A Benchmark for D2D in Cellular Networks: The Importance of Information

A Benchmark for D2D n Cellular Networks: The Importance of Informaton Yğt Özcan, Catherne Rosenberg Unversty of Waterloo {yozcan,cath}@uwaterloo.ca Fabrce Gullemn Orange Labs, France fabrce.gullemn@orange.com Abstract Many new moble applcatons create traffc among cellular users. We defne ntra-cellular traffc as the traffc from one cellular user to another user n the same cellular network. Ths type of traffc ntroduces new challenges for cellular network operators. Most work n the lterature focuses on the possblty to utlze the drect lnks between those users, f they are close to each other (ths s called devce-to-devce (D2D) communcaton), to by-pass the base staton. However, mplementng D2D s not easy, especally because detectng that a traffc s ntra-cellular s dffcult. In ths paper, we assume that we know how to detect f a traffc s ntra-cellular or not and focus on desgnng a type-aware scheduler (.e., a scheduler whch has the nformaton on the type of traffc) n a case where drect communcatons between users s not enabled. Ths scheduler can be seen as the benchmark aganst the case where drect communcatons are allowed. We show that performance gan can be obtaned by jontly schedulng the uplnk and downlnk wth respect to the case where the scheduler s blnd to the types. We show for a homogeneous network that when the traffc types are known to a scheduler, a sgnfcant performance gan (up to 28%) can be acheved compared to the case where the traffc types are not known. We also analyze heterogeneous networks that consst of macro cells and small cells and show that up to a 36% performance gan can be obtaned by performng type-aware user assocaton jontly wth user schedulng. Index Terms User Schedulng, Uplnk, User Assocaton, D2D, Farness I. INTRODUCTION A recent trend n cellular networks s the so called Devceto-Devce (D2D) communcatons that enable cellular users, close to each other, to exchange data drectly wthout usng the Base-Statons (BS) as a relay node [1]. Although t has been a hot topc n the last few years, many challenges reman to mplement D2D communcatons. For example, nterference management s complcated by D2D communcatons, detectng that a traffc s ntra-cellular (IC) s also hard, and t s not easy to obtan the channel gans between the cellular users and hence to decde f an IC traffc should use D2D communcatons or be sent va BS(s). In ths paper, we focus on IC traffc when D2D communcatons are not allowed,.e., the network operates n a classc cellular mode. We show that there s a sgnfcant performance gan f the network processes, such as user schedulng and user assocaton, are performed wth the knowledge of traffc types even when the drect lnks between users are not utlzed. However, ths requres the jont operaton of the uplnk and downlnk. 978-1-5386-3531-5/17/$31. c 217 IEEE We beleve that the benchmark aganst the D2D case (.e., where drect communcatons are allowed), whch s compared for schedulng or user assocaton, should be type-aware snce t s unfar to assume that ths nformaton s avalable for the D2D case and s not avalable for the case where drect communcatons are not allowed. User schedulng [2] s the process of allocatng rado resources and power to users at a very short tme scale. In a conventonal cellular network, uplnk and downlnk schedulng are performed separately. There are dfferent challenges for uplnk schedulng and downlnk schedulng. For example, n a realstc mult-cell system, nter-cell nterference (ICI) plays a crucal role n system performance and dealng wth ICI s not easy especally on the uplnk. The power budget on the downlnk of a cell comes from a sngle source (the BS) whle t comes from dfferent sources (the user equpments (UE)) on the uplnk. Apart from all those challenges, we show that there s an addtonal challenge that arses f we want to take advantage of the knowledge that a traffc s IC. We wll use the term of flow f j for a undrectonal traffc between cellular users and j. If and j are UEs belongng to the same cellular network, we say the flow s IC, f s a UE and j s a node outsde the cellular network, we call t an uplnk flow, and f j s a UE and s a node outsde the cellular network, we call t a downlnk flow. In a conventonal cellular system, an IC flow f j would use two rado lnks, one of whch s from to ts BS (uplnk) and the other one s from the BS of j to j (downlnk). Snce these two rado lnks are coupled, we should, f at all possble, couple ther schedulng to avod congeston. Indeed, n a conventonal system, f s very close to ts own BS, t mght be allocated a very hgh rate and ths could be a problem on the downlnk of j especally f j s far from ts BS. In practcal systems, ths problem would translate nto buffer overflows. Note that the BSs for and j mght be dfferent or mght be the same. To llustrate the gan of a type-aware soluton, we wll restrct our study to a sngle macro cell (whle takng ICI from the rest of the cells nto account) and only call IC flows the flows for whch and j share the same BS. However, we can generalze the concept n a CRAN-based system [3] to the case where and j are on dfferent BSs f these BSs are connected to the same CRAN, snce we could coordnate the schedulng of the uplnk of and the downlnk of j wthn the CRAN. We show n ths paper that the performance can be sg-

nfcantly mproved when the uplnk and downlnk of an IC flow are jontly scheduled (ths requres the knowledge of the type of a flow). We call ths type of schedulers type-aware and we call the schedulers that do not take the type of flows nto account and hence schedule the uplnk and the downlnk ndependently type-blnd. In a cellular network, each UE has typcally multple flows, possbly of dfferent types. Therefore, the ssue of farness among users or flows arses. In ths paper, we defne the concept of devce farness that ensures farness at the devcelevel rrespectve of the number of flows each user has. We wll explan the type-aware scheduler n an homogeneous context and then focus on heterogeneous networks (HetNets), whch consst of macro base statons (MBS) and small cells (SC) [4]. In that case, user assocaton (UA), the process of assocatng each user to ether an MBS or one of the small cells, s crtcal. We show that when UA s type-aware, system performance can be further mproved. In summary, our contrbutons can be descrbed as follows: We propose an uplnk scheduler that offers a better granularty than the one proposed n [5]. Ths wll be crtcal for the type-aware scheduler. We revst the concept of farness n the case of multple flows per UE and propose a sngle metrc that measures (devce) farness and effcency at the same tme. We frst formulate and study the couplng of the uplnk and the downlnk schedulers n the type-aware case for an homogeneous system. We compare, for dfferent mxes of flows, the gans n performance wth respect to the typeblnd case, where the schedulers are decoupled. Fnally, we consder a HetNet confguraton, for whch we formulate and study a type-aware UA. We compare the gans n performance wth respect to the type-blnd UA case for dfferent mxes of flows. The two man messages of the paper are that 1) mportant network processes, such as user schedulng and assocaton, should be performed wth the knowledge of the type of flows; 2) the uplnk and downlnk should be jontly scheduled to obtan the best performance when there s IC traffc n the system. Ths s easy to do when the source and the destnaton of a flow are assocated to the same BS or to dfferent BSs n the same CRAN. Next, we outlne the related work n Secton II. We explan the system model n Secton III. We defne the farness and effcency metrc n Secton IV. We explan the type-blnd and type-aware schedulers n Sectons V and VI, respectvely for a homogeneous system. We compare the performance of the two schedulers n Secton VI-B. We examne user assocaton and user schedulng n HetNets wth IC flows n Secton VII. A. D2D communcatons II. RELATED WORK D2D communcaton [1] has emerged as a new paradgm that allows cellular users to communcate drectly by bypassng the BS(s). Many works n the lterature study resource allocaton problem for D2D communcaton such as [6] and [7]. However, they do not consder a benchmark that takes nto account the traffc types and farness among users. B. Coupled Uplnk and Downlnk Schedulng In a conventonal cellular system, the uplnk and downlnk resources are separated from each other ether n the frequency or tme doman. The frst one s called Frequency Dvson Duplexng (FDD) and the latter s called Tme Dvson Duplexng (TDD) [8] and the schedulng of the resources are decoupled. There s some work on dynamcally allocatng the resources between the uplnk and downlnk such as Dynamc TDD [9], [1]; however, none of them coordnates the schedulng of the uplnk and the downlnk and they do not consder IC traffc. C. Farness wth IC Traffc In a cellular system, where UEs can have multple flows of possbly multple types, the noton of farness has to be revsted carefully. Dfferent farness crtera for D2D communcatons are defned n [11]. However, only one type of flow per user s consdered. We wll defne a new farness metrc for multple types of flows per devce. D. User Schedulng on the Uplnk User schedulng on the downlnk has been wdely studed n the lterature [2], whereas the lterature for the uplnk s scarce. Most uplnk work n the lterature consders smplstc scenaros. For example, most of them consder a sngle cell system whle gnorng the ICI. However, ICI plays a crucal role that has a drect mpact on the system performance [12], [13]. Snce the ICI cannot be known exactly on the uplnk (whle t can be on the downlnk under certan assumptons), t has to be estmated. In a realstc system, some of the resources mght be lost due to bad ICI estmaton and t s mportant to consder these losses when quantfyng the performance of an uplnk scheduler. Most of the uplnk work also uses a rate functon of the type log(1+sinr) [14] nstead of a pece-wse constant rate functon smlar to the one used n LTE, whch gves very dfferent results. An uplnk scheduler s proposed n [5] that works wth a unque ICI estmate for all PRBs n a frame. We wll show that ths scheduler s not flexble enough for the case of IC traffc and we wll propose a modfed verson that acheves a better granularty. In summary, there s no work focusng on farness and how IC flows should be dealt wth n a conventonal network once ther type s detected wth a realstc model. However, ths would be the far benchmark for the case where D2D communcatons are allowed. III. SYSTEM MODEL We consder a TDD OFDMA system where the tme s dvded nto subframes (of unt duraton) and the avalable frequency band s parttoned nto subchannels. A Physcal Resource Block (PRB) s the smallest schedulng unt that conssts of one subchannel c and one subframe t. A multcell envronment s consdered, where each cell has one MBS equpped wth an omn-drectonal antenna. For the HetNet confguraton we consder n Secton VII, there are also two

SCs n each cell. We focus on the macro cell n the mddle (that we call cell ) whle takng nto account the ICI receved from the other cells. A UE has a power budget of P U, an MBS of P M and a SC of P S. There are rm subchannels allocated to the system. A reuse factor r s mplemented among the macro cells, whch means the group of macro cells that use the same set of subchannels are allocated M subchannels. We assume that all the subchannels have the same characterstcs and are flat for a gven par {,j} (where s a UE and j s a BS) durng a schedulng frame, whch s composed of T subframes. A. The Flows In our system, a user may have up to four types of flows: U/L: Uplnk flow to the Internet D/L: Downlnk flow from the Internet IC o : From to another devce n the same macro cell IC d : From another devce n the same macro cell to Hence, we categorze a flow from to a devce outsde cell as an uplnk flow and a flow from a devce outsde cell to as a downlnk flow. We assume that each user has, at most, one flow of the frst three types (t can have multple flows of the fourth type). Let y() be the destnaton of the IC o flow of user (f any) and let z() be the source of the IC d flow of user (f any). We defne the throughput for each flow type as λ UL, λ DL, λ ICo, and λ IC d for the U/L, D/L, IC o and IC d flows of user, respectvely. An IC flow contans two hops: the hop between the source (ether or z()) and the BS and the hop between the BS and destnaton (ether or y()). We assume that the bnary matrx X, whose dmenson s 4xN, showng whether a user has a gven type of flow or not, s gven. More specfcally: X(1,) = 1 f devce has a U/L flow X(2,) = 1 f devce has a D/L flow X(3,) = 1 f devce has a IC o flow X(4,) = 1 f devce has IC d flow(s) B. SINR and Power If transmtter s gven PRB (c,t) to transmt to recever j wth power p, the SINR on that PRB at j s: γ j (c,t) = p Gc,j µ+i j (c,t), (1) where G c,j s the channel gan between and j on c, µ s the thermal nose on that channel, and I j (c,t) s the ICI at j due to co-channel transmsson on c at t. We assume that there s a rate functon, f(.) that maps the SINR on each subchannel to a correspondng data rate for a gven block error rate. It s constant per part. It selects the best modulaton and codng scheme (MCS) for a gven SINR. On the downlnk, we assume that a BS allocates all ts power equally to ts allocated subchannels and we know the nterferers whch are the other BSs transmttng on the same channels as the MBS n cell. Then, f we assume that the channel gans between and all these BSs are known exactly, we can compute exactly the ICI seen at each user devce and hence the SINR. On the uplnk calculatng the ICI on the uplnk (.e., seen by the BS) s not as easy as calculatng t for the downlnk snce we do not know how the power s used and who the nterferers n the other cells are (t depends on the schedule n the cells). Hence, we have to estmate the ICI and take decodng errors, due to a bad estmaton of the ICI, nto account. The fnal parameter that we ntroduce s < β < 1, whch determnes how much of the schedulng frame tme s allocated to the downlnk (βt ) and the uplnk ((1 β)t ). Selectng β mght not be so straghtforward when IC traffc s present. IV. A SINGLE METRIC FOR FAIRNESS AND EFFICIENCY Snce each user mght have a dfferent number of flows, t s very mportant to decde how to defne farness among those users. A network operator can offer farness to flows rrespectve of the devces on whch they are or t can offer farness to devces wthout consderng the number of flows each devce has. We focus on a devce farness, where each devce s treated as a sngle entty rather than consderng each flow separately. Ths s because offerng flow farness mght cause unfarness among the users wth dfferent numbers of flows by assgnng hgher weghts to the users wth hgher numbers of flows. To ths end, we defne a utlty functon for each user that s the geometrc mean (GM) of the throughput of each flow of types 1, 2, and 3. The reason why we do not nclude type 4 flows,.e., IC d flows, s that we do not want to double count flows. Ths wll become clearer when we defne the objectve functon across all users n the cell. Let F() be the set of flows of types 1, 2, and 3 of user where 1 F() 3. Then, the utlty ϕ of user s defned as: ϕ = F() λ j, (2) j F() where F() = {j {1,2,3} X(j,) = 1}. Note that f we use an arthmetc mean nstead of a geometrc mean n Eq. (2), we mght assgn zero resource to some IC flows. Cell MBS Fg. 1: Homogeneous network confguraton wth a reuse factor (r) of 3. The cells nterferng wth cell are hghlghted n yellow. V. TYPE-BLIND SCHEDULING In ths secton, we explan how user schedulng s performed n a conventonal homogeneous cellular network. We consder the homogeneous network shown n Fgure 1 1. Typcally, user 1 The hexagonal shape of the coverage areas s only to be taken symbolcally. It does not represent the exact geometrcal shape of a coverage area.

schedulng s performed separately for the uplnk and the downlnk and the scheduler does not know f a flow s IC or not,.e., t s type-blnd and we explan ts operaton n ths subsecton. It allocates resources on the downlnk for a tme βt and then on the uplnk for the remanng frame tme. The downlnk scheduler that we descrbe s state-of-the-art (SoA) whle the uplnk scheduler s new snce the SoA s not adequate as wll be dscussed. A. Downlnk Scheduler We consder a smple downlnk scheduler [15], where a BS allocates equal power to all ts avalable subchannels and serves one user at a tme on all the subchannels. Then, the users are tme scheduled. Wth these assumptons, we can compute the exact ICI (and the SINR) seen at each user and hence, knowng the rate functon f(.), we can pck the best MCS,.e., the one that yelds the maxmum achevable rate for each user. For a gven realzaton ω, where a realzaton corresponds to the random deployment of the users wthn cell and ther correspondng channel gans, let r be the rate user sees (over all the channels) when t s scheduled and U be the set of users assocated to BS. Then, assumng the full buffer case, the followng problem maxmzes the proportonal far objectve functon: P DL(ω) : max log(λ ) (3) α,λ s.t. λ = α r, U (4) α βt (5) where λ s the throughput user sees and α s the fracton of tme user s scheduled. Note that P DL (ω) s a convex problem and t was prevously shown that the optmal scheduler allocates equal tme to each user [15] f there s no addtonal constrant,.e., λ = βt U r. B. Uplnk Scheduler As dscussed above, schedulng on the uplnk s more challengng. Frst, the ICI cannot be known exactly snce the transmtters and the power they allocate on each subchannel n the neghborng cells are unknown. Furthermore, power allocaton s not as smple as downlnk snce there are multple possble transmtters n a cell. The scheduler proposed n [5] allocates m 1 subchannels to user for the duraton of a frame, where m s an nteger. The power budget of user s dvded equally between these m channels. The scheduler uses the same ICI estmate Î on all subchannels. Ths scheduler s not flexble enough for the type-aware scheduler because t mght be necessary to allocate a user less than T PRBs (.e., one subchannel durng the whole frame). Hence, we propose a scheduler that can be seen as a more flexble verson of the scheduler proposed n [5]. We contnue to use the same ICI estmate Î on all subchannels. We assume the subchannels are organzed nto blocks of dfferent szes and that a UE can only be allocated one block at a tme for transmsson. If a UE s allocated a block of 1 k M subchannels at a gven tme, we assume that ts power budget s shared equally among the k subchannels. Let the number of blocks of sze k be t k. Our uplnk scheduler computes for every frame the values oft k (snce the realzaton can change from one frame to another) and allocates a block of sze k to user for a fracton of tme θ k. Let R k (Î) be the rate seen by user on a subchannel block of sze k when the ICI estmate s Î. Ths can be computed by frst computng the SINR wth equaton (1) wth Î as the ICI estmate and then mappng ths SINR to a data rate usng the rate functon f(.) and k. Specfcally, for a realzaton ω, gven Î, R k(î) and U, the uplnk scheduler solves the followng problem P UL (ω, Î): P UL(ω, Î) : s.t. λ (Î) = M max log(λ (Î)) (6) (θ k),(t k),(λ ((Î)) θr k k (Î), U (7) M θ k (1 β)t, U (8) θ k t k (1 β)t, k {1..M} (9) M kt k M (1) t k Z +, θ k, k {1..M}, U (11) The throughput λ (Î) of user s defned as the sum of rates t sees on each block (constrant (7)). Constrant (8) ensures that the total tme a user s scheduled cannot exceed the uplnk frame duraton. Constrant (9) ensures that the total tme users are scheduled on blocks of sze k cannot exceed t k (1 β)t. Constrant (1) enforces that the total number of subchannels allocated to the blocks cannot exceed the total number of subchannels M. A crucal part of ths scheduler s the computaton of the R k (Î) s. If we use an optmstc ICI estmate (.e., a small value for Î), we mght see many losses snce the real ICI mght be much hgher. We defne the goodput seen by a user as the effectve rate ths user sees after takng nto account PRB losses 2. For a low value of Î, we wll show that the GM estmated by solvng P UL (ω, Î) s very dfferent from the goodput GM. We llustrate ths numercally next. We consder the 19 cell system shown n Fgure 1 and focus on cell. We only consder the sx other cells that use the same set of subchannels as cell. P U s set to 24 dbm. The number of subchannels M used by cell s 33. We use the followng dstance based path loss formula:128.1+37.6 log 1 (d/1) [8]. The antenna gans are 15 db for the BS and db for the UEs. Penetraton loss s set to 2 db. We obtan the 2 Note that on the downlnk, the scheduler computes the goodput drectly snce we assume that t has the exact ICI value.

channel gans by further applyng a log-normal shadowng of 8 db standard devaton. We use the pece-wse constant rate functon gven n Table III of [15]. The number of users n U s set to 1. We assume there are the same number of users n each of the sx cells. Snce we focus on proportonal farness (PF), effcency and farness can be measured usng a sngle metrc, the geometrc mean (GM) of the user throughputs [16] defned as Γ(ω) = (Π N =1 λ(î))1/n, where N s the number of users and λ (Î) s the throughput of user when the ICI estmate s Î. We consder a snapshot scenaro n whch we create a global realzaton made of N = 1 users per cell. We schedule each cell locally usng the same ICI estmate Î and obtan the estmated GM for cell as the value of the local objectve functon. The resultant schedule s mapped to the PRBs for each cell. We can then compute the goodput GM snce we now have the real ICI values (once we know the schedulng n each cell, we know the exact ICI). We perform ths smulaton for multple tme slots wth dfferent PRB allocaton and take the tme average. The decodng rule s as follows for a gven PRB: If the real SINR s hgher than the threshold of the MCS, the user gets the rate of that MCS from the PRB. Otherwse, the PRB cannot be decoded and we consder t lost. We repeat ths computaton for 1 realzatons and take the average GM goodput for cell. The results are gven n Fgure 2. GM Throughput (Mb/s) 3.2 2.8 2.4 2 1.6 1.2 Estmated GM Goodput GM.3.6.9 1.2 1.5 1.8 Estmated Interference Î 1-13 Fg. 2: Comparson of goodput and estmated GMs as a functon of Î for the uplnk scheduler We can see that the throughput computed wth P UL (ω, Î) s sgnfcantly lower than the real goodput for low values of Î. However, the estmated throughput and the goodput overlaps after some pont. In the followng, we wll select the lowest value of Î that yelds a dfference of less than.5% between the two curves. A. Formulaton VI. TYPE-AWARE SCHEDULING Recall that an IC flow (undrectonal by defnton) uses smultaneously the uplnk and the downlnk. If ts uplnk and downlnk schedulng are not coupled as n the type-blnd case, t s possble that the flow receves a hgher goodput on the uplnk than on the downlnk and ths would create a buffer overflow at the BS. To avod overflows and wastage, we have s defned as the mnmum of two dfferent equatons, one correspondng to the throughput on the uplnk hop and the other to the throughput on the downlnk hop. Both throughputs must be equal to each other to avod wastage or overflow. In a sense, we do rate matchng to avod possble overflow at the downlnk buffers, whch we do not model. The throughput of the uplnk to constran the goodput seen by an IC flow on the uplnk to be equal to the goodput seen on the downlnk. Ths couples the schedulng on the uplnk and the downlnk and makes the computatons of the schedules more dffcult. We wll show next how to do t and then what can be ganed n terms of performance by dong t. We formulate the problem for the optmal type-aware scheduler. Our am s to be proportonally far n the utltes (defned n Eq. (2)) of the users. Snce we focus on devce farness, each flow of each user s not treated as a separate entty, but we consder a user as a sngle entty n our schedulng problem. To avod double-countng, we do not nclude IC d flows n the computaton of the utlty of a UE and hence we do not explctly take them nto account n the problem but each IC o flow for s an IC d flow for another UE. We consder only the frst 3 rows of the matrx X. Specfcally, for a user wth an IC o flow,.e., an ntracellular flow orgnated n, the IC o throughput λ IC (resp. downlnk) flow of UE s denoted as λ UL (resp. λ DL ). If there s no flow of ths type, the throughput s zero. We use the uplnk and downlnk schedulers defned n the prevous secton. However, we need to extend the notaton snce each user mght have dfferent types of flows. Prevously, we used α for the fracton of tme user s served on the downlnk. Now, we defne α DL for the fracton of tme user s served on the downlnk for ts D/L flow and IC o and α IC flow, respectvely. Smlarly, we extend the notaton of θ k to and θ k,ic as the fracton of tme user uses subchannel block k on the uplnk for ts U/L and IC o flows, respectvely. For a realzaton ω, we formulate P OPT (ω, Î) (see the box n the next page), gven {(F()), X, (y()), β, Î, (R k(î)), (r )}. The varables are {(λ IC ), (λ DL ), (λ UL ), (α DL ), (α IC ), (θ k,ic ), ( ), (ϕ ), and (t k )}. The throughput of the U/L flow of user s defned by constrant (14) and of the D/L flow by constrant (16). The throughput of the IC o flow of user s defned by (15) and (17). Constrants (22), (23), (24), and (25) ensure that a devce does not get resources f t does not have a flow that uses that type of resources. Constrants (18) and (21) ensure that the tme users are scheduled on a subchannel cannot exceed the total uplnk and downlnk subframe tme, respectvely. Snce the objectve functon s the GM of user utltes and each utlty s the GM of flow throughputs, we guarantee that none of the flows gets a zero rate. P OPT (ω, Î) s an NP-hard problem snce t s a mxed nteger program. For reasonable sze problems, t can be solved by commercal solvers such as Bonmn [17]. Its computatonal complexty s hgh but ths s not a problem for our offlne study, whch s focused on showng how much we can gan by jontly schedulng the uplnk and downlnk when the types of the flows are known.

B. Numercal Results In ths secton, we compare the performance of the typeaware scheduler wth the type-blnd scheduler. We consder the same cellular system wth the same parameters as descrbed n Secton V. We set P M to 46 dbm. The destnaton node y() of the IC o flow of each user s selected randomly (and hence a devce can receve multple IC flows). We select Î so that losses are neglgble as dscussed prevously. Our performance metrc s the GM of the ϕ of the users. We consder two scenaros: Scenaro 1: 1 users n cell wth all three types of flows,.e., X(1,) = X(2,) = X(3,) = 1, Scenaro 2: D users wth an IC o flow,.e. X(3,) = 1, and {1 D} users wth U/L and D/L flows and no IC o flow,.e., X(1,) = X(2,) = 1. P OPT (ω, Î)) : s.t. ϕ = F() λ UL = λ IC = λ DL λ IC k {1...M} max log(ϕ ) (12) λ j, U, (13) j F() R k (Î), U (14) k {1...M} θ k,ic R k (Î), U (15) = α DL r, U (16) = α IC r y(), U (17) ( +θ k,ic ) t k (1 β)t, k {1...M} (18) ( +θ k,ic ) (1 β)t, U (19) k {1...M} M kt k M (2) (α DL +α IC ) βt (21) X(1,), U, k {1...M} (22) θ k,ic X(3,), U, k {1...M} (23) α DL X(2,), U (24) α IC X(3,), U (25), θ k,ic, U, k {1...M} (26) α DL, α IC, U, (27) t k Z +, k {1...M} (28) In the type-blnd case, the flows wthn a UE usng the uplnk (resp. the downlnk) are aggregated and offered a goodput whch s ndependent on the composton of the aggregaton. We start wth the frst scenaro where all users have all types of traffc. It s seen n Fgure 3a that there s a sgnfcant performance dfference between the two schedulers. Note that both schedulers acheve ther peak performance when β s.5, whch means equal tme for the uplnk and downlnk. In that case, there s a 14% gan for the type-aware scheduler. Next, we consder the second scenaro. It s mportant to note that the two schedulers perform exactly the same f there s no IC traffc n the network. Fgure 3b shows the performance of the two schedulers when D s 2 and 1. The dfference n GM utlty s 9% for D = 2, whereas t reaches 28% for D = 1. To examne ths further, we plot Fgure 3c whch shows the performance of the two schedulers as D ncreases when β =.5. The gan obtaned wth the typeaware scheduler ncreases wth the amount of IC traffc. By avodng wastage and overflows, the type-aware scheduler can do much better that the type-blnd one. Hence, the researchers who study the performance gan of D2D communcatons should use the type-aware scheduler as ther benchmark snce ths s what can be acheved wth a well desgned scheduler when drect communcatons s not enabled. There are two man reasons for ths dfference. Frst, the typeblnd scheduler does not lmt the throughput of the uplnk hop of an IC flow f the downlnk hop has worse channel characterstcs. Ths avods some of the data to be transmtted on the second hop. Furthermore, snce the type-blnd scheduler does not know the flow types, t cannot share the resources n an effcent way between the flows. VII. JOINT USER ASSOCIATION AND USER SCHEDULING IN HETEROGENEOUS NETWORKS We now examne the effects of type knowledge on the UA process of an HetNet. We consder the cellular network shown n Fgure 1 wth two small cells (SCs) added to each cell at a dstance of 23 meters left and rght of the MBS. We contnue to focus on cell but now the users n U have the choce to assocate wth the MBS or one of the two SCs. For ths case, an IC flow s defned between two users n U, rrespectve of ther assocaton. We consder an orthogonal deployment, where c subchannels are allocated to the small cells and M c to the MBS. For downlnk schedulng, we assume each BS (MBS and SC) allocates equal power to ts subchannels and serve one user at a tme. For the uplnk, we adapt P UL (ω, Î) to the HetNet case. For the ICI estmaton, we consder two estmates, one for the MBS and one for the SCs. These two estmates are ndependent of each other due to the orthogonal deployment. We performed smulatons to obtan a goodput vs. ICI estmates graph smlar to Fgure 2 and we selected estmates for the MBS and SCs to avod losses. The results of these smulatons are not gven here due to lack of space. UA s a crtcal process that assocates each user to a sngle BS. Furthermore, the best performance can be obtaned only when t s jontly performed wth user schedulng [15]. Here, we compare the performance of jont type-aware UA/schedulng and type-blnd UA. For the type-blnd UA, we use the optmal UA for the downlnk, whch can be found by solvng the nteger program descrbed n [15]. Once the UA s gven, the user schedulng can be performed ndependently at each BS for the type-blnd scheme as explaned n Secton VI. For the type-aware case, we perform the UA and schedulng jontly whle couplng the uplnk and downlnk. We assume that the BSs of a macro-cell are coordnated usng a CRAN

GM Utlty (Mb/s) 5.35.3 5.15.1.5 Type-Aware Scheduler Type-Blnd Scheduler.1.3.5.6.7.9 Fracton of downlnk tme β (a) Scenaro 1: GM utlty vs β GM Utlty (Mb/s).9.7.6.5.3.1 TAS D=2 TBS D=2 TAS D=1 TBS D=1.1.3.5.6.7.9 Fracton of downlnk tme β (b) Scenaro 2: GM utlty vs β for D=2 and D=1 GM Utlty (Mb/s).9.7.6.5.3.1 Type-Aware Scheduler Type-Blnd Scheduler 1 2 3 4 5 6 7 8 9 1 Number of users wth only ntra-cellular flow (D) (c) Scenaro 2: GM utlty vs D wth β=.5 Fg. 3: GM comparson for the type-aware and type-blnd schedulers for dfferent scenaros n the homogeneous case [3]. The problem formulaton s not gven n ths paper for brevty but essentally, we need to ntroduce bnary varables to ndcate to whch BS a user s assocated, and then solve P OPT (ω, Î) wth the addtonal UA and HetNet constrants. We consder Scenaro 2, whch was explaned n the prevous secton wth β =.5. We use the system parameters descrbed n [15] and set P S to 3 dbm. The performance dfference of the type-aware UA and type-blnd UA s gven n Fgure 4 as a functon of c, the number of subchannels allocated to the small cells. GM Utlty (Mb/s) 1.9.7.6.5.3 TAS D=2 TBS D=2 TAS D=1 TBS D=1 3 6 9 12 15 18 21 24 27 3 33 Number of subchannels allocated to the small cells (c) Fg. 4: GM comparson for the type-aware scheme (TAS) and typeblnd scheme (TBS) as a functon of c n the HetNet scenaro We consder two cases where D, the number of users wth IC flows, s 2 and 1. It s obvous that when the UA and schedulng s performed wth the knowledge of the type of traffc, the performance s much better. Furthermore, the dfference ncreases as D ncreases. The maxmum performance s acheved for both schemes when 18 subchannels are allocated to the SCs and n that case, the GM dfference s 11% and 36% for D = 2 and D = 1, respectvely. VIII. CONCLUSION We analyze cellular networks wth ntra-cellular (IC) traffc and show that the operaton of the network can be mproved sgnfcantly f the traffc types are known. Essentally, user schedulng should be performed jontly on the uplnk and downlnk for IC traffc to avod resource losses caused by bottlenecks. We also clam that a far benchmark to use to evaluate the performance gans of D2D drect communcatons should be type-aware snce any soluton nvolvng D2D drect communcatons would requre the knowledge of the type of the traffc. We also show that user assocaton n an Hetnet should also be type-aware. REFERENCES [1] G. Fodor et al., Desgn aspects of network asssted devce-to-devce communcatons, IEEE Comm. Mag., vol. 5, no. 3, pp. 17 177, 212. [2] F. Capozz et al., Downlnk Packet Schedulng n LTE Cellular Networks: Key Desgn Issues and a Survey, IEEE Communcatons Surveys Tutorals, vol. 15, no. 2, pp. 678 7, Second 213. [3] A. Checko et al., Cloud RAN for Moble Networks - A Technology Overvew, IEEE Communcatons Surveys Tutorals, vol. 17, no. 1, pp. 45 426, Frstquarter 215. [4] A. Damnjanovc et al., A survey on 3GPP heterogeneous networks, IEEE Wreless Com., vol. 18, no. 3, pp. 1 21, June 211. [5] A. Kumar and C. Rosenberg, Energy and Throughput Trade-Offs n Cellular Networks Usng Base Staton Swtchng, IEEE Transactons on Moble Computng, vol. 15, no. 2, Feb 216. [6] Q. Ye et al., Dstrbuted resource allocaton n devce-to-devce enhanced cellular networks, IEEE Trans. on Communcatons, vol. 63, no. 2, pp. 441 454, Feb 215. [7] C. H. Yu et al., Resource sharng optmzaton for devce-to-devce communcaton underlayng cellular networks, IEEE Transactons on Wreless Communcatons, vol. 1, no. 8, pp. 2752 2763, August 211. [8] 3GPP TS 36.211 v1., 3rd Generaton Partnershp Project, Techncal Specfcaton Group Rado Access Network; Evolved Unversal Terrestral Rado Access (EUTRA); Physcal Channels and Modulaton (Release 1). [9] Z. Shen et al., Dynamc uplnk-downlnk confguraton and nterference management n TD-LTE, IEEE Comm. Mag., vol. 5, pp. 51 59, 212. [1] S. Km and J. W. Lee, Jont resource allocaton for uplnk and downlnk n wreless networks: A case study wth user-level utlty functons, n IEEE VTC Sprng 29, Aprl 29, pp. 1 5. [11] P. C. Nguyen and B. D. Rao, Far Schedulng Polces Explotng Multuser Dversty n Cellular Systems Wth Devce-to-Devce Communcatons, IEEE Trans. on Wreless Communcatons, vol. 14, no. 9, pp. 4757 4771, Sept 215. [12] D. C. Dmtrova et al., Scheduler-dependent Inter-cell Interference and Its Impact on LTE Uplnk Performance at Flow Level, ser. WWIC 11. Berln, Hedelberg: Sprnger-Verlag, 211. [13] A. Racz, N. Reder, and G. Fodor, On the Impact of Inter-Cell Interference n LTE, n IEEE GLOBECOM, 28, pp. 1 6. [14] C. Sh, M. Hong, S. Nagaraj, and P. Flemng, Uplnk dstrbuted power and recever optmzaton across multple cells, n IEEE WCNC, 212. [15] D. Fooladvanda and C. Rosenberg, Jont resource allocaton and user assocaton for heterogeneous wreless cellular networks, IEEE Trans. on Wreless Communcatons, vol. 12, no. 1, pp. 248 257, January 213. [16] F. Kelly, Chargng and rate control for elastc traffc, European Transactons on Telecommuncatons, vol. 8, no. 1, pp. 33 37, 1997. [17] Bonmn (basc open-source mxed nteger programmng), http://projects.con-or.org/bonmn.