NOMA for 5G Wireless Communication Systems

Transcription

1 SCHOOL OF ELECTRICAL ENGINEERING AND TELECOMMUNICATIONS NOMA for 5G Wreless Communcaton Systems by Stella Ho Thess submtted as a requrement for the degree Bachelor of Engneerng (Electrcal Engneerng) Submtted: 26 th October 2017

2 Abstract Non-orthogonal multple access (NOMA) as one of the upcomng and promsng multple access technologes has a sgnfcant mpact on the development of the 5G wreless communcaton systems, whch states n [1]- [25]. In ths report, a lterature revew on the NOMA related works of 5G communcaton network s presented. A systematc approach to analyze the dfferences between NOMA and OMA s provded as well. A detaled descrpton of downlnk system model s llustrated by usng mathematcal equatons. The resource allocaton desgn,.e., user parng and power allocaton, s formulated as a non-convex optmzaton problem. In general, there s no systematc approaches for solvng ths knd of problems effcently. As a result, low computatonal complexty resource allocaton s desgned. Specfcally, a user parng scheme, namely user data rate requrement-based selecton scheme, s proposed as a suboptmal soluton to solve the resource allocaton problem. Ths proposed algorthm, whch takes nto account user channel condton, user data rate requrement and the maxmum transmt power constrants, s descrbed n detal. Besdes, smulaton s performed to llustrate the system performance of the proposed algorthm. Furthermore, we have dscussed n the aspect of average system throughput, weak user s achevable data rate and multuser dversty. The future work s ncluded at the end of ths thess. 2

3 Acknowledgements I would lke to thank all the people who have made contrbutons towards my research work--- NOMA for 5G Wreless Communcaton Systems. Frst and foremost, my supervsor, Dr. Derrck Wng Kwan Ng, for helpng me develop a sold understandng n the feld of the 5G network, and always supportng me to overcome all the dffcultes through the entre work. I could never have gone so far wthout you. No words can express my grattude. Assocate Professor We Zhang, for gvng your fully attenton to my presentaton and provdng valuable comments at the end of my semnar. My frend, Ycong Cao, for ntroducng me to my supervsor, Dr. Derrck Ng, always answerng my questons that related to 5G network wth hs patence and helpng me overcome my depresson. You are a wonderful lstener and a nce frend. My frends, Yue L, Exa Su, Amee Chen, Sja Chen, Run Sh, Karl Huang and Mthun Powar for partcpatng and supportng n my semnar and poster day. My presentaton could not be done so well wthout your encouragements. My frends, Frank Ca, Chuy Zhou, Melane Lng, Irs Qn, Vck Peng, Andy Su, Magge Tan, Zunzun Du and And Zhang, for always belevng n me, encouragng me and helpng me overcome all the dffcultes n my lfe. Last but not least, I would lke to thank my whole famly for always supportng me fnancally and mentally. 3

4 Abbrevatons The abbrevaton used n ths report as shown below: NOMA Non-Orthogonal Multple Access OMA Orthogonal Multple Access FDMA Frequency Dvson Multple Access TDMA Tme Dvson Multple Access CDMA Code Dvson Multple Access OFDMA Orthogonal Frequency Dvson Multple Access 5G Ffth-generaton 4G Fourth-generaton 3G Thrd-generaton 2G Second-generaton IoT Internet-of-Thngs QoS Qualty-of-Servce SIC Successve Interference Cancellaton CCI Co-channel Interference BS Base Staton SINR Sgnal-to-Nose-plus-Interference Rato KKT Karush-Kuhn-Tucker MIMO Multple-nput multple-output 4

5 Table of Contents Abstract... 2 Acknowledgements... 3 Abbrevatons... 4 Table of Contents... 5 I. Introducton... 7 II. Lterature Revew... 9 A. Comparson of NOMA and conventonal OMA... 9 B. Motvaton III. System Model A. NOMA System Overvew B. Interference Management IV. Problem Formulaton A. The nstantaneous weghted throughput B. Optmzaton Problem Formulaton V. Detaled Desgn A. User Parng Algorthm B. Power Allocaton Algorthm Optmzaton Problem for Power Allocaton Per Subcarrer Soluton for Optmzng Power Allocaton Per Subcarrer Optmzaton Problem for Power Allocaton to Each Subcarrer Soluton for Optmzng Power Allocaton to Each Subcarrer VI. Smulaton Approach A. Smulaton Desgn Proposed Algorthm Compared Algorthms B. Smulaton Results Average System Throughput Weak User Achevable Data Rate

6 3. Multuser Dversty VII. Future Work VIII. Concluson Bblography Appendces... Error! Bookmark not defned. 6

7 I. Introducton Nowadays, wth the fast growth of moble nternet and rapd development of the Internet-of- Thngs (IoT), accordng to [1], [2] and [3], multple requrements n 5G networks that needed to be perfectly fulflled are n the aspects of enhancng moble broadband, msson crtcal servce, and massve IoT. To meet the demand of enlargng moble broadband, extreme capacty s expected to be 10 Tbps per km 2, and extreme data rate s expected to reach to Mult-Ggabts per second. In other words, hgh spectral effcency should be acheved so that 5G networks are able to handle explosve data traffc. For msson crtcal control, ultra-low latency needs to be as low as 1 mllsecond. Snce one of the basc requrements for the next-generaton wreless communcaton system s to support massve IoT devces, t requres the 5G network to be capable of severng users or/and devces that used n challengng locatons, refers to [1]- [6], [9] [15], [22], [23], [30], [31] and [40]. In practce, varous multple access scheme has been mplemented n varous wreless communcaton systems for dfferent applcatons. As [4] stated, the am of multple access schemes s to serve multple users by usng lmted bandwdth and power resources. In the hstory of wreless communcaton systems, the frst generaton (1G) used FDMA as ts multple access scheme, and the multple access scheme for second generaton (2G) was manly TDMA. As for the 3G and 4G networks, CDMA was appled for 3G communcaton systems. OFDMA as a prmary form of orthogonal multple access (OMA) has been wdely employed for the 4G network. In TDMA and OFDMA schemes, dfferent users are assgned to be served n dfferent orthogonal resource n tme or frequency doman correspondngly. The spectral effcency of these conventonal orthogonal multple access schemes s small snce the lmted bandwdth resource s not well-used n the case that a sngle user wth poor channel gan occupes the whole bandwdth. On the other hand, CDMA scheme operates under the condton that ts chp rate s much hgher than ts nformaton data rate. Due to the strngent demand of handlng ultra-hgh data rate n the 5G network, e.g. 10 Gbps peak data rate, expectng the chp rate to be fast enough and overtake the nformaton data rate s unrealstc due to the lmtaton of hardware at present [3], [4]. 7

8 As [4] - [7] mentoned, NOMA s an upcomng physcal layer communcaton technque, has made a promsng canddate n the feld of the 5G wreless communcaton systems. By usng non-orthogonal resource allocaton, NOMA multplexes multple users nto one subcarrer to allow the share of resource between users, whch result n the suffcent use of the bandwdth resource and the mprovement n spectral effcency. NOMA enables multple users to transmt nformaton on the same frequency resource at the same tme wth dfferent power levels, n other words, the BS can serve multple users on the same frequency resource at the same tme, whch has a sgnfcant mpact on latency reducton durng transmsson. Snce NOMA tends to gather users wth dstnctve channel gans nto the same subcarrer, and allocate the user wth poor channel gan nto hgh power level. As a result, the data rate of the weak users s boosted compared to conventonal OMA. However, based on [6] - [9], because multple users are multplexed durng transmsson, the mutual nterference s unavodable. A proper nterference management s expected. In NOMA scheme, the user wth the better channel condton s responsble to mnmse the nterferences and nose n the system by decodng and employng SIC at the recever, accordng to [12], [19], [22], [27] and [37]. By usng power allocaton scheme and user parng selecton scheme, NOMA provdes a substantal mprovement n spectral effcency, latency, and user farness. In ths project, we am to desgn a computatonal effcent resource allocaton scheme whch maxmzes the system spectral effcency. In partcular, the resource allocaton desgn s formulated as a non-convex optmzaton problem whch takes nto account the user channel condtons, user data rate requrement, and the maxmum transmt power constrant. 8

9 II. Lterature Revew A. Comparson of NOMA and conventonal OMA OMA has been wdely used n past few decades n exstng moble communcaton systems, e.g. 4G LTE, 3G, 2G, etc. In those conventonal multple access schemes, dfferent users are allocated to orthogonal resources n ether the tme or the frequency doman n order to allevate nter-user nterference. However, t comes at the expense of low spectral effcency based on [1], [4], [12], [13]. For example, as shown n Fgure 1, n OFDMA schemes that commonly used n current 4G communcaton systems, a gven wde frequency band s dvded nto multple orthogonal subcarrers. Snce OFDMA s tryng to mnmze nter-user nterferences, whch results n that system only allows each subcarrer to be allocated to at most one user. Whereas, NOMA s capable of assgnng multple users nto one subcarrer to share the transmtted power on the same frequency resource or n the same tme slot, refers to [20], [25], [28] and [35]- [39]. Fgure 1 A comparson between NOMA and OMA n frequency doman. Also, n most of the practcal scenaros, conventonal OMA allocates all the resources to the user wth the best channel gan for maxmzng the system data rate. However, such an allocaton does not pay much attenton to the weak users, conventonal OMA tends to gnore the weak user 9

10 at most of the tme [4]. Whle, accordng to [4], [6], [7] and [9], NOMA s able to balance the resource allocaton farness between two pared users, whch s benefcal to the users wth a poor channel condtons n the system. It s obvous to be seen that a certan farness between users s generated n NOMA scheme. Due to the unfarness n resource allocaton between users, as mentoned above, n conventonal OMA, the user wth the poor channel gan s requred to wat for transmsson whle usng tme dvson. In contrast, snce NOMA enables multple users to share the resources on the same frequency doman, the base staton can serve multple users at the same tme. As a result, the latency durng transmttng data s sgnfcantly reduced, compared to OMA [1], [4]. Snce two users are pared on each subcarrer, mutual nterference s expected between them. In fact, the performance of NOMA s senstve to the desgn of resource allocaton for mtgatng nterference. Partcularly, careful power control s needed at the transmtter sde to harness the nterference [4]. Besdes, successve nterference cancellaton should be performed at the recever of strong user. On the other hand, user parng s also mportant for nterference management, [6] - [9], [17]- [26]. Compared to conventonal OMA scheme, NOMA has a better performance n the aspects of spectral effcency, latency, and user farness, whch s promsng soluton for the fundamental ssues n the 5G communcaton network requrements. However, due to the exsted mutual nterference between users n NOMA scheme, nterferences are expected to be managed durng transmsson, stated n [4], [7], [17], [34], [35] and [41]. B. Motvaton Nowadays, heterogeneous and strngent requrements for the 5G of the wreless communcaton system are mposed to equp wth the fast growth of moble nternet and rapd development of IoT. For example, t s expected there wll be 50 bllon wreless communcaton devces by 2020 due to the roll-out of IoT [10]. Based on the released data from Csco VNI Moble Data Traffc Forecast ( ), as provded n Fgure 2, the global moble data s expected to ncrease 8- fold from and the data traffc predcts to reach to 30.6 exabytes per month [11]. 10

11 However, spectrum resource s lmted n practcal systems. Therefore, the requrements for the next-generaton of the wreless communcaton system should be upgraded to be able to handle explosve data traffc, n other words, achevng hgh spectral effcency wth lmted spectrum s necessary. Fgure 2. Global moble data growth presented by hstogram. Due to the ncreasng demand of the Internet-of-Thngs (IoT) wth varous Qualty-of-Servce (QoS) requrements, the new multple access technologes should be capable of supportng massve connectvty of users and/or devces, whch demands low latency n transmsson [1] - [3], [29]- [37]. Accordng to [2], Leadng the world to 5G, conducted by Qualcomm Technologes Inc., n addton to the requrements as stated above, deep and unversal coverage s also one of the needs n 5G networks, whch means the new qualfed multple access technologes are encouraged to reach challengng locatons. Therefore, guaranteeng user farness s requred n the 5G networks and the weak users n the system should be consdered as mportant as other users, nstead of gnorng them, accordng to [1]- [9], [15], [22], [23], [30], [31], [40] and [41]. As a result, NOMA has been consdered as a promsng canddate for the 5G moble networks to fulfl these strngent requrements. In fact, varous ndustral companes, such as Huawe technologes and NTT DOCOMO, are pushng ths technology nto the standard of 5G. So, there s an emergng need n studyng NOMA. Unfortunately, NOMA s yet to become a mature and qualfed multple access technology. There are varous fundamental ssues n practcal 11

12 mplementaton. For nstance, one crtcal problem n NOMA scheme s that ts system performance s senstve to resource allocaton [1], [4]. However, the effcent algorthm s stll unknown at ths pont n the lterature on studyng NOMA, based on [7], [12], [14]- [19], [20], [32] and [36]- [39]. 12

13 III. System Model In ths work, a downlnk communcaton scenaro wth one Base Staton and two users are consdered. Wthout loss of generalty, t s assumed that user m and user n are pared together for NOMA scheme as an llustraton. In ths work, there are two users on each subcarrer snce the ncreasng number of users multplexed on the same subcarrer cause the growth of hardware complexty and processng delay. Therefore, the case of two users per subcarrer s studed n the system model. A. NOMA System Overvew Fgure 3. A system model of NOMA communcaton system. Fgure 3 shows that there are two users that multplexed nto one subcarrer. User n s closer to the BS compared to User m, whch mples User n has a better channel condton comparng to User m. The Base Staton optmzes the transmt power for each user on each subcarrer. In partcular, nstead of allocatng all the power to one User, User n wth stronger channel condton s allocated less transmtted power and more transmt power s allocated to User m. Compared to conventonal OMA, User m s allocated wth non-zero power whch provdes certan farness n resource allocaton. Assgnng User n wth less power leads a small decrease n ts capacty but a sgnfcantly good effect on User m's. Therefore, user parng and power allocaton are able to strke a balance between the system performance and resource allocaton farness. 13

14 B. Interference Management Durng transmsson, there are some nterference and nose exsted n the system, such as cochannel nterference (CCI) and whte Gaussan nose, refers to [4], [7], [17], [34] and [35]. In ths secton, the mpact of nterference on the system performance and nterference management n NOMA scheme are dscussed by usng mathematcal equatons. The receved sgnals at user m and user n on subcarrer are gven by y m = P m ρ m h m x m + P n ρ m h m x n + z m, and y n = P n ρ n h n x n + P m ρ n h n x m + z n, (1) where x m denotes the symbol transmtted from the BS to user m on subcarrer ; p m denotes the transmtted power of the sgnal ntended for user m on subcarrer ; h m denotes the small-scale fadng coeffcent varable; ρ m denotes the jont effect of path loss and shadowng between the BS and user m; z m denotes the whte Gaussan nose on subcarrer at user m. We assume h m 2 h n 2, whch ndcates User m s further away from BS and has a poor channel condton compared to User m. The average of the message transmtted ε { x m 2 } = 1 wthout loss of generalty, where ε{ } denotes the statstcal expectaton [7]. In NOMA scheme, only the strong user s able to decode and remove CCI from the weak user by employng SIC. For User n, as the strong user n the system model. At frst, under a certan condton that s log 2 (1 + p m ρ n h n 2 z n + p n ρ n h n 2 ) log 2 (1 + p m ρ m h m 2 z m + p n ρ m h m 2 ), x m s decoded, whch result n User n s achevable rate at ths stage s log 2 (1 + p n ρ m h m 2 z m + p m ρ m h m 2 ) and the value p n ρ m h m 2 of SINR s z m + p m ρ m h m 2. Next, the x m s obtaned from the receved sgnal y n by performng a subtracton, y n P m ρ n h n x m = P n ρ n h n x n + z n, so that the nterference caused by User m s removed. Then, SIC s performed at the recever end. The achevable rate after employng SIC s log 2 (1 + p n ρ n h n 2 ) and SINR at ths stage s p n ρ n h n 2. It s obvous that SINR s reduced z n after applyng SIC. In NOMA, User m, as a weak user, also has an achevable rate gven by z n 14

15 log 2 (1 + p m ρ m h m 2 z m + p n ρ m h m 2 ), whch suggests both users n the system can get a certan amount of data rate. Whereas, n conventonal OMA, due to the orthogonal subcarrer allocaton, t may not be possble to gan a certan amount of data rate for the weak user. 15

16 IV. Problem Formulaton In ths secton, the nstantaneous weghted throughput s frst defned to be the adopted performance measure for the NOMA system. Subsequently, the power and subcarrer allocaton desgn problem s formulated as an optmzaton problem. A. The nstantaneous weghted throughput Accordng to [7], [12] and [16]- [28], the key concept n NOMA scheme s that system assgns dfferent level of power recourse to the multplexed users wth varous channel condton so that the system performance can be maxmzed. Snce multple users are multplexed nto one subcarrer, mutual nterference s unavodably ntroduced nto the system and should be removed by employng SIC. In partcular, for a gven subcarrer, user n s defned as the user wth strong channel gan n the two user-pared system, whch means only user n s capable of decodng and applyng SIC to elmnate CCI. The other user m s treated as the weak user that multplexed wth user n on the same subcarrer. Therefore, the nstantaneous weghted throughput on subcarrer s gven by U m,n (p m, p n, s m,n ) = s m,n [ω m log 2 (1 + p m ρ m h m 2 z m + p n ρ m h m 2 ) + ω n log 2 (1 + p n ρ n h n 2 z n ) ] (2) where ω m s a postve constant wth the range of 0 ω m 1, t denotes the prorty of user m n resource allocaton. The subcarrer allocaton ndcator s a bnary varable whch s gven by s m,n = { 1, 0, f user m and user n are multplexed on subcarrer wth H m Hn otherwse where H m = ρ m h m 2, and H m H n s defned. z m (3) B. Optmzaton Problem Formulaton In ths project, our desgn ams to maxmze the weghted throughput n the system va desgnng the jontly optmal power and subcarrer allocaton polcy. The polcy desgn can be formulated as the followng optmzaton problem: maxmze p,s N F =1 m=1 n=1 ), K K U m,n (p m, p n, s m,n N F K K =1 m=1 n=1, s. t. C1: s m,n (p m + p n ) P max 16

17 C2: s m,n {0, 1},, m, n, K K m=1 n=1, C3: s m,n 1, C4: p m 0,, m. (4) C1 s the power constrant for base staton where P max s the maxmum transmt power allowance. C2 s the constrant for the bnary optmzaton varables. C2 and C3 are mposed to guarantee that each subcarrer s allocated at most 2 users. C4 s the non-negatve transmt power constrant. In fact, the problem s a non-convex optmzaton problem. In other words, there s no wellknown systematc and effcent approaches for solvng these problems. Fgure 4 A llustraton of non-convex optmzaton. As shown n Fgure 4, to spot a global optmum, all local optma should also be obtaned for comparson as well. In two-dmensonal space, there are multple local optma ponts. All the ponts are expected to be found out n order to acheve to the globally optmal soluton. More mportantly, n hgh dmenson, the number of ponts that needs to be searched are usually growng exponentally wth the numbers of optmzaton varables. Consequently, fndng the globally optmum soluton s computatonally ntensve and may be nfeasble for devces wth lmted computatonal capablty. A suboptmal desgn, whch can strke a balance between computatonal complexty and performance for NOMA systems s proposed and ntroduced n the secton of detaled desgn. 17

18 V. Detaled Desgn It needs to be mentoned that the proposed algorthm s not the optmal desgn for solvng the non-convex optmzaton problem as mentoned n the secton of problem formulaton. Snce the formulated problem s a hgh-dmensonal optmzaton problem, whch means the number of possble solutons grow exponentally wth respect to the numbers of optmzaton varabless. It s mpossble to obtan the best soluton wthout dong exhaustve research. Thus, the proposed algorthm s defned as a suboptmal soluton for solvng ths optmzaton problem. A. User Parng Algorthm The conventonal user selecton algorthm, namely channel gan-based selecton scheme, tends to focus on parng two users only accordng to ther dstnctve user channel gan and underestmate the mportance of consderng user data rate requrements n NOMA system. Thereby, to optmze the user parng selecton, the proposed user parng scheme, namely user data rate requrement-based selecton scheme, takes nto account both user channel condtons and user data rate requrements. For user parng soluton, the desgned work bascally revolves around fndng a suboptmal soluton by balancng between user s channel condton and user data rate requrement. One of the possble soluton of user parng that mentoned at the prmary stage s to put two factor, whch are user channel condton and user data rate requrement, nto one metrc through multplcaton of them. In that way, both user channel gan and user data requrement wegh equally n the system. Whereas, t s lkely to exst such stuaton that two users from a pared group do not have dstnctve channel condton, snce the strong user and weak user n NOMA system are not dstngushed by user channel gan, but by the multplcaton of channel gan and data rate requrement, nstead. Therefore, ths soluton s abandoned and excluded n the proposed algorthm. 18

19 Fgure 5 The proposed user parng algorthm. The proposed algorthm s llustrated by Fgure 5. Frst, by sortng all users based on ther channel gans, whch the user wth the strongest user channel gan s ranked frst, the proposed scheme classfes the frst half of users that placed n the front nto strong users group n the system and the rest users are treated as weak users. Only weak users are allowed to be pared up wth strong users, whch ensures that two users n every two-user pared group have dstnctve channel gans and thereby enhance the performance gan acheved by NOMA compared to OMA. Second, snce all strong users and weak users are beng dstngushed, the proposed algorthm consders weak users data rate requrements by sortng weak users agan but based on ther data rate requrements. The reason that strong users data rate requrements are beng neglected s the lmtaton of mprovements on ther achevable data rate due to ther better channel condtons that n contrast to weak users. Then, the proposed user parng scheme favortes the weak user wth the hghest user data rate requrement and par t up wth the strongest user n the system. The weak user that has a low user data rate requrement s treated as the weak user wth the least prorty n the system, and therefore beng selected to group wth the least strong user. Ths algorthm clearly shows ts rule regardng user parng selecton, whch s defned that the user wth a more strngent requrement for ts data rate has the hgher prorty n user selecton scheme. 19

20 B. Power Allocaton Algorthm One of the conventonal suboptmal power allocaton solutons s equal power allocaton. Specfcally, the transt power of the base staton s equally dstrbuted to each subcarrer, whch can be easly mplemented n practce but lack of effectveness. The desgned power allocaton soluton s proposed to maxmze the system performance to certan extent. The man drecton of solvng the power allocaton problem n the desgned work s convex optmzaton approach, refers to [7], [12], [16], [17] and [32]. The structure of the optmzaton problem s exploted and thereby a locally optmal soluton s expected to be found out va computatonal effcent algorthms. The proposed power allocaton algorthm has two convex optmzaton approaches, whch targets on optmzng both the allocated power to each pared user n each subcarrer and the transmt power that dstrbuted to each subcarrer. 1. Optmzaton Problem for Power Allocaton Per Subcarrer The convex optmzaton approach regardng power allocaton to each pared user n each subcarrer s gven by maxmze p m,p n R = ω m log 2 (1 + H m p m 1+ p n H m ) + ω n log 2 (1 + H n p n ), s. t. C1: p m + p n p max, C2: p m 0, p n 0. The objectve functon that appled n the convex optmzaton problem (5) s the weghted throughput on subcarrer. The constrant functon C1 mples the sum of power that dstrbuted to each pared user n each subcarrer at most equals to the power that assgned to ths subcarrer. In order to maxmze the objectve functon, n general, all the power that assgned to the subcarrer should be used up by the two pared-up users, whch ndcates the sum of power that allocated to two users n the subcarrer equals to the maxmum power that dstrbuted nto ths subcarrer by the proposed algorthm. The constrant functon C2 represents the non-negatve nature of powers for selected users. (5) 20

21 2. Soluton for Optmzng Power Allocaton Per Subcarrer In subcarrer, p n denotes the power that assgned to the strong user. For fxed p n, the rsng of achevable data rates n the overall subcarrer s assocated wth the ncreasng of the power that assgned to the weak user, whch s p m. Then, the relevant equaton, p m = p max p n, should be establshed so that the achevable rate of the weak user, R(p m ), can be maxmsed. Thus, the achevable rate of the weak user s gven by R = ω m log 2 (1 + H m (p max p n ) 1+ p n H ) + ω n log 2 (1 + H n p n ) m = ω m log 2 (1 + H m p max ) ω m log 2 (1 + p n H m ) + ω n log 2 (1 + H n p n ) (6) Then, to fnd extreme pont, the ntegral of R(p m ) wth respect to p m s shown as followng, dr(p m ) dp m = ω m H m + ω n H n (1+ p n H m ) ln 2 (1+ p n H n ) ln 2 = ( ω nh n ω m H m ) (ω m ω n )H m H n p n (1+ p n H m )(1+ p n H n ) ln 2 (7) NOMA scheme tends to gves weak user hgh user prorty n power allocaton n each subcarrer, whch mples ω m ω n, should be fulflled. Addtonally, the non-negatve power constrant should be satsfed as well. As a result, the zero pont of dr(p m ) dp m s gven by p m = ( ω nh n ω m H m ) (ω m ω n )H m H n (8) Therefore, the maxmum value of R s acheved under the condtons that p m = ( ω nh n ω m H m ) (ω m ω n )H m H n and p m = p max p n. 3. Optmzaton Problem for Power Allocaton to Each Subcarrer The convex optmzaton approach regardng the transmtted power allocaton to each subcarrer s gven by maxmze p max [ω m log 2 (1 + H m p N m =1 + ω n log 2 (1 + H n p n )], N 1+ p n H m ) s. t. C1: =1 p max P max. (9) The prmal constrant functon C1 s subjected to ensure all the powers that dstrbuted to each subcarrer do not exceed the maxmum transmt power n the system. To optmze the use of 21

22 power resource, all the maxmum transmt power should be dstrbuted nto subcarrers. Also, N denotes the overall number of subcarrers n the system. 4. Soluton for Optmzng Power Allocaton to Each Subcarrer As stated above, for maxmum weghted throughput on subcarrer, p m = ( ω nh n ω m H m ) (ω m ω n )H m H n and p m = p max p n are derved equatons that requres to be satsfed. Hence, the objectve functon can be smplfed nto ω m log 2 (1 + H m (p N max p F n ) =1, seeng that ω n log 2 ( p n H m ) H n p n ) s treated as a constant for solvng ths optmzaton problem. Consderng the smplfed prmal functon shown above and ts constrant, the Lagrange equaton for maxmzaton s gven by L = ω m log 2 (1 + H m (p N max p F n ) N =1 + λ( F =1 p m p max ) (10) 1+ p n H m ) Thus, the Lagrange dual functon s gven by maxmze λ 0 nf L = ω m log 2 (1 + H m (p max =1 + λ( =1 p m p max (11) p max N F p n ) 1+ p n H ) m N F ) Accordng to KKT condton, the extreme pont s taken by dl dp max = H m (1+ p n H m + H m (p max p n )) ln 2 + λ = 0 (12) By solvng equaton (12), the values of λ and p max are gven by λ = H m (1+ p n H m + H m (p max p n )) ln 2 (13) p max = [ 1 1+ p n H + m λ ln 2 H ] m (14) 22

23 the optmzed soluton for power allocaton to all the subcarrer can be found when λ = H m (1+ p n H m + H m (p max and p p max = [ 1 n )) ln 2 1+ p n H + m λ ln 2 H ] m. However, due to computatonal complexty of fndng the optmal ponts, all optmzaton problems are solved by employng CVX modelng system va Matlab. 23

24 VI. Smulaton Approach All smulatons are mplemented va Matlab. A. Smulaton Desgn The system model that used for smulaton s a downlnk communcaton scenaro wth two users per subcarrer and sngle antenna, that s NOMA-OFDM. The number of downlnk users s set to be 6 for analyss on average system throughput and weak user s achevable data rate. In all the smulatons, the number of subcarrers n the system model s fxed to 64. Due to the lmted tme for smulatons, the mplementaton loops have been downszed. The numbers of path loss realzaton and channel realzaton are assgned to be 100 and 1 respectvely. The data that obtaned under ths crcumstance may have a small mpact on the accuracy of the results but s enough to present varous algorthms trends n ther system performances. In order to get more accurate data for analyzng multuser dversty, the number of path loss realzaton s changed to 1,000. The algorthms that descrbed as followng are smulated user parng models for analyss. 1. Proposed Algorthm The explct explanaton of the proposed algorthm s stated n Detaled Desgn. Concsely, the proposed algorthm manly optmzes user parng scheme n NOMA. Accordngly, ts compared algorthms are the algorthms that have varous user selecton scheme but use the same power allocaton soluton. 2. Compared Algorthms All compared algorthms perform user parng based on only the channel gans of users. The selecton algorthms, except random user parng algorthm, ensure that two users n every twouser pared group have dstnctve channel gans, whch maxmze the performance gan acheved by NOMA n contrast to OMA. The compared algorthms that employed n smulatons are descrbed and shown below n ths secton. 24

25 Random parng algorthm s the user parng scheme that par two users randomly and wthout consderng both users channel condtons and users data rate requrements. Ths method of user selecton has the least complexty to be performed n NOMA system. However, t also the most neffectve algorthm n user parng snce the condton that two users n every two-user pared group have dstnctve channel gans cannot be guaranteed. In addton, there s a possblty that not all the users are beng selected and pared up by applyng random parng algorthm, whch mples lack of user farness. Conventonal user parng algorthm only devotes ts effort to the strongest and weakest users for user parng n NOMA system, whch hghlghts the lack of user farness that exsted n ths user selecton scheme. On the other hand, two users wth the most dstnctve channel condtons share the power resource allocated nsde a subcarrer, whch s expected to have the best outcome on the acheved performance gan, compared to other compared algorthms. The low-complexty channel gan-based user parng algorthm that llustrated n Fgure 6. were establshed at prmary work stage as a proposed user selecton scheme. Fgure 6 The low-complexty user parng algorthm. Ths user parng algorthm ensures every two pared users n the system has certan dfferent channel gans. However, the dfference between two pared users channel condton s not beng maxmzed, whch s not effcent for user parng. Also, ths method of user parng guarantees every user n the system s selected nto at least one subcarrer so that user farness s able to be strengthened. 25

26 B. Smulaton Results The performances on the average system throughput and weak user s achevable data rate have been analyzed and the results are shown below. Addtonally, the multuser dversty of the proposed algorthm has been examned as well. 1. Average System Throughput Average system throughput (bt/s/hz) Random parng algorthm Conventonal users parng algorthm Low-complexty channel gan-based user parng algorthm Proposed algorthm Maxmum transmt power (dbm) Fgure 7 Average system throughput VS Maxmum transmt power. It s clearly llustrated by Fgure 7. that the proposed algorthm has the best system performance on weghted system throughput, compared to other smulated algorthms. The proposed algorthm has more effcent performance on average system throughput whle ncreasng the amount of maxmum transmt power. As expected, random parng algorthm has the worst outcome regardng average system throughput due to t neffectveness on user selecton. The low-complexty channel gan-based user parng algorthm ensures every user nsde system s selected and allocated nto each subcarrer, whch comes at the expense of low weghted system throughput n contrast to the conventonal user parng algorthm that lack of carng user farness. The conventonal user selecton scheme that sacrfcng user farness for mprovement on the weghted throughput on 26

27 each subcarrer, as predcted, has a great result on average system throughput, especally when the maxmum transmt power s less than 12 dbm. However, t tends to lose ts leadng poston wth the ncrement of the maxmum transmt power that used n the system. Whle the amount of maxmum transmt power that put nto the system keeps ncreasng, the superorty of applyng the proposed algorthm for enhancng average system throughput s more obvous. In other words, the gap of the system throughput performances between the proposed algorthm and the conventonal one s enlarged whle scalng the transmt power. That s because the proposed algorthm has hgher flexbltes for utlzng the degree of freedom among all other compared user parng schemes. 2. Weak User Achevable Data Rate Seeng that the proposed algorthm performance on the average system throughput s extremely closed to the conventonal algorthm system performance and the weak user have a hgh prorty for power allocaton n each subcarrer n NOMA, those two user parng schemes are selected for comparson of weak user s achevable data rate. Weak user's achevable data rate (bt/s/hz) Weak user wth the poorest channel gan n conventonal algorthm Weak user wth the poorest channel gan n proposed algorthm Weak user wth the hghest data rate requrement n proposed algorthm Maxmum transmt power (dbm) Fgure 8 Weak User s Achevable Data Rates VS Maxmum transmt power. Shown by Fgure 8, the weak user's achevable data rate n the smulated system based on the proposed algorthm s mproved remarkably. The reason that the proposed scheme has a better outcome on mprovng the weakest user s achevable data rate s that t has a hgh level of 27

28 flexbltes for explotng the use of the degree of freedom, compared to the conventonal user selecton scheme. Snce the proposed algorthm devotes ts effort to mprove the achevable data rate of the weak user wth a more strngent requrement for ts data rate, ts system performance on achevable data rate s nspected as well. The results are showng that the proposed algorthm favortes the weak user wth the hghest data rate requrement rather than the weak user wth the poorest channel gan when the maxmum transmt power s lmted. However, when system has suffcent transmt power, all weak users' achevable data rates are sgnfcantly ncreased n spte of data rate requrements and channel gans. In other words, the proposed algorthm has a substantal achevement on user farness. 3. Multuser Dversty Due to tme lmtaton, only the proposed user selecton scheme has been tested n the aspect of multuser dversty. The number of path loss realzaton s changed from 10 to 1,000 for accuracy. The test result s llustrated n Fgure 9. Average system throughput (bt/s/hz) Proposed algorthm Number of downlnk users Fgure 9 Weak User s Achevable Data Rates VS Number of Downlnk Users. It s evdent that the slop of ncrement s beng decreased and as a result, the average system throughput by employng the proposed algorthm wll reach to ts saturaton state, whch s around bt/s/hz, whle ncreasng the number of downlnk users. However, the saturated value of system performance on average throughput by applyng the conventonal algorthm s 28

29 beng estmated as around bt/s/hz, whch s much more mpressve n contrast to the proposed algorthm. Seeng that t s doubtless that the weghed system throughput s heghtened wth the ncreasng of downlnk user, a notceable declne n ts rate of ncrements also appears whle the number of users that nvolved s boosted. Snce t s challengng to create user farness among a large number of downlnk users, t s an acceptable outcome that the saturated value on average system throughput by usng the proposed algorthm s much small than usng the conventonal algorthm, whch trends to neglect the user farness n exchange of elevatng system throughput. To summares, the proposed user parng algorthm provdes superor mprovements n aspect of the weghted system throughput and user farness, compared to other smulated user parng algorthms, whch meets the objectves. Whereas, not as expected, the proposed scheme s system performance on multuser dversty s not mpressve n contrast to the conventonal algorthm, due to ts ntenton of ensurng user farness n the system. 29

30 VII. Future Work The system model that employed and analyzed s a downlnk communcaton system wth sngle antenna. The development plan on the proposed desgn s to apply MIMO (multple-nput multple-output) technque nto NOMA system, whch ndcates that the system model wll be modfed nto a wreless communcaton scenaro wth mult antenna. In addton, another future drecton s to desgn a computatonal resource allocaton algorthm ncludng beamformng desgn, user schedulng desgn and successve nterference cancellaton order desgn. 30

31 VIII. Concluson To date, the lterature revew on the NOMA related works for 5G communcaton networks has been presented n ths report. A systematc approach to analyze the dfferences between NOMA and OMA has been provded. Specfcally, the benefts n applyng NOMA over OMA are revealed. Besdes, the desgn has been formulated by usng optmzaton framework. The proposed algorthm wth low computatonal complexty, namely data rate requrement-based scheme, has consdered user channel condton, user data rate requrement and the maxmum transmt power constrants, whch conventonal algorthms fals to do. By smulaton of varous user parng algorthm va Matlab, the proposed user selecton scheme has shown ts superor performance on the average system throughput and user farness n contrast of other conventonal algorthms. Whereas, ts ntenton of ensurng user farness comes at the expense of unmpressve outcome on ts multuser dversty. In addton, the future drectons for extendng my current works has been outlned as well. 31

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