed as CN(0 1205902119877)


In the second phase after the relay applies AF protocolthe received signal at 119880119897 can be written as

119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)

where 119899119880119897 is the complex additive Gaussian noise at 119880119897 anddistributed as CN(0 1205902119880119897) and 119875119877 is the transmit power at 119877119866 denotes the amplifying factor and can be chosen as

119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)

In order to provide notational simplicity we assume that 119875119904 =119875119877 = 119875 1205902119877 = 1205902119880119897 = 1205902 In addition 120574 = 1198751205902 denotes theaverage SNR

After the SIC process implemented at the receiver of 119880119897the SINR for the 119897th user can be obtained as [89]

120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)

whereΨ119897 = sum119871119894=119897+1 119886119894 Then the received SINR by the 119871th usercan be simply expressed as [89]

120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)

Since channel parameters are Nakagami-119898 distributed|ℎ119883|2 squared envelope of any unordered link 119883 where 119883 isin119878119877 119877119880119897 follows Gamma distribution with CDF

119865|ℎ119883|2 (119909) = 120574 (119898119883 119909 (119898119883Ω119883))Γ (119898119883)= 1 minus 119890minus119909(119898119883Ω119883)119898119883minus1sum

119899=0

(119898119883Ω119883119909)119899 1119899

(44)

In (44) right hand side of the equation is obtainedby using the series expansion form of incomplete Gammafunction [72 eq (83526)] and119898119883 denotes the Nakagami-119898parameter belonging to the link119883

Furthermore the PDF and CDF of the ordered squaredenvelope |ℎ119883|2 can be written by using (44) as [89]

119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896 119862119871minus119897119896 119891|ℎ119883|2 (119909) [119865|ℎ119883|2 (119909)]119897+119896minus1 (45)

119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)

where 119876 = 119871(119871 minus 119897)(119897 minus 1) and 119862119870119896 = ( 119870119896 ) represents thebinomial combination

411 Outage Probability of Cooperative NOMA By using theapproach given in [89] the OP of the 119897th user can be writtenas119875out119897 = 1

minus Pr(10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162 gt 120578lowast119897 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 gt 120578lowast119897 (1 + 12057410038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162)120574 (10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162 minus 120578lowast119897 ) )

(47)

The OP expression given in (47) can be mathematicallyrewritten as

119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691

+ intinfin120578lowast119897

119891|ℎ119877119880119897 |2 (119909) 119865|ℎ119878119877|2 (120578lowast119897 (1 + 120574119909)120574 (119909 minus 120578lowast119897) ) 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198692

(48)

Then by using (44) and (45) 1198692 can be calculated as

1198692 = 1 minus 1198691 minus 119876119871minus119897sum119896=0

119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896

1119899sdot intinfin120578lowast119897

119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593

times 119890minus(120578lowast119897 (1+120574119909)119898119878119877120574Ω119878119877(119909minus120578lowast119897 )) (120578lowast119897 (1 + 120574119909)119898119878119877120574Ω119878119877 (119909 minus 120578lowast119897 ) )119899 119889119909

(49)

In (49) by using binomial expansion [72 eq (1111)] 120593can be obtained in closed form as

120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0

119862119897+119896minus1119905 (minus1)119905sdot 119890minus119909(119898119877119880119905Ω119877119880)119909119901120599119901 (119905 119898119877119880)

(50)

where 120599119886(119887 119892119888) denotes multinomial coefficient given in (26)Furthermore if we substitute derivative of (44) and (50)

into (49) and then by using some algebraic manipulations 1198692can be obtained in closed form Then by substituting 1198692 into(48) we can obtain the OP of 119897th user in closed form as

119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902

(minus1)119905+119896 119862119871minus119898119896 119862119897+119896minus1119905 119862119899119894 119862119901+119898119877119880minus1119902

sdot 120599119901 (119905 119898119877119880)119899Γ (119898119877119880) times (119898119877119880Ω119877119880)(2119898119877119880minus119902+119894minus1)2

sdot 120588(119894+119902+1)2(119905 + 1)(119902minus119894+1)2 (119898119878119877Ω119878119877)119899minus119894 120578lowast119899minus119894+119901+119898119877119880minus1minus119902119897

times 119890minus(120578lowast119897 119898119877119880(119905+1)Ω119877119880)119890minus(120578lowast119897 119898119878119877Ω119878119877) times 2times 119870119902minus119894+1(2radic120588119898119877119880 (119905 + 1)Ω119877119880 )

(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2

U1 TheoU2 TheoU3 Theo

Dashed and solid lineSimulation

Figure 9 Outage probability of NOMA versus SNR in case 119889119878119877 =05 and different Nakagami-119898 parameters

where the binomial expansion [72 eq (1111)] and the integralrepresentation in [72 eq (34719)] are used for the deriva-tion In (51) 120588 = 120578lowast119897 119898119878119877(1 + 120574120578lowast119897 )120574Ω119878119877 and sum119896119899119905119901119894119902 equivsum119871minus119897119896=0sum119898119878119877minus1119899=0 sum119897+119896minus1119905=0 sum119905(119898119877119880minus1)119901=0 sum119899119894=0sum119901+119898119877119880minus1119902=0 (sdot) notations areused to provide a short hand representation 119870V(sdot) denotesthe Vth ordermodified Bessel function of second kind [72 eq(84071)]TheOP expression in (51) is in a simpler formwhencompared to equivalent representations in the literature

412 Numerical Results of Cooperative NOMA In this sec-tion we provide numerical examples of the provided theoret-ical results obtained for the OP of NOMA and validate themby Monte Carlo simulations We assume that the distancesbetween the BS and the mobile users are normalized to oneso that Ω119878119877 = 119889minus120581119878119877 and Ω119877119880 = (1 minus 119889119878119877)minus120581 where 120581 = 3 is thepath loss exponent In all figures 119871 = 3 users and 1198861 = 121198862 = 13 1198863 = 16 120574th1 = 09 120574th2 = 15 120574th3 = 2 parametershave been used

In Figure 9 we present the OP performance of NOMAversus SNR As can be seen from the figure theoreticalresults are well matched with simulations In addition OPperformances of the second and third users are better thanthat of the first user and also the same at high SNR regionMoreover as the channel parameters increase the OPs of allusers increase

Figure 10 plots the OP performance of NOMA versusthe normalized distance between the BS and the relay Asseen from the figure while the optimal relay location of theuser with the strongest channel condition is near the BSthe other usersrsquo optimal relay locations are far from the BSsince the userwithworse channel has higher power allocationcoefficient

mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR



Figure 10 Outage probability of NOMA versus 119889119878119877 in case 120574 =20 dB and different Nakagami-119898 parameters

5 Practical Implementation Aspects

In the literature power allocation and user clustering aregenerally considered as the main problems in NOMA sys-tems and several strategies are proposed to provide efficientsolutions to these issues As also considered in [131ndash133]these problems are formulated as an optimization problemand the corresponding solution procedures are also pro-posed Besides these studies such as [54 134 135] pro-pose approaches that are suitable to real-time applicationsImperfect CSI is assumed in the corresponding system mod-els However real-time implementation challenges are notconsidered in most of the studies and the associated imple-mentation design which may provide effective solutions tothese challenges is not mentioned In this section thesechallenges are highlighted and important design componentsare explained In the following subsection some studies thatinclude real-time implementation of NOMA are mentionedand challenges of such real-time implementations will bedetailed

51 Related Works The number of studies that target real-time implementation of NOMA is very limited To thebest of the authorsrsquo knowledge beyond three main studiessuch content is not included in any other study at thetime of preparation of this paper In [136] single user-(SU-) MIMO is integrated to downlink and uplink NOMAand extensive computer simulations provide detailed rateevaluation between OMA and NOMA methods Moreovera comprehensive testbed is created to experiment downlinkNOMA with SU-MIMO setup under real-time impairmentsTurbo encoding is also utilized in the implementation and aSIC decoding structure which also includes turbo decodingand MIMO detection is proposed Due to usage of a wider


bandwidth NOMA provides data rate improvement of 61in this experiment scenario Reference [137] targets improperpower allocation issue which is seen as a performancelimiting factor in conventional NOMAmodels By exploitingthe physical-layer network coding (PNC) in NOMA theauthors propose network-coded multiple access (NCMA)Adaptation of PNC provides an additional transmissiondimension and the received signals via two different dimen-sions increase the throughput significantly when comparedto the conventional NOMA systems It is validated by experi-mental results that the proposed NCMA variations providenoticeable performance improvements under the power-balanced or near power-balanced scenarios As the finalstudy in [138] software defined radio (SDR) implementationof downlink NOMA is realized to evaluate the performancedifferences betweenNOMAandOMA techniquesMoreoverprotocol stack of LTE is modified to propose a suitableprotocol stack for NOMA Besides thesemultilayermodifica-tions detailed experiments are also carried outMeasurementresults demonstrate the performance advantages of NOMAover OMA

Since superposition coding and NOMA are very similarin context studies on superposition coding also contain thesame valuable outcomes In [139] advantages of superpo-sition coding over time division multiplexing approach interms of improving the quality of the poor links are validatedvia an SDR platform Accordingly the packet error rate ismeasured and need of a joint code optimization is shownMoreover an improved packet error rate performance that isobtained with superposition coding when compared to theresults of time division multiplexing utilization is demon-strated Similarly in [140] the authors propose a schedulerbased on superposition coding and it is demonstrated thatsuperposition coding based resource allocation can providea data rate improvement up to 25 when compared to theorthogonal access techniques

These studies provide significant insights about real-time implementation aspects of NOMA However severalpractical challenges are not yet considered in available works

52 Implementation Challenges Practical implementationchallenges of NOMA are considered in some surveys In[141] the authors focus on multicell NOMA and the relateddesign issues in the environment in the presence of a strongintercell interference (ICI) Since future wireless networksare expected to be densely deployed NOMA techniqueis considered to be a candidate technique ICI should beconsidered due to the potential effects of interference betweenadjacent BSs Theoretical details of single-cell and multicellNOMA solutions are detailed and the capacity analysis isprovided Moreover some major implementation issues arehighlighted Hardware complexity and error propagationissues of SIC implementation are detailed Then the impor-tance of CSI is highlighted and the damaging effects ofimperfect CSI on the performance of NOMA are explainedMultiuser power allocation and clustering are also empha-sized To limit ICI between adjacent cells the authors proposethat users should be clustered properly and power allocationmechanism should be operated efficiently Integration of

fractional frequency reuse with NOMA is also consideredas a major challenge and such integration should be allo-cated properly to obtain significant gains Lastly security ishighlighted as another challenge and the implementationof physical layer security techniques is seen as a difficulttask As demonstrated with computer simulations targetingto demonstrate the performance limitation of interferenceproper ICI cancellation is very significant to obtain a robustperformance in multicell NOMA systems

In [142] challenges of downlink and uplink NOMAimplementations and their implementation differences areexplained As the first challenge implementation complex-ity is highlighted where it is pointed out that downlinkNOMA brings more complexity because of the utilizationof iterative detection procedures multiple times at multiplereceive nodes when compared to the central receiver nodeas applicable in uplink NOMA systems Secondly intra-cellintracluster interference is stated as a crucial issue forboth systems due to interference effects between users Asthe third challenge SIC receivers which are implementeddifferently in downlink and uplink cases are consideredLastly ICI is elaborated It is shown that ICI is more effectivein uplink case and could limit performance significantlyHowever it is not that effective in downlink case and theobserved performance degradation is comparable to that ofobserved in OMA systems Moreover some critical pointsare listed Firstly propagation errors in SIC receivers arementioned as an important performance limiting factor andinterference cancellation schemes are considered necessaryto improve these effects Secondly multicell NOMA is high-lighted where obtaining the same single-cell NOMA gainsover OMA in multicell scenarios becomes challenging Usergroupingscheduling power allocation and ICI mitigationare also considered as crucial items to obtain an improvedperformance Besides these implementation issues integra-tion of NOMA-based wireless backhauling to small cells andcooperative schemes are highlighted as necessary precautionsto increase NOMArsquos applicability in real-time

In [143] implementation issues of NOMA are discussedand listed Decoding complexity error propagation anderrors that faced power balanced scenarios are also men-tioned As less considered issues quantization errors that leadto degradation of weak signals power allocation complexitydue to difficulty of optimization of proper power levels to allusers residual timing offset that leads to synchronization lossand error increment are highlighted Furthermore signalingand processing overhead due to learning procedure of CSI arealso listed as a critical inefficiency source

Some of the main problems that are mentioned in thesestudies and other issues that are not yet discussed in theliterature will be listed and detailed below

(1) Hardware ComplexityWhen compared to OMA NOMAcauses increased complexity on the hardware side due to SICimplementation To obtain the usersrsquo symbols that transmitor receive with lower power symbols high power symbolsare required to be estimated first with the SIC detector If thenumber of users especially is high or fast signal transmissionis required the SIC procedure that is used multiple times


in addition to the detection delay could cause importantlimitations for battery-limited devices Since longer batterylife is desired in consumer electronics implementation ofNOMA particularly in dense networks could be ineffi-cient This issue may limit usage of NOMA Effective userclustering and power allocation are crucial to alleviate thisproblem

(2) Error Propagation in SIC Implementation According tothe main principle of NOMA on the receiver side theuser with better channel conditions is estimated first viaSIC detection Therefore the success of the reception ofmain signal depends on successful estimation of the highpower signals Since channel and hardware impairmentsare effective in the reception process SIC detection canbe negatively affected It is not straightforward for NOMAsystems to ideally estimate channel due to the presence ofcarrier frequency offset (CFO) timing offset (TO) and otherhardware related impairments Thus erroneous detectionand error propagation are probable in the SIC detectionprocess To overcome this and to improve the transmissionquality more robust solutions are necessary Rather thanchanging the main detector components improving theestimation quality of mentioned impairments is a moreeffective approach to obtain a practical performance gain

(3) Optimal Pilot Allocation Since multiple signals aretransmitted in an overlapped fashion interference emergesand error performance starts to degrade in NOMA whencompared to OMA systems It is a clear fact that perfect ornear-perfect CSI is amust to obtain a good performance Pilotpositions and the number of allocated pilots are importantdesign considerations in NOMA implementation These arecritical even in OMA systems due to uncertain channelcharacteristics in wireless communication environmentsHowever due to the inherent interference optimal pilotallocation is more critical for NOMA systems and carefuldesign is required Therefore channel characteristics shouldbe tracked efficiently and accurately to allocate sufficientnumber of pilots at proper positions which could result ingood error performance in NOMA systems

(4) Instantaneous CSI Requirement Besides pilot allocationissues in NOMA implementations another basic CSI estima-tion issue exists in this process Allocation of a previouslyallocated frequency band to a secondary user brings a seriousproblem CSI for the transmission of this user should beestimated with orthogonal transmissions This inevitablyblocks the transmission of main user and results in anunfavorable situation It is not clear whether this issue can betolerated or not in real-time Moreover in dense networksinstantaneous band allocation may be required and in thesecases this issue may become more critical Effective andpractical solution to this problem is very important for thefuture of NOMA systems As a road map suggestion pilotcontamination problem in massive MIMO systems may beconsidered and corresponding solutions like [144] may beapplied to NOMA systems However differences between thelogics of these techniques should also be taken into account

(5) Carrier Frequency Offset and Timing Offset EstimationDue to the nature of wireless devices CFO and TO emergefrequently during communication Low-quality clocks espe-cially that are included in such devices cause significant CFOand TO thus leading to a significantly degraded transmis-sion quality Usage of multicarrier waveforms like OFDMrenders robust CFO and TO estimation and provides the nec-essary correction In the point-to-point OMA transmissionsjoint estimation of CFO and TO is quite straightforwarddue to distinguishability of received signals Even in thesecases these impairments could cause serious performancedegradation However this is not valid for NOMA becauseof the reception of signals in an overlapped fashion Thisissue has not yet been considered in the literature Effectivesolutions and practical approaches are required to guaranteea good transmission quality in NOMA Highly accuratesynchronization support to devices can overcome such dis-turbances however lower cost expectations prevent sucha solution Therefore particularly in uplink transmissionsdistinguishability of overlapped signals should be achieved

53 Lessons Learned In order to capture the full set ofadvantages of NOMA in real-time that are validated inthe theoretical studies possible major challenges should beinvestigated and a comprehensive implementation strategythat overcomes these challenges should be determinedThereare few studies in the literature that list these challenges butthere are some challenges that have not yet been consideredFrom this perspective in this section previously mentionedchallenges are evaluated and important ones are given withother undetected major challenges These also provide top-ics that deserve attention from the researchers who targetimproving NOMArsquos applicability

6 Conclusion

NOMA schemes are proposed to improve the efficient usageof limited network sources OMA based approaches that usetime frequency or code domain in an orthogonal mannercannot effectively utilize radio resources limiting the numberof users that can be served simultaneously In order toovercome such drawbacks and to increase themultiple accessefficiency NOMA technique has been recently proposedAccordingly users are separated in the power domain Such apower-domain based multiple access scheme provides effec-tive throughput improvements depending on the channelconditions

In OMA differences between channels and conditionsof users cannot be effectively exploited It is quite possiblefor a user to be assigned with a large frequency bandwhile experiencing deteriorating channel conditions Suchuser cases limit the effectiveness of OMA based approachesHowever according to the NOMA principle other userswho may be experiencing better channel conditions canuse these bands and increase their throughput Moreovercorresponding users who are the primary users of these bandscontinue to use these bands In such deployments power levelof users is selected in a way to target a certain maximumerror rate Furthermore the performance of NOMA can


be significantly improved using MIMO and cooperativecommunication techniques

In this paper we provide a unified model system modelfor NOMA including MIMO and cooperative communi-cation scenarios Implementation aspects and related openissues are detailed A comprehensive literature survey is alsogiven to provide an overview of the state-of-the-art

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

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[2] J G Andrews S Buzzi and W Choi ldquoWhat will 5G berdquo IEEEJournal on Selected Areas in Communications vol 32 no 6 pp1065ndash1082 2014

[3] T Rappaport S Sun R Mayzus et al ldquoMillimeter wave mobilecommunications for 5G cellular it will workrdquo IEEE Access vol1 pp 335ndash349 2013

[4] E G Larsson O Edfors F Tufvesson and T L MarzettaldquoMassive MIMO for next generation wireless systemsrdquo IEEECommunications Magazine vol 52 no 2 pp 186ndash195 2014

[5] M Kamel W Hamouda and A Youssef ldquoUltra-dense net-works a surveyrdquo IEEECommunications SurveysampTutorials vol18 no 4 pp 2522ndash2545 2016

[6] K Higuchi and Y Kishiyama ldquoNon-orthogonal access withsuccessive interference cancellation for future radio accessrdquo inProceedings of APWCS 2012 Kyoto Japan 2012

[7] Q C Li H Niu A T Papathanassiou and GWu ldquo5G networkcapacity Key elements and technologiesrdquo IEEE Vehicular Tech-nology Magazine vol 9 no 1 pp 71ndash78 2014

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[9] Z Yuan G Yu and W Li ldquoMulti-User Shared Access for 5GrdquoTelecommunications Network Technology vol 5 no 5 pp 28ndash30 May 2015

[10] H Nikopour and H Baligh ldquoSparse code multiple accessrdquo inProceedings of the IEEE 24th Annual International SymposiumonPersonal Indoor andMobile Radio Communications (PIMRCrsquo13) pp 332ndash336 IEEE London UK September 2013

[11] R Hoshyar F P Wathan and R Tafazolli ldquoNovel low-densitysignature for synchronous CDMA systems over AWGN chan-nelrdquo IEEE Transactions on Signal Processing vol 56 no 4 pp1616ndash1626 2008

[12] J Zeng D Kong X Su L Rong and X Xu ldquoOn theperformance of pattern division multiple access in 5G systemsrdquoin Proceedings of the 8th International Conference on WirelessCommunications and Signal Processing WCSP 2016 pp 1ndash5Yangzhou China October 2016

[13] J Huang K Peng C Pan F Yang and H Jin ldquoScalable videobroadcasting using bit division multiplexingrdquo IEEE Transac-tions on Broadcasting vol 60 no 4 pp 701ndash706 2014

[14] L Dai B Wang Y Yuan S Han C I and Z Wang ldquoNon-orthogonal multiple access for 5G solutions challenges oppor-tunities and future research trendsrdquo IEEE CommunicationsMagazine vol 53 no 9 pp 74ndash81 2015

[15] ldquoFramework and overall objectives of the future development ofIMT for 2020 and beyondrdquo Tech Rep ITU-R M2083-0 2015httpwwwituintITU-R

[16] S Hao J Zeng X Su and L Rong ldquoApplication scenarios ofnovel multiple access (NMA) technologies for 5Grdquo in Advancesin Intelligent Systems and Computing vol 570 pp 1029ndash1033Springer Cham Switzerland 2017

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[113] Z Yang Z Ding Y Wu and P Fan ldquoNovel Relay SelectionStrategies for CooperativeNOMArdquo IEEETransactions onVehic-ular Technology vol 66 no 11 pp 10114ndash10123 2017

[114] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008

[115] Y Liu Z Ding M Elkashlan and H V Poor ldquoCooperativeNon-orthogonal Multiple Access with Simultaneous WirelessInformation and Power Transferrdquo IEEE Journal on SelectedAreas in Communications vol 34 no 4 pp 938ndash953 2016

[116] R Sun Y Wang X Wang and Y Zhang ldquoTransceiver designfor cooperative non-orthogonal multiple access systems withwireless energy transferrdquo IET Communications vol 10 no 15pp 1947ndash1955 2016

[117] Y Zhang and J Ge ldquoPerformance analysis for non-orthogonalmultiple access in energy harvesting relaying networksrdquo IETCommunications vol 11 no 11 pp 1768ndash1774 2017

[118] W Han J Ge and J Men ldquoPerformance analysis for NOMAenergy harvesting relaying networks with transmit antennaselection and maximal-ratio combining over nakagami-m fad-ingrdquo IET Communications vol 10 no 18 pp 2687ndash2693 2016

[119] N T Do D B Da Costa T Q Duong and B An ldquoA BNBFUser Selection Scheme for NOMA-Based Cooperative RelayingSystems with SWIPTrdquo IEEE Communications Letters vol 21 no3 pp 664ndash667 2017

[120] N T Do D Benevides Da Costa T Q Duong and B AnldquoTransmit antenna selection schemes for MISO-NOMA coop-erative downlink transmissions with hybrid SWIPT protocolrdquoin Proceedings of the 2017 IEEE International Conference onCommunications ICC 2017 France May 2017

[121] Z Yang Z Ding P Fan and N Al-Dhahir ldquoThe Impact ofPower Allocation on Cooperative Non-orthogonal MultipleAccess Networks with SWIPTrdquo IEEE Transactions on WirelessCommunications vol 16 no 7 pp 4332ndash4343 2017

[122] M Ashraf A Shahid J W Jang and K-G Lee ldquoEnergy Har-vesting Non-Orthogonal Multiple Access System with Multi-Antenna Relay and Base Stationrdquo IEEE Access vol 5 pp 17660ndash17670 2017

[123] Y Xu C Shen Z Ding et al ldquoJoint beamforming and power-splitting control in downlink cooperative SWIPT NOMA sys-temsrdquo IEEE Transactions on Signal Processing vol 65 no 18 pp4874ndash4886 2017

[124] J So and Y Sung ldquoImproving Non-Orthogonal Multiple Accessby Forming Relaying Broadcast Channelsrdquo IEEE Communica-tions Letters vol 20 no 9 pp 1816ndash1819 2016

[125] C Zhong and Z Zhang ldquoNon-Orthogonal Multiple AccesswithCooperative Full-Duplex Relayingrdquo IEEECommunicationsLetters vol 20 no 12 pp 2478ndash2481 2016

[126] Z Zhang Z Ma M Xiao Z Ding and P Fan ldquoFull-duplexdevice-to-device-aided cooperative nonorthogonal multipleaccessrdquo IEEE Transactions on Vehicular Technology vol 66 no5 pp 4467ndash4471 2017

[127] H Huang J Xiong J Yang G Gui and H Sari ldquoRate RegionAnalysis in a Full-Duplex-Aided Cooperative NonorthogonalMultiple-Access Systemrdquo IEEE Access vol 5 pp 17869ndash178802017

[128] G Liu X Chen Z Ding Z Ma and F R Yu ldquoHybrid Half-DuplexFull-Duplex Cooperative Non-Orthogonal MultipleAccessWith Transmit Power Adaptationrdquo IEEE Transactions onWireless Communications vol 17 no 1 pp 506ndash519 2018

[129] X Yue Y Liu S Kang A Nallanathan and Z Ding ldquoExploitingFullHalf-Duplex User Relaying in NOMA Systemsrdquo IEEETransactions on Communications vol 66 no 2 pp 560ndash5752018

[130] L Zhang J Liu M Xiao G Wu Y-C Liang and S LildquoPerformance Analysis and Optimization in Downlink NOMASystems with Cooperative Full-Duplex Relayingrdquo IEEE Journal


on Selected Areas in Communications vol 35 no 10 pp 2398ndash2412 2017

[131] S Timotheou and I Krikidis ldquoFairness for Non-OrthogonalMultiple Access in 5G Systemsrdquo IEEE Signal Processing Lettersvol 22 no 10 pp 1647ndash1651 2015

[132] M-R Hojeij J Farah C A Nour and C DouillardldquoResource allocation in downlink non-orthogonal multipleaccess (NOMA) for future radio accessrdquo in Proceedings of the81st IEEE Vehicular Technology Conference VTC Spring 2015UK May 2015

[133] F Liu P Mahonen and M Petrova ldquoProportional fairness-based user pairing and power allocation for non-orthogonalmultiple accessrdquo in Proceedings of the 26th IEEE Annual Inter-national Symposium on Personal Indoor and Mobile RadioCommunications PIMRC 2015 pp 1127ndash1131 China September2015

[134] F Fang H Zhang J Cheng and V C M Leung ldquoEnergy-efficient resource scheduling forNOMA systemswith imperfectchannel state informationrdquo in Proceedings of the 2017 IEEEInternational Conference on Communications ICC 2017 FranceMay 2017

[135] Z Yang Z Ding P Fan and G K Karagiannidis ldquoOn thePerformance of Non-orthogonal Multiple Access SystemsWithPartial Channel Informationrdquo IEEE Transactions on Communi-cations vol 64 no 2 pp 654ndash667 2016

[136] F-L Luo and C Zhang Non-Orthogonal Multiple Access(NOMA) Concept and Design Wiley-IEEE Press 2016

[137] H Pan L Lu and S C Liew ldquoPractical Power-Balanced Non-Orthogonal Multiple Accessrdquo IEEE Journal on Selected Areas inCommunications vol 35 no 10 pp 2312ndash2327 2017

[138] X Wei H Liu Z Geng et al ldquoSoftware Defined RadioImplementation of a Non-Orthogonal Multiple Access SystemTowards 5Grdquo IEEE Access vol 4 pp 9604ndash9613 2016

[139] S Vanka S Srinivasa andM Haenggi ldquoA practical approach tostrengthen vulnerable downlinks using superposition codingrdquoin Proceedings of the 2012 IEEE International Conference onCommunications ICC 2012 pp 3763ndash3768 Canada June 2012

[140] P Vizi S Vanka S Srinivasa M Haenggi and Z GongldquoScheduling using Superposition Coding Design and softwareradio implementationrdquo in Proceedings of the 2011 IEEE Radioand Wireless Symposium RWS 2011 pp 154ndash157 USA January2011

[141] W ShinMVaezi B LeeD J Love J Lee andHV Poor ldquoNon-Orthogonal Multiple Access in Multi-Cell Networks TheoryPerformance and Practical Challengesrdquo IEEE CommunicationsMagazine vol 55 no 10 pp 176ndash183 2017

[142] H Tabassum M S Ali E Hossain M J Hossain and DI Kim ldquoNon-orthogonal multiple access (NOMA) in cellularuplink and downlink Challenges and enabling techniquesrdquohttparxivorgabs160805783

[143] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-Domain Non-Orthogonal Multiple Access (NOMA) in5G Systems Potentials and Challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017

[144] J Jose A Ashikhmin T L Marzetta and S Vishwanath ldquoPilotcontamination and precoding inmulti-cell TDD systemsrdquo IEEETransactions on Wireless Communications vol 10 no 8 pp2640ndash2651 2011

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either a specific time slot frequency band or code in order toavoid multiple access interference The previous generationsof networks have employedOMA schemes such as frequencydivision multiple access (FDMA) of first generation (1G)time division multiple access (TDMA) of 2G code divisionmultiple access (CDMA) of 3G and orthogonal frequencydivision multiple access (OFDMA) of 4G In NOMA multi-ple users can utilize nonorthogonal resources concurrently byyielding a high spectral efficiency while allowing some degreeof multiple access interference at receivers [6 7]

In general NOMA schemes can be classified into twotypes power-domain multiplexing and code-domain multi-plexing In power-domain multiplexing different users areallocated different power coefficients according to their chan-nel conditions in order to achieve a high system performanceIn particularmultiple usersrsquo information signals are superim-posed at the transmitter side At the receiver side successiveinterference cancellation (SIC) is applied for decoding thesignals one by one until the desired userrsquos signal is obtained[8] providing a good trade-off between the throughput ofthe system and the user fairness In code-domain multi-plexing different users are allocated different codes andmultiplexed over the same time-frequency resources such asmultiuser shared access (MUSA) [9] sparse code multipleaccess (SCMA) [10] and low-density spreading (LDS) [11]In addition to power-domain multiplexing and code-domainmultiplexing there are other NOMA schemes such as patterndivision multiple access (PDMA) [12] and bit division mul-tiplexing (BDM) [13] Although code-domain multiplexinghas a potential to enhance spectral efficiency it requires ahigh transmission bandwidth and is not easily applicableto the current systems On the other hand power-domainmultiplexing has a simple implementation as considerablechanges are not required on the existing networks Also itdoes not require additional bandwidth in order to improvespectral efficiency [14] In this reviewtutorial paper we willfocus on the power-domain NOMA

Although OMA techniques can achieve a good systemperformance evenwith simple receivers because of nomutualinterference among users in an ideal setting they still donot have the ability to address the emerging challenges dueto the increasing demands in 5G networks and beyond Forexample according to International Mobile Telecommunica-tions (IMT) for 2020 and beyond [15] 5G technology shouldsupport three main categories of scenarios such as enhancedmobile broadband (eMBB) massive machine type commu-nication (mMTC) and ultrareliable and low-latency com-munication (URLLC)Themain challenging requirements ofeMBB scenario are 100Mbps user perceived data rate andmore than 3 times spectrum efficiency improvement overthe former LTE releases to provide services including highdefinition video experience virtual reality and augmentedreality Since a large number of IoT devices will have accessto the network the main challenge of mMTC is to provideconnection density of 1 million devices per square kilometerIn case of URLLC the main requirements include 05msend-to-end latency and reliability above 99999 [16ndash18] Byusing NOMA scheme for mMTC and URLLC applicationsthe number of user connections can be increased by 5 and

9 times respectively [18] Also according to [19] NOMA hasbeen shown to bemore spectral-efficient by 30 for downlinkand 100 for uplink in eMBB when compared to OMATherefore NOMA has been recognized as a strong candidateamong all MA techniques since it has essential features toovercome challenges in counterpart OMA and achieve therequirements of next mobile communication systems [20ndash22] The superiority of NOMA over OMA can be remarkedas follows

(i) Spectral efficiency and throughput in OMA such asin OFDMA a specific frequency resource is assignedto each user even it experiences a good or badchannel condition thus the overall system suffersfrom low spectral efficiency and throughput In thecontrary in NOMA the same frequency resource isassigned to multiple mobile users with good andbad channel conditions at the same time Hence theresource assigned for the weak user is also used bythe strong user and the interference can be mitigatedthrough SIC processes at usersrsquo receivers Thereforethe probability of having improved spectral efficiencyand a high throughput will be considerably increasedas depicted in Figure 1

(ii) User fairness low latency and massive connectivityin OMA for example in OFDMA with schedulingthe user with a good channel condition has a higherpriority to be servedwhile the user with a bad channelcondition has to wait for access which leads to a fair-ness problem and high latencyThis approach can notsupport massive connectivity However NOMA canservemultiple users with different channel conditionssimultaneously therefore it can provide improveduser fairness lower latency and higher massive con-nectivity [20]

(iii) Compatibility NOMA is also compatible with thecurrent and future communication systems since itdoes not require significant modifications on theexisting architecture For example NOMA has beenincluded in third generation partnership project long-term evolution advanced (3GPP LTE Release 13) [23ndash29] More detailed in the standards a downlinkversion of NOMAmultiuser superposition transmis-sion (MUST) has been used [23] MUST utilizesthe superposition coding concept for a multiusertransmission in LTE-A systems In 3GPP radio accessnetwork (RAN) while using MUST the deploymentscenarios evaluation methodologies and candidateNOMA scheme have been investigated in [24ndash26]respectivelyThen system level performance and linklevel performance of NOMA have been evaluated in[27 28] respectively Next 3GPP LTE Release 14 hasbeen proposed [29] in which intracell interferenceis eliminated and hence LTE can support down-link intracell multiuser superposition transmissionAlso NOMA known as layered divisionmultiplexing(LDM) is used in the future digital TV standardATSC 30 [30] Moreover the standardization studyof NOMA schemes for 5GNewRadio (NR) continues


Power PowerNOMA

Frequency Frequency

OMA (OFDMA based)










Base station(BS)

s

Power



detectionUl signal


detectionU2 signal

signalSIC for U1

detectionU1 signal

U1

U1

U2

U2

Ul

Ul

UL

UL



119904 = 119871sum119894=1

radic119886119894119875119904119909119894 (1)


119910119897 = ℎ119897119904 + 119899119897 = ℎ119897 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119897 (2)


SINR119895rarr119897 = 119886119895120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119895+1 119886119894 + 1 (3)


SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1 (4)


SINR119871 = 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162 (5)


119877NOMA-d119897 = log2 (1 + SINR119897)

= log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1) (6)



119897=1


log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162)


rBase station

(BS)signals

U1

U2

Ul

UL

x1

x2

xl

xL

SIC for U1 U2 UL


= 119871minus1sum119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003816100381610038161003816ℎ11989710038161003816100381610038162)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) (7)



119897=1



119903 = 119871sum119894=1

ℎ119894radic119886119894119875119909119894 + 119899 (9)



SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574sum119897minus1119894=1 119886119894 1003816100381610038161003816ℎ11989410038161003816100381610038162 + 1 (10)


SINR1 = 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162 (11)



119897=1

log2 (1 + SINR119897)= log2 (1 + 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162)+ 119871sum119897=2


119897=1

119886119897 1003816100381610038161003816ℎ11989710038161003816100381610038162)

(12)



119897=1

1003816100381610038161003816ℎ11989710038161003816100381610038162) (13)



119877OMA119897 = 120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (14)


119877OMAsum = 119871sum

119897=1

120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (15)


119877OMAsum = 119871sum

119897=1

1119871 log2 (1 + 120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (16)



119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (17)


119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) le 119871sum119897=1


sum (18)









3 MIMO-NOMA






NOMAOMA

NOMAOMA


2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)



2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)


















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Power PowerNOMA

Frequency Frequency

OMA (OFDMA based)










Base station(BS)

s

Power



detectionUl signal


detectionU2 signal

signalSIC for U1

detectionU1 signal

U1

U1

U2

U2

Ul

Ul

UL

UL



119904 = 119871sum119894=1

radic119886119894119875119904119909119894 (1)


119910119897 = ℎ119897119904 + 119899119897 = ℎ119897 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119897 (2)


SINR119895rarr119897 = 119886119895120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119895+1 119886119894 + 1 (3)


SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1 (4)


SINR119871 = 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162 (5)


119877NOMA-d119897 = log2 (1 + SINR119897)

= log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1) (6)



119897=1


log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162)


rBase station

(BS)signals

U1

U2

Ul

UL

x1

x2

xl

xL

SIC for U1 U2 UL


= 119871minus1sum119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003816100381610038161003816ℎ11989710038161003816100381610038162)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) (7)



119897=1



119903 = 119871sum119894=1

ℎ119894radic119886119894119875119909119894 + 119899 (9)



SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574sum119897minus1119894=1 119886119894 1003816100381610038161003816ℎ11989410038161003816100381610038162 + 1 (10)


SINR1 = 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162 (11)



119897=1

log2 (1 + SINR119897)= log2 (1 + 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162)+ 119871sum119897=2


119897=1

119886119897 1003816100381610038161003816ℎ11989710038161003816100381610038162)

(12)



119897=1

1003816100381610038161003816ℎ11989710038161003816100381610038162) (13)



119877OMA119897 = 120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (14)


119877OMAsum = 119871sum

119897=1

120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (15)


119877OMAsum = 119871sum

119897=1

1119871 log2 (1 + 120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (16)



119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (17)


119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) le 119871sum119897=1


sum (18)









3 MIMO-NOMA






NOMAOMA

NOMAOMA


2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)



2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)


















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Base station(BS)

s

Power



detectionUl signal


detectionU2 signal

signalSIC for U1

detectionU1 signal

U1

U1

U2

U2

Ul

Ul

UL

UL



119904 = 119871sum119894=1

radic119886119894119875119904119909119894 (1)


119910119897 = ℎ119897119904 + 119899119897 = ℎ119897 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119897 (2)


SINR119895rarr119897 = 119886119895120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119895+1 119886119894 + 1 (3)


SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1 (4)


SINR119871 = 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162 (5)


119877NOMA-d119897 = log2 (1 + SINR119897)

= log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1) (6)



119897=1


log2(1 + 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574 1003816100381610038161003816ℎ11989710038161003816100381610038162sum119871119894=119897+1 119886119894 + 1)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162)


rBase station

(BS)signals

U1

U2

Ul

UL

x1

x2

xl

xL

SIC for U1 U2 UL


= 119871minus1sum119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003816100381610038161003816ℎ11989710038161003816100381610038162)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) (7)



119897=1



119903 = 119871sum119894=1

ℎ119894radic119886119894119875119909119894 + 119899 (9)



SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574sum119897minus1119894=1 119886119894 1003816100381610038161003816ℎ11989410038161003816100381610038162 + 1 (10)


SINR1 = 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162 (11)



119897=1

log2 (1 + SINR119897)= log2 (1 + 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162)+ 119871sum119897=2


119897=1

119886119897 1003816100381610038161003816ℎ11989710038161003816100381610038162)

(12)



119897=1

1003816100381610038161003816ℎ11989710038161003816100381610038162) (13)



119877OMA119897 = 120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (14)


119877OMAsum = 119871sum

119897=1

120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (15)


119877OMAsum = 119871sum

119897=1

1119871 log2 (1 + 120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (16)



119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (17)


119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) le 119871sum119897=1


sum (18)









3 MIMO-NOMA






NOMAOMA

NOMAOMA


2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)



2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)


















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



rBase station

(BS)signals

U1

U2

Ul

UL

x1

x2

xl

xL

SIC for U1 U2 UL


= 119871minus1sum119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003816100381610038161003816ℎ11989710038161003816100381610038162)+ log2 (1 + 119886119871120574 1003816100381610038161003816ℎ11987110038161003816100381610038162) (7)



119897=1



119903 = 119871sum119894=1

ℎ119894radic119886119894119875119909119894 + 119899 (9)



SINR119897 = 119886119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120574sum119897minus1119894=1 119886119894 1003816100381610038161003816ℎ11989410038161003816100381610038162 + 1 (10)


SINR1 = 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162 (11)



119897=1

log2 (1 + SINR119897)= log2 (1 + 1198861120574 1003816100381610038161003816ℎ110038161003816100381610038162)+ 119871sum119897=2


119897=1

119886119897 1003816100381610038161003816ℎ11989710038161003816100381610038162)

(12)



119897=1

1003816100381610038161003816ℎ11989710038161003816100381610038162) (13)



119877OMA119897 = 120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (14)


119877OMAsum = 119871sum

119897=1

120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (15)


119877OMAsum = 119871sum

119897=1

1119871 log2 (1 + 120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (16)



119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (17)


119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) le 119871sum119897=1


sum (18)









3 MIMO-NOMA






NOMAOMA

NOMAOMA


2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)



2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)


















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119877OMA119897 = 120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (14)


119877OMAsum = 119871sum

119897=1

120572119897log2(1 + 120573119897120574 1003816100381610038161003816ℎ11989710038161003816100381610038162120572119897 ) (15)


119877OMAsum = 119871sum

119897=1

1119871 log2 (1 + 120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (16)



119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) (17)


119897=1

1119871 log2 (120574 1003816100381610038161003816ℎ11989710038161003816100381610038162) le 119871sum119897=1


sum (18)









3 MIMO-NOMA






NOMAOMA

NOMAOMA


2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)



2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)


















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



NOMAOMA

NOMAOMA


2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)



2

4

6

8

10

12

14

16

18

20

Sum

rate

(bps

Hz)


















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia















119903119897 = 1003817100381710038171003817hl1003817100381710038171003817 119871sum119894=1

radic119886119894119875119904119909119894 + hHl1003817100381710038171003817hl1003817100381710038171003817nl (21)





Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Base stationBS

U1

Ul

UL

Nr

Nr

Nr

h

hl

hL



10038171003817100381710038171003817hl100381710038171003817100381710038172 = 119873119903sum119894=1

1003816100381610038161003816ℎ11989711989410038161003816100381610038162 119897 = 1 2 119871 (23)



(119898119909Ω )119896 1119896 119891119883 (119909) = (119898Ω)119898 119909119898minus1Γ (119898)119890minus119898119909Ω

(24)



(119898119909Ω )119904 1119904= 1sum119903=0

119903(119898119873119903minus1)sum119904=0

(minus1)119903 120599119904 (119903 119898119873119903) 119909119904119890minus119903119898119909Ω(25)


120599119886 (119887 119892119888) = 11198861198890119886sum120588=1

(120588 (119887 + 1) minus 119886) 119889120588120599119886minus119887 (119887 119892119888) 119886 ge 1 (26)




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(27)





119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119897+119905sum119903=0

119903(119898119873119903minus1)sum119904=0


(28)



119877sum = 119871sum119897=1


119864 [12 log2 (1 + SINR119897)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

+ 119864 [12 log2 (1 + SINR119871)]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119877119871

(29)


119877119871 = 119871minus1sum119897=1


119864[12 log2(1 + 119886119897sum119871119894=119897+1 119886119894 + 1120574 1003817100381710038171003817hl10038171003817100381710038172)] (30)



119877infin119871= 12119871minus1sum

119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894) (31)



119877119871 = 119864 [12 log2 (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]= 12 ln 2119864 [ln (1 + 119886119871120574 1003817100381710038171003817hL10038171003817100381710038172)]


(32)


119865hL2 (119909)= 1+ 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896 120599119899 (119896119898119873119903) 119909119899119890minus119896119898119909Ω(33)


119877119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0


119909119899119890minus119896119898119909Ω1 + 119886119871120574119909 119889119909⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟119868

(34)


119868 = 1(119886119871120574)119899minus1 intinfin

0

119906119899119890minus119896119898119906119886119871120574Ω1 + 119906 119889119906 (35)


119868 asymp 120585 = ln (119886119871120574Ω119898119896)119886119871120574 119899 = 0Γ (119899) (Ω119898119896)119899119886119871120574 119899 gt 0 (36)


119877infin119871 = 1198861198711205742 ln 2 119871sum119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585 (37)



119897=1

log2(1 + 119886119897sum119871119894=119897+1 119886119894)+ 1198861198711205742 ln 2 119871sum

119896=1

119896(119898119873119903minus1)sum119899=0

(119871119896) (minus1)119896+1 120599119899 (119896119898119873119903) 120585(38)



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



(mNr) = (2 4)

(mNr) = (2 2)

2 4 6 8 10 12 14 160SNR (dB)

Exact

Simulation U1

Simulation U2

Conventional OMA

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y


2 4 6 8 10 12 14 16 18 200SNR (dB)

Sum rate

Rate U1

Rate U2


0

05

1

15

2

25

3

35

4

45

Sum

rate

(bps

Hz)





4 Cooperative NOMA




1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1st phase2nd phase

Basestation

(BS)

Relay(R)

U1

U2

(a)

1st phase2nd phase

Relay(R)Base

station(BS)

ℎSR

ℎRU1

ℎRU

ℎRU

U1

Ul

UL

(b)

















119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














119910119877 = ℎ119878119877 119871sum119894=1

radic119886119894119875119904119909119894 + 119899119877 (39)




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119910119877119880119897 = radic119875119877119866ℎ119878119877ℎ119877119880119897 119871sum119894=1

radic119886119894119875119904119909119894 + radic119875119877119866ℎ119877119880119897119899119877+ 119899119880119897

(40)


119866 = radic 119875119877119875119904 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 1205902119877 (41)



120574119877119880119897 = 1198861198971205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 1003816100381610038161003816100381621205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162Ψ119897 + 120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119897 100381610038161003816100381610038162) + 1 (42)


120574119877119880119871 = 1198861198711205742 1003816100381610038161003816ℎ11987811987710038161003816100381610038162 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162120574 (1003816100381610038161003816ℎ11987811987710038161003816100381610038162 + 10038161003816100381610038161003816ℎ119877119880119871 100381610038161003816100381610038162) + 1 (43)



119899=0

(119898119883Ω119883119909)119899 1119899

(44)



119891|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0


119865|ℎ119883|2 (119909) = 119876119871minus119897sum119896=0

(minus1)119896119897 + 119896 119862119871minus119897119896 [119865|ℎ119883|2 (119909)]119897+119896 (46)




(47)


119875out119897 = int120578lowast1198970119891|ℎ119877119880119897 |2 (119909)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟1198691



1198692

(48)



119898119878119877minus1sum119899=0

(minus1)119896 119862119871minus119897119896


119891|ℎ119877119880119897 |2 (119909) (119865|ℎ119877119880119897 |2 (119909))119897+119896minus1⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟120593


(49)


120593 = 119897+119896minus1sum119905=0

119905(119898119877119880minus1)sum119901=0


(50)



119875out119897 = 1 minus 119876 sum119896119899119905119901119894119902





(51)


10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

5 10 15 20 25 300SNR (dB)

mSR = mRU = 1

mSR = mRU = 2








mSR = mRU = 1

mSR = mRU = 2

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100

Out

age p

roba

bilit

y

02 03 04 05 06 07 08 0901dSR
























6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



















6 Conclusion








References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







References

























































































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























































































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


A Tutorial on Nonorthogonal Multiple Access for 5G and Beyond2017/11/23 ·...

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Transcript of A Tutorial on Nonorthogonal Multiple Access for 5G and Beyond2017/11/23 ·...