Inerference Coordinaion Sraegies for Conen Updae Disseminaion in LTE-A Vincenzo Sciancalepore Insiue IMDEA Neworks, Universiy Carlos III of Madrid, Spain, and DEIB - Poliecnico di Milano, Ialy Vincenzo Mancuso Insiue IMDEA Neworks, and Universiy Carlos III of Madrid, Spain Alber Banchs Insiue IMDEA Neworks, and Universiy Carlos III of Madrid, Spain Shmuel Zaks Dep. of Compuer Science, Technion, Haifa, Israel, Insiue IMDEA Neworks, and Universiy Carlos III of Madrid, Spain Anonio Capone Dpo di Eleronica, Informazione e Bioingegneria, Poliecnico di Milano Milan, Ialy Absrac Opporunisic raffic offloading has been proposed o ackle overload problems in cellular neworks. However, hey only address he problem of deadline-based conen propagaion in he cellular sysem, given wireless environmen characerizaion. In conras, we cope wih he raffic offloading issue from anoher perspecive: he base saion inerference coordinaion problem. In paricular, we aim a he minimizaion of he oal ransmission ime spen by he base saions in order o injec conens ino he nework, and we leverage he recenly proposed ABSF echnique o keep under conrol inercell inerference. We formulae an opimizaion problem, prove ha i is NP- Complee, and propose a near-opimal heurisic. Our proposed algorihm subsanially ouperforms classical inercell inerference approaches proposed in he lieraure, as we evaluae hrough he simulaion of dense LTE-A nework scenarios. I. INTRODUCTION A number of web and smarphone applicaions have recenly appeared, which cause he generaion of a huge volume of raffic for mobile devices. A large fracion of he raffic generaed by such applicaions consiss in he disribuion of conen updaes such as social nework updaes and noificaions, road raffic updaes, map updaes, and news feeds (e.g., waze, an app for a social nework for navigaion, includes all he above menioned feaures). Along wih he appearance of such applicaions, some schemes have been recenly proposed o offload he raffic generaed by hem in he cellular nework. In paricular, he device-o-device (D2D) paradigm has been proposed o assis he base saion in he conen disribuion [], [2], [3]: wih D2D communicaions enabled, he base saion delegaes a few mobile users (conen injecion) o carry and spread conen updaes o he oher users (conen disseminaion). Alhough he conen disseminaion phase inroduces delays, D2D-based conen updae disribuion is possible since i carries raffic wih no sric real-ime consrains, and whose conen s lifeime lass for a few minues. Mos of he currenly available offloading proposals, e.g., [2], [4], focus on he characerizaion of conen disseminaion and he design of conen injecion sraegies, bu largely neglec he opimizaion of radio resources in he injecion 978--4799-3360-0/4/$3.00 c 204 IEEE phase, i.e., he process of injecing a conen in a subse of he mobile user populaion, which produces bursy and periodic raffic. While his has been parially addressed, e.g., in [2], which has considered he impac of opporunisic resource uilizaion in he conen injecion sraegies, heir analysis is resriced o a single cell and does no consider he inerference caused by oher cells. We ackle he raffic offloading issue from a differen and unexplored perspecive: he inercell inerference coordinaion problem. The raionale behind our approach is wofold: (i) inerference is a key facor in dense neworks, where he single cell sudy case is no represenaive of a real nework; (ii) conen injecion operaions are impaced by nework speed, which, in urn, srongly depends on inercell inerference. To address he inercell inerference coordinaion problem, in his paper we adop he he Almos Blank Sub-Frame (ABSF) mechanism recenly defined for LTE-A [5]. This mechanism assigns resources in such a way ha a subframe be blanked for some base saions, hus prevening heir aciviy when he inerference exceeds a hreshold. A key advanage of his echnique is ha, by adoping a semi-disribued inercell inerference coordinaion (ICIC) paradigm in which a cenral server simply announces o base saions he paern of resources o be used, i grealy reduces he complexiy of inercell inerference coordinaion operaions. While ABSF has only been proposed very recenly and hence has no been horoughly evaluaed, some early sudies (like our recen work in [6]) have shown is poenial o improve performance. When scheduling he ransmission of conen updaes a base saions, our main objecive is o minimize he ime required for hese ransmissions, since (i) he faser conens are injeced, he sooner hey can be disseminaed, and hus offloading performance is opimized; and (ii) he less ime required for he ransmissions, he more resources are freed for oher applicaions. We show ha he problem of finding an ABSFbased scheduling algorihm ha minimizes he ime required for conen updae ransmissions while saisfying he conen deadlines is NP-Complee and NP-Hard o approximae. Thus, we design BSB, an algorihm ha runs in polynomial ime and
achieves sub-opimal nework performance, ye i ouperforms he sae of he ar mechanisms proposed in he lieraure. In paricular, our simulaions show ha BSB allows o abae he base saion ime devoed o conen disribuion by a facor 3 or larger, while boosing he abiliy of D2D schemes o reach he full se of conen subscribers. The conribuion of our work can be summarized as follows: (i) we formulae a base saion scheduling problem and we show ha i is NP-Complee; (ii) we design and validae a pracical algorihm for he compuaion of ABSF paerns; (iii) while available works on inercell inerference coordinaion assume ha a few inerferes dominae he overall received inerference experienced by a device, we show ha, in a dense nework scenario, a much broader se of inerferes needs o be aken ino accoun for inerference coordinaion; (iv) we show ha channel-opporunisic D2D schemes are seriously impaired by non-ideal conen injecion operaions. II. D2D-ASSISTED CONTENT UPDATE DISTRIBUTION In his secion, we presen he scenario addressed by his paper as well as he overall framework of our sysem and is building blocks. A. Conen disribuion scenario The scenario addressed by his paper consiss in a LTE cellular nework wih N base saions, each of which covers a user se U b, where b is he base saion index. Each user subscribes a conen c i C, wih conen lengh L c and a deadline T c by which he conen needs o reach all subscribed users. Muliple users can reques he same conen, and a dynamic scenario is considered, where users join and leave. In order o disribue a conen o muliple users in a scenario like his, while offloading he base saion as much as possible, we exploi D2D: he base saion delivers he conen o a subse of he subscribed users, which hen opporunisically share his conen wih oher users via shor-range communicaion echnologies such as WiFi-Direc, WiFi or Blueooh. The main objecive of his paper, in he conex of he above scenario, is o design a sraegy o deliver conen o users ha minimizes he oal resources required by he base saions, as his frees resources ha can used by oher applicaions. An addiional benefi of our approach is ha power consumpion of base saions decreases, since i depends on he oal aciviy ime of base saions. In order o achieve he objecive, we need o address he following wo challenges: Inra-BS opimizaion: we need o selec he opimal se of users in a cell ha receive he conen from he base saion, o ensure ha (i) he conen reaches all subscribers in he cell by he deadline; and (ii) resources required from he base saions are minimized. Iner-BS opimizaion: in addiion o deermining he ransmissions ha need o be performed by each base saion, we also need o schedule each of hese ransmissions among base saions, aking ino accoun he inerference beween base saions in such a way ha he oal ime required by hese ransmissions is minimized. While he issue of inra-bs opimizaion has already been addressed by a number of works in he lieraure [4], [6], [7], our focus here is on he iner-bs opimizaion. To address his, we use ICIC echniques ha, by improving he specral efficiency of he celluar nework, reduce he ransmission imes required by base saions o disribue he conen. In he following, we presen he mechanism ha we use for he inra- BS par, and he assumpions for he iner-bs opimizaion problem ha we ackle in his paper. B. Inra-BS conen disribuion The ransmission process for a paricular conen in a base saion is divided ino he following wo phases: ) Conen injecion: Iniially, when a new conen updae is available, base saions immediaely send i o a subse of he conen-subscribed users. To do his, a mulicas group ransmission is used since his is a very efficien sraegy o reach muliple users in jus one ransmission. As mulicas requires a ransmission a he leas user rae of all mulicas receivers [8], for a given mulicas rae, only a par of he users in he group will be able o decode he message (i.e., hose whose channel condiion enables hem o receive a he chosen rae). 2) Conen disseminaion: In order o reach hose users ha do no receive he conen in he injecion phase described above, in he disseminaion phase, he conen is spread opporunisically in he group. I follows from he above descripion ha he choice of he mulicas rae for he iniial injecion involves he following rade-off: (i) if he seleced mulicas rae is oo low, he number of bis injeced will be small and hus efficiency will be low, (ii) however, if he seleced rae is oo high, he iniial injecion will only involve few users and hence conen is unlikely o spread o all subscribed users by he deadline. To address he above rade-off, in his paper we adop he soluion proposed in [2] o selec he opimal rae for he mulicas ransmission while ensuring ha he conen reaches all users by he deadline. In paricular, by solving he corresponding opimizaion problem, [2] proposes o he une he rae a which base saion b performs he mulicas ransmission o subscribed-user group a ineresed in he conen c i a ime, according o he following expression: r b a() = argmax ϕ a (, y), a G b ; () y [r,r 2,...,r s b ] i where r u is he rae of a generic user u, s b i is he oal number of users ineresed in conen c i, i.e., he subscriber group size, G b is he se of groups acive under base saion b, and ϕ a (, y) is defined as s b i ϕ a (, y)= y χ a(, y) κ a (, y) y ru()+ s b i κ y>ru(). (2) a(, y) u= The value κ a (, y) is he oal number of users in group a which can decode he mulicas message, while χ a (, y) is he oal number of users which will have he conen when he conen deadline expires (i includes also κ a (, y)). Noe ha χ a (, y) depends on he average iner-conac rae amongs he users in he nework and he conen disseminaion deadline,
which corresponds o he conen deadline T c according o [2], where he injecion ime is negleced. In conras, in our simulaions, we assume a reasonable value for he conen disseminaion deadline equal o 50 seconds, ha is 50% of he oal conen deadline T c. C. Iner-BS scheduling Following he previous explanaion, during conen injecion, base saions schedule he mulicas ransmissions o injec he conen o a subse of users. In a scenario wih muliple base saions like he one considered here, we need o cope wih he inercell inerference (ICI) problem when scheduling hese ransmissions. To address he above problem, in his paper we adop he ABSF paradigm. In order o schedule he conen ransmissions following his paradigm, we need o allocae hem o differen subframes in each base saion. Since a single ransmission does no suffice o ransmi an enire conen, we need o divide he conen in differen chunks, and ransmi as much chunks as possible in each subframe. Following he sraegy of [2], only one group is opporunisically scheduled in each subframe and he ransmission rae used is ra b given in (). We denoe by a G b a group formed by he se of users ineresed in a specific conen under base saion b. Thus, d b = G b C groups are placed in each cell, and each base saion is loaded wih d b conen updae ransmissions. In a subframe i, he maximum rae ha can be decoded by a user u is given by he Shannon capaciy limi: ) S r u (i) =B T log 2 u(i) b N 0 + (3) j b Ij u(i)x ij where B T is he bandwidh, N 0 is he noise power, Su b is he power of he signal received by user u from base saion b, Iu j is he power of he inerference from base saion j and x ij is a binary value which indicaes wheher saion j is scheduled in subframe i. Since he subframe i can be seen as he base saion allocaion round, as explained in he nex secion, hereafer he wo erms subframe and round are used inerchangeably. According o he explanaion provided before, he conen chunks for group a are ransmied a a rae ra, b which implies ha hose users whose ransmission rae saisfies r u (i) ra b will be able o decode while he ohers will no be able o decode hem. Noe ha, since ra b is he smalles ransmission rae among hose mobile users ha can decode he ransmission, we can express i as follows: ) a (i) =ra b Su = B T log 2 b (i) N 0 + j b Ij u (i)x (4) ij where u is he user in group a wih he wors channel condiions among he ones ha can decode he ransmission, i.e., u = argmin{sinr j : ra b r j }. j a III. BASE STATION TRANSMISSION TIME MINIMIZATION Here, we formulae he iner-bs scheduling inroduced before as an opimizaion problem, and show ha i is NP- Complee and NP-hard o approximae. Then, we provide a sufficien condiion o solve he problem, which we will leverage o generae ABFS paerns (see Secion IV). A. Problem formulaion As explained in he previous secion, he efficiency of he conen disseminaion depends on he speed of he conen injecion process, and herefore our goal when designing he iner-bs scheduling is o minimize he ime needed o injec he conen. In view of his, we formulae he following opimizaion problem, which aims o minimize he sum of subframes used by he base saions o serve he raffic demand, subjec o being able o send he enire conen wihin is lifeime T c. Problem BS-SCHEDULE Inpu: A collecion of N base saions B = {, 2,,N}, and disinc mulicas groups A = {a b,a b 2,,a b d b } associaed wih base saion b B. Posiive consans N 0, τ, Θ, L c, B T. Ineger Z>0. For a mulicas group a associaed wih base saion b: Sa(i), b w a (i) and Ia(i) j for every j B \{b} and every i =, 2,,Z. Quesion: Is here a scheduling of he base saions in a mos Z rounds, such ha ( ) Z Ψ b S b a(z)= τb T x ib w a (i)log 2 + a(i) i= N 0 + L c, j b Ij a(i)x ij a {,.., d b },b {,.., N}, and N N Z TTOT b = τ x ib Θ? b= b= i= In Problem BS-SCHEDULE, each erm TTOT b = τ Z i=0 x ib = τz b represens he aciviy ime of base saion b (τ is he subframe duraion). The erm w a (i) represens he amoun of resources alloed o group a in subframe i. Given ha only one group can be scheduled in one subframe, we have w a (i) =if he subframe is compleely devoed o his group and 0 oherwise. Ia(i) j is defined as he power of inerference from base saion j, experienced in subframe i by he user having he wors channel condiion in he mulicas group a. Z is he number of subframes ha correspond exacly o he conen lifeime inerval T c, while Θ is he upper bound for he aggregae ransmission ime of he sysem. Transmission raes are compued using Shannon capaciy formula. B. Complexiy of Problem BS-SCHEDULE Classical wireless scheduling problems, e.g., scheduling and channel assignmen, have been shown o be NP-Hard [9], [0]. However, we are he firs o address he complexiy of base saion resource allocaion wih deadlines and mulicas ransmissions using variable raes. Specifically, we show ha problem BS-SCHEDULE is NP-Complee when Z 3 for bounded inerferences, and for Z =2 for unbounded inerferences. These NP-Compleeness resuls apply o very special insances of he problem (d b = for every base saion b).
Theorem. Problem BS-SCHEDULE is NP-Complee, for any Z 3, even when all inerferences are {0, }. Skech of Proof: I is clear ha he problem is in NP. For he NP-Hardness we use a reducion from he problem GCk of graph k-coloring (see []). We are given an insance I GCk = H(V,E) of Problem GCk, and consruc an insance I BS-SCHEDULE of Problem BS-SCHEDULE. Assume V = {, 2,,n}. The base saions are B = {b,b 2,,b n }, and he users U = {u,u 2,,u n }, where for every base saion b is serving user u. In addiion, Z = k, N 0 = τ = B T = L c =, Θ=n, and Su b (i) =w a (i) = for every i =, 2,,Z, =, 2,,n. Las, for every =, 2,, n, every j and every i =, 2,, Z, Iu bj (i) =if (i, j) E and is 0 oherwise. We have o show ha here is a k-coloring of I GCk if and only if for I BS-SCHEDULE here is a scheduling of he base saions in a mos k rounds, wih Ψ b u (Z) =L c, and n = T b TOT n. Given a graph k-coloring of I BS-SCHEDULE, wih colors, 2,,k. If a node is colored p, hen we schedule saion b in round p, for p =, 2,,k. Ψ b u (Z) = ( ) Z i= x ib log 2 + + for every. j Ib j u (i)x ij Since all base saions b j scheduled wih b are such ha (j, )/ E, and since each base saion( is scheduled ) in exacly one round, herefore Ψ b u (3) = log 2 + n =. = T b TOT = n since each saion is scheduled in exacly one round. Conversely, assume ha for I BS-SCHEDULE here is a general scheduling of a mos k rounds, such ha for each user Ψ b u (k) and n = T b TOT n. Ψb u (k) > 0 implies ha each user and hus each saion is scheduled in a leas one round. n = T b TOT n implies ha each saion and hus each user is scheduled in exacly one round. Moreover, if user u i is scheduled wih user u j, hen (i, j) / E (oherwise Ψ bi u i (Z) < = L c ). Therefore assigning color p o nodes associaed wih he saions in round p, for p =, 2,,k, resuls in a k-coloring of he graph I GCk. Theorem 2. Problem BS-SCHEDULE is NP-Complee for Z =2. Skech of Proof: We use a reducion from a variaion of he Pariion problem. We erm his Problem MPAR. Inhe Pariion problem we are given inegers A = {a,a 2,,a n }, such ha n j= a j =2S, and have o deermine wheher here exis {a,a 2,,a k } Asuch ha k j= a j = S (see []). In he modified version MPAR (ha can be shown o be NP- Complee) we are given inegers A = {x,x 2,,x 2n }, S> 0, S<x i < 2S for all i, such ha 2n j= x j =2(n+)S, and have o deermine wheher here exis {x,x 2,,x n} A such ha n x j = F, where F =(n +)S. We are given an insance I of MPAR, and consruc an insance I BS-SCHEDULE of Problem BS-SCHEDULE as follows. The base saions are B = {b,b 2,,b 2n }, and he users U = {, 2,, 2n}; base saion b i is serving user i. Z = 2, N 0 = F, τ = B T = L c =, Θ = n, and Su b (i) =2F, w a (i) =for i =, 2, =, 2,,n. Las, for every =, 2,,n, every j and every i =, 2: Iu bj (i) =x j + xi n. We have o show ha here is a soluion o I if and only if here is a scheduling for I BS-SCHEDULE in a mos 2 rounds, such ha for each user Ψ b u (2) =L c, and n = T b TOT n. Assume here is a soluion o I. Thus we assume he exisence of a {x,x 2,,x n} A such ha n x j = F. Schedule he base saions b x,b x 2,,b x n in he firs round and he oher n base saions in he second round. Clearly n = T b TOT n. Every user is hus scheduled in exacly one round, and hus Ψ b 2F u (2) = log 2 + F + { } x j + x = i n ) ( ) j=,2,,n,j i 2F log 2 F + n =log x j 2 + 2F F +F =. Conversely, assume a soluion o I BS-SCHEDULE. Since each inerference is posiive, and since n = T b TOT n, i follows ha each saion is scheduled in exacly one round. Assume he base saions a he firs round are b,b 2,,b k, and in he second round are b k+,,b 2n.Ifk n hen one of hese rounds has more han n base saions. Assume, wih no loss of generaliy, ha k > n. This means ha { } x j + xi n j =, 2,,k,j i > ns + nxi n > F, for every i =, 2,,k, hus Ψ bi u i (2) <, a conradicion. Therefore k = n. The inerference of each of he ) 2F users in he firs (second) round is log 2 F + n i= xi 2F (log 2 F + 2n ). So, n i= x i = 2n i=n+ x i = F, i=n+ xi ) and all inerferences are. When considering he minimizaion version of he problem (o deermine a scheduling wih smalles number of rounds), we use [2], which shows ha for all ɛ>0, approximaing he chromaic number of a given graph G =(V,E), V = n wihin n ɛ, is NP-hard. Since coloring G wih n colors is rivial, his means ha his resul is raher srong. Using i we show ha Problem BS-SCHEDULE is raher difficul o approximae, as follows: Theorem 3. For all ɛ>0, approximaing wihin n ɛ he minimal number of rounds required o solve Problem BS- SCHEDULE wih n base saions is NP-hard. Skech of Proof: Following he same reducion from GCk, as done in he proof of Theorem, i is clear ha he insance of BS-SCHEDULE can be scheduled in k rounds if and only if he given graph can be colored wih k colors. Therefore he exisence of an algorihm wih approximaion raio n ( ɛ) for BS-SCHEDULE will imply he exisence of an algorihm wih he same approximaion raio for GCk. C. Sufficien condiion for Problem BS-SCHEDULE Since, as we have shown above, Problem BS-SCHEDULE is NP-complee and NP-hard o approximae, in he following we provide a sufficien condiion ha guaranees ha he enire conen is delivered before is lifeime, i.e., in Z subframes. Recalling ha only one group can be acive in a subframe
and using (4), we can wrie he following ideniy: ) ( S B T w a (i)log 2 a(i) b db ) N 0 + w α (i) =. j b Ij a(i)x ij α= α (i) Wih he above, he condiion ha a conen of size L c is delivered wihin Z subframes, as given in he saemen of Problem BS-SCHEDULE, can be rewrien as follows: ( Z db ) w α (i) τ x ib L c. (5) i= α= α (i) from which we derive he following sufficien condiion o guaranee ha all users under base saion b can complee heir download in Z subframes: d b w α (i) α= α (i) τ Z j= x jb = τz b, i {,.., Z}. (6) L c L c Le us now consider he wors user as he one wih he minimum SINR a any subframe i such ha x ib =, resuling in achievable rae equal o min (i). From Eq. (6) and min (i), we can obain a sronger sufficien condiion o guaranee ha all users of base saion b complee heir download: d b α= w α (i) α (i) d b min (i) τz b L c, i {,.., Z}, b N. (7) Therefore, i is sufficien o guaranee ha he ransmission rae of all saions is above he following hreshold for he scheduling o be doable: min (i) h = d bl c τz b x ib, (8) a {,.., d b },b {,.., N},i {,.., Z}. where we recall ha Z b = Z i= x ib is he number of subframes in which base saion b is acive. In conclusion, from (4) and (8), we derive ha i is sufficien o schedule a base saion when all is scheduled users have a leas he following SINR: SINR 2 d b Lc τz b B T =. TH. (9) Noe ha he above equaion defines an SINR hreshold TH ha depends, in addiion o some consans, on he number of subframes Z b in which base saion b is allowed o ransmi. Nex, we derive a lower bound on Z b for which he iner-bs scheduling guaranees ha d b conen injecions are doable wihin he deadline. D. Lower bound for Z b The hroughpu of a base saion b can be bounded by he following expression: d b L c τ d b Z a= i= w = d bl c R MAX, (0) a(i)x ib τz b where R MAX is he maximum ransmission rae permied in he nework (e.g., R MAX = 93.24 Mbps in an FDD LTE nework using 20 MHz bandwidh). Therefore, here is a lower bound for Z b below which he conen injecion of d b conens canno be guaraneed: Z b d bl c, b B. () τr MAX Since we aim o minimize he oal ransmission ime, which is given by Θ=τ b B Z b, i is reasonable o assume ha an ICIC algorihm ha approximaes he soluion of Problem BS-SCHEDULE will be able o complee he injecion of d b conens a base saion b in a number of subframes ha is close o he bound given above, i.e., Z b = d bl c τr MAX. Wih his approximaion, we can express he hreshold TH in (9) as a funcion ha does no depend on Z b. The above provides a sufficien condiion o guaranee ha d b conens are delivered wihin heir lifeime; in paricular, we have found a hreshold TH for he SINR of users o be scheduled. In Secion IV, we leverage his resul for he design of our ICIC algorihm. E. Maximum number of conens Before describing our heurisic for Problem BS- SCHEDULE in Secion IV, we compue he maximum number of conens ha can be handled by a base saion. This resul will be useful in Secion V, when i comes o evaluae he performance of ICIC schemes. To achieve our goal, we assume ha all he base saions have, a leas on average, he same number of conens o injec in inerval T c. If all base saions have he same number of conens o injec, we can derive an upper bound for Z b. The oal number of subframes used by all base saions canno exceed b B Z b = NZ b.ifz is he oal number of subframes in which he conen is valid, we have ha NZ b Z and hus, we can derive an upper bound for Z b as follows: Z b Z, b B. (2) N From () and (2), we obain he following range for Z b : d b L c Z b Z, b B. (3) τr MAX N From he analysis above, we can hen compue he maximum number of injecable conens ha can be handled by a base saion while guaraneeing ha all conens are served wihin he deadline T c =τz. In paricular, from (3), i is clear ha he Z b range is no empy under he following condiion, which gives an upper bound for d b : d b d b = τzr MAX L c N. (4) IV. BASE STATION BLANKING ALGORITHM In his secion, we propose BSB (Base Saions Blanking), an algorihm o approximae he opimal soluion of Problem BS-SCHEDULE formulaed in Secion III. BSB relies on he sufficien condiion given by (9). Following his condiion, BSB aims o find an opimal ABSF paern, i.e., an allocaion of base saions o subframes, in which base saion can parially inerfere wih each oher, while guaraneeing a minimum SINR o any mobile device ha migh be scheduled. Noe ha
our algorihm is mean o allocae ABSF paerns, and does no impose any user scheduling policy. A schemaic view of BSB is repored here. BSB runs in a LTE-A nework, and requires he presence of a cenral conroller, namely he Base Saions Coordinaor (BSC), which could be run on he Mobiliy Managemen Eniy (MME) [3]. Our algorihm requires cooperaion beween he BSC and base saions, which can be implemened over he sandard X2 inerface [5]. The main role of BSC is o collec SINR saisics from he base saions, run BSB, and announce ABSF paerns o he base saions, as deailed in wha follows: BSB Algorihm The BSC collecs user saisics, pus all acive base saions in a candidae se, and checks wheher he resuling SINR for each user is above he SINR hreshold TH. If a leas one user does no reach he SINR hreshold: compue he mos inerfering base saion b remove b from he candidae se, check he SINR of all users of he remaining base saions. Repea he check and remove base saions from he candidae se unil all remaining users mee he SINR consrain. The resuling se of base saions is scheduled in he firs subframe and insered in a prioriy- lis. In general, a each subframe, scheduled base saions are added o he prioriy-k lis, where k is he number of subframes in which a base saion has been scheduled so far. All oher base saions go o a prioriy-0 lis. For each successive subframe, populae he candidae se wih he prioriy-0 lis and repea he operaion described for he firs subframe unil he SINR consrain is me. Then, for k =, 2,..., in increasing order: add o he candidae se all base saions in he prioriy-k lis, remove base saions which cause SINR below TH only if hey belong o he prioriy-k lis. The algorihm sops when he prioriy lis is empy. The BSC issues he resuling ABSF paern o each base saion via he X2 inerface. In he above descripion, he inerference caused by a base saion is compued as he aggregae sum of inerferences caused owards all users of all oher bees saion in he candidae se. The hreshold TH is compued based on d b and he lowes possible value for Z b, given by (). The scheduling paern compued wih BSB can range beween and N subframes. However, since he sandard specifies ha ABSF paerns should be issued every 40 subframes, he BSB paern is repeaed in order o cover a muliple of 40 subframes. The obained sequence of scheduling paerns represens he ABSF paern according o [5]. For each subframe, he algorihm sars by selecing he full se of base saions ha have no been scheduled in previously alloed subframes. The raionale behind his choice is wofold: (i) he aggregae inerference caused by a base saion grows wih he size of he candidae se, and hus he imporance of he inerference generaed by a base saion is more properly quanified by he full candidae se; (ii) exising ICIC algorihms sugges o miigae inerference by prevening he ransmission of a few base saions, beginning wih he mos inerfering one [6], [4], [7]. Once a base saion receives is ABSF paern, i can schedule is users accordingly. The complexiy of BSB is dominaed by he number of base saion, as saed in he following heorem. Theorem 4. The complexiy of BSB is O(U N 3 ), where U = max {U b}, and N = B. b B Skech of Proof: The BSB algorihm runs in a mos N rounds, corresponding o N allocaed subframes: in he wors case, exacly one base saion is allocaed in exacly one subframe. A subframe q =, 2,..., N, here are a mos q prioriy liss. In he wors case, he prioriy-0 lis conains N q + base saions and each oher prioriy lis conains base saion. Evaluaing he SINR for all users of base saions in prioriy- 0 requires checking all reconfiguraions wih N q+, N q,..., base saions in he candidae se. Checking he possibiliy o add o he resuling scheduled se any base saion in he oher prioriy liss is a mos involving N q +2 base saions for considering prioriy- lis, N q + 3for prioriy-2 and so on unil N base saions for he las prioriy lis. Overall, he cos per subframe is O(U N 2 ). Therefore, in he wors case, in which N subframes are needed, he complexiy is O(U N 3 ). V. PERFORMANCE EVALUATION Here we sudy he impac of BSB on he performance of D2D-assised conen updae disribuion. We benchmark he performance achieved wih BSB agains he one achieved under differen frequency reuse schemes (in paricular frequency reuse, 3, and 5), and agains a sae-of-he-ar dynamic resource allocaion scheme proposed for ICIC in LTE-like neworks [4]. We refer o he laer as ECE. Differenly from BSB, ECE assigns resource blocks raher han subframes, hus implemening a scheme for sof fracional frequency reuse [5]. For all esed resource allocaion mechanisms, we adop he opporunisic user scheduling scheme presened in [2]. Summarizing, we compare five iner-bs resource allocaion mechanisms, as repored in Table I. As concerns he sysem parameers used in our performance evaluaion, we use FDD LTE frame specificaions, wih 20 MHz bandwidh disribued over 00 frequency chunks, resuling in 00 resource blocks per ime slo, i.e., 200 resource BSB FR FR3 FR5 ECE TABLE I: Resource allocaion mechanisms ABSF paerns are compued according o BSB No inerference coordinaion is enforced Base saions are allocaed differen frequencies, according o a frequency reuse 3 scheme, and each base saion uses /3 of he band available Base saions are allocaed differen frequencies, according o a frequency reuse 5 scheme, and each base saion uses /5 of he band available LTE resource blocks are allocaed o base saions according o [4].
blocks per LTE subframe [6]. Transmission power is fixed o 40 W, anenna gain and pah loss are compued according o [7], and he specral noise densiy is 3.98 0 2 W/Hz for all nodes [8]. Modulaions and coding schemes are seleced according o he SINR hresholds repored in [6]. while he raio beween ransmied power and noise, for each pair of ransmiing base saion and user in he nework (be i signal or inerference), is compued as for Rayleigh fading, wih average given by ransmission power and pah loss. D2D communicaions occur ouband (i.e., on a channel no inerfering wih any of he base saions), and mobile devices exchange daa when heir disance is 30 m or less. Conen updaes occur synchronously every T c = 00 s. Each conen updae consiss in a file of 8 Mbis, and each mobile device is ineresed in a mos one conen. Background raffic is also generaed in some of our experimens, and consiss in random file requess, uniformly disribued over ime, wih file size equal o 8 Mbis. Background file requess are deal wih and scheduled as conen updaes for single-user groups. As concerns he mobiliy of users, we accoun for a Random Waypoin mobiliy model over a regular grid [9]. Iniially each mobile user is assigned a uniform locaion in he area. The mobile user chooses a random uniformly disribued desinaion, i.e., a waypoin P u, and a speed V n, uniformly disribued in range [, 2] m/s, independenly of pas and presen speed values. Then, he mobile user ravels oward he newly chosen desinaion a consan speed V n. Upon arrival o desinaion P u, he mobile user randomly chooses anoher desinaion and speed. Noe ha, a he considered low speed, he resuling conac ime is long (several seconds). Therefore, we assume ha complee file ransfers are possible during he conac ime. All experimens refers o a dense LTE deploymen, wih 5 o 7 overlapping cells, and several hundreds of mobile users. Each experimen includes 50 conen updaes for each conen, wih period 00 s (i.e., he experimen simulaes 5 000 s), and is repeaed 20 imes. Average and 95% confidence inervals are repored in he figures. When using BSB, a specific ABSF paern is issued every 40 subframes, which is he value specified by he sandard [5]. A. Base saion ransmission ime For he firs se of resuls, we simulae he nework depiced in Fig., wih 5 base saions and 750 mobile devices. Therefore, in he described resuls, scheme FR represens he case wih no ICIC, while FR5 guaranees no inerference. Fig. 2 shows he per-base saion average ransmission ime, expressed in erms of used subframes, when he simulaneous updae of 20 conens is periodically disribued in he nework. No background raffic was injeced during he experimen. For he case of ECE, in which resource blocks are alloed raher han subframes, we coun he oal number of used resource blocks, and normalize ha number wih respec o he number of resource blocks per subframe. BSB clearly ouperforms all oher schemes and uses a number of subframes very close o he lower edge of he inerval prediced in (3). Moreover, BSB ouperforms FR3 and ECE by a facor 3, and up o 5 for FR, ECE, BSB FR5 2 5 Band Band Band 3 4 Band Band 600 m 2 5 Band 5.2 Band 5.5 Band 5. 3 4 Band 5.3 Band 5.4 600 m 300 m 300 m 20 6 2 8 4 0 FR3 2 MHz Band 3.2 3 Band 3.3 5 Band 3.3 Band 3. 4 Band 3.2 600 m Band Fig. : Nework scenario wih 5 base saions placed a regularly spaced posiions, and 750 users (no shown in he figure) randomly dropped ino an area of 600 m 300 m. For each esed scheme, he figure repors he baseband bandwidh used by he each base saion. Number of used subframes 9000 8000 7000 6000 5000 4000 3000 2000 000 0 2 3 4 5 Base Saion ID 300 m FR5 FR3 FR ECE BSB Fig. 2: Conen updae ransmission ime wih 5 base saions, 750 users, and no background raffic. CDF 0 0 0 0 2 FR5 FR3 FR ECE BSB 0 3 0 0 20 30 40 50 60 70 80 90 00 Delivered conen [%] Fig. 3: Conen updae success probabiliy wih 5 base saions, 750 users, and no background raffic. he case of FR5. Noe ha, for a fair comparison o BSB and ECE, frequency reuse schemes simulaed in he experimen allocae only /n, n {, 3, 5} of he available bandwidh o each base saion. Wih he daa repored in he figure, i is clear ha BSB improves he resuls of FRn, n {3, 5}, by a facor n. Therefore, we could exrapolae ha modifying FR3 and FR5 schemes using n imes he bandwidh used by BSB would achieve similar resuls as BSB. Indeed, we have
validaed such an inuiive resul by running an experimen in which all base saions always use he enire 20 MHz bandwidh. Resuls, no repored here for lack of space, show negligible performance differences (below %) beween he schemes. However, we remark ha BSB would require /n of he frequencies needed by frequency reuse schemes. B. Success probabiliy For he same se of experimens commened in Secion V-A, Fig. 3 repors he cumulaive disribuion funcion (CDF) of he porion of delivered conen updaes, under he esed schemes. For his performance meric, we coun he number of conen updaes ha were correcly and enirely delivered o he subscribers, and normalize o he number of subscribers. BSB emerges as he scheme ha guaranees he highes conen delivery probabiliies, resuling in an average 97.24% of delivered conens. Noiceably, FR, FR3, FR5 and ECE perform much wors han BSB. This resul poins ou ha boh saic frequency planning schemes and classic resource allocaion schemes are no able o cope wih he inerference generaed in dense environmens. Moreover, FR3 achieves by far he wors resuls. Therefore, comparing FR (all base saions use he same wide bandwidh) and FR3 (a mos wo base saions share he same bandwidh, which is /3 of he one used under FR), we argue ha he inerference generaed by few neighbors in a dense scenario is much less imporan han he available bandwidh. As a consequence, specral efficiency over wide frequency bands is key o boos nework performances, while bandwidh fragmenaion due o frequency planning is undesirable. C. Impac of background raffic To show he efficacy of BSB in more generic raffic scenarios, in addiion o periodic conen updaes, we nex simulae background file requess uniformly disribued over ime a differen reques raes. Noe ha (4) expresses he maximum number of conens ha can be disribued wih guaraneed maximum ransmission ime. Tha expression can be also inerpreed as he maximum cell load ha can be handled by a base saion while guaraneeing ha conen updaes will be delivered wihin he deadline (wih each conen uni used for d b corresponding o an offered load L c/(τz)). Therefore, we expec ha BSB is able o handle a background raffic equivalen o, a mos, (d b d b) L c /(τz) bps. Wih 8-Mbi background files, d b = 20, L c = 8 Mbis, τz = 00 s, and 5 base saions, he maximum background raffic is 2.25 requess per second. In Fig. 4, we show he impac of background raffic on he probabiliy o complee he conen updae disribuion, for various background loads. Similarly o he case in which no background raffic is injeced, BSB ouperforms oher schemes. Ineresingly, BSB is more robus o background raffic han oher schemes, as shown by he fac ha conen delivery probabiliy under BSB is barely affeced by he background raffic. The performance of BSB sars degrading only when he offered background exceeds 3 file requess per second, which is well above 2.25 requess per second, i.e., Success Probabiliy 00 95 90 85 FR5 FR3 FR ECE BSB 80 0 0.5.5 2 2.5 3 Background raffic [requess/second] Fig. 4: Conen updae success probabiliy wih 5 base saions, 750 users, and background raffic. TABLE II: Scenario wih 7 base saions, 000 users and 30 conens o disseminae ICIC Transmiing Time Throughpu Delivery Success scheme [subframes in T c] [Mb/s] Probabiliy FR5 4047 6.90 89.98% FR3 6024 39.84 87.4% FR 84 20.02 95.50% ECE 624 37.87 92.27% BSB 292 82.4 97.37% he maximum value ha guaranees he doabiliy of conen ransmission wihin he deadline, according o (4). In conras, frequency reuse schemes and ECE are seriously impaired by he background raffic as soon as he offered load reaches as low as background file reques per second. D. Impac of nework size Table II illusraes a performance comparison in case of 7 base saions and 000 conen subscribers, wih 30 conens o be simulaneously disribued every 00 s. No background raffic was considered in his experimen. The able shows ha he average base saion aciviy ime is minimal under BSB operaions, and oher schemes needs much higher uilizaions. Being he overall load he same for all cases, he hroughpu susained while ransmiing is much higher for BSB han for any oher scheme. Noiceably, BSB is only 0% below he maximum achievable LTE rae (he rae corresponding o perfec channel qualiy a any ime). Moreover, BSB ouperforms all oher schemes also in erms of delivered conens. Mos imporanly, BSB achieves a 97.27% success probabiliy, which means ha D2D conen disseminaion is almos perfec when combined wih BSB. VI. RELATED WORK Our proposal can be classified as semi-disribued [5], since i relies on a cenral eniy ha coordinaes scheduling resources (ABSF paerns), while each base saion remains responsible for scheduling is users. In his secion, we commen on oher semi-cenralized ICIC schemes ha have been proposed in he lieraure. The auhors of [4], [20] design a heurisic o allocae resource blocks when adjacen cells inerfere wih each oher. Their approach allows he reuse of resource blocks in cell ceners, while users a he cell edge, which suffer higher
inerference, canno be allocaed specific resource blocks, as figured ou by he proposed heurisic. However, differenly from our proposal, ha work only considers avoiding he inerference of he wo mos inerfering base saions. As a resuls, we have shown in Secion V ha heir approach is no suiable for dense neworks. Similarly, he proposal in [2] assigns resource blocks via a cenral eniy. However, [2] allocaes resources no only o base saions bu also o users, based on backlog and channel condiions, and hence resuls in inracable complexiy, in conras o our approach which has a much lower complexiy. The auhor of [7] uses graph heory o model nework inerference. Tha work proposes a graph coloring echnique o cope wih inerference coordinaion, based on wo inerference graphs: one ouer graph using global per-user inerference informaion, and an inner graph using local informaion, available a he base saion, and global consrains derived from he global graph. To reduce he complexiy of he proposal, [7] uses geneic algorihms o seek a subopimal resource block allocaion. However, differenly from BSB, ha approach does no allow o use a generic user scheduler, since users are allocaed according o he inner graph coloring problem. In our previous work on ICIC [6], we have invesigaed on he opimizaion of ABSF paern allocaions in a fully sauraed nework. However, ha work does no accoun for conen deadlines, and herefore he choice of he SINR hreshold o be used in a real nework was no invesigaed. Moreover, he resource allocaion proocol proposed in [6] is far from being hroughpu maximal, since i is designed for achieving fairness among base saions, and so i does no guaranee he delivery of conens wihin a given deadline. None of he above works ackle he impac of inerference in dense scenarios, in presence of offloading raffic sraegies. VII. CONCLUSIONS In his paper, we formulaed a base saion scheduling problem o minimize he ime required o injec conens in a D2D-assised cellular offloading sysem. We proved ha he problem is NP-complee and NP-hard o approximae, and proposed BSB, an ICIC algorihm ha approximaes he soluion of he formulaed problem. BSB algorihm is mean o allocae ABSF paerns o base saions, and does no impose any user scheduling policy. Therefore, BSB can be used in combinaion wih any user scheduling scheme implemened a he base saion. For a dense mulicellular environmen, we showed ha inerference coordinaion is key o successfully operae conen disribuion schemes based on D2D communicaions. We also showed ha curren diffused pracices based on frequency reuse schemes and/or on he mos inerfering base saion se are no accurae for dense deploymens. Indeed, our proposed algorihm subsanially ouperforms classical inercell inerference approaches proposed in he lieraure. 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