Optial Powe Masking in Soft Fequency Reuse based OFDMA Netwoks Mathias Bohge Jaes Goss, Ada Wolisz Technische Univesität Belin, TKN Goup, Einsteinufe 25, 10587 Belin, Geany Eail: bohge@tkn.tu-belin.de, Tel.: +49 (30) 314-23833 RWTH Aachen Univesity, UMIC Reseach Cente, Mies-van-de-Rohe-St. 15, 52074 Aachen, Geany Eail: goss@uic.wth-aachen.de, Tel.: +49 (241) 8020741 Univesity of Califonia, Bekeley, BWRC, 2108 Allston Way, Suite 200, Bekeley, CA 94704-1302, USA Eail: awo@ieee.og Abstact Soft fequency euse is a stong tool fo co-channel intefeence itigation in cellula OFDMA/LTE netwoks. The pefoance of such netwoks significantly depends on the configuation of the powe asks that ipleent the soft fequency euse pattens. In this pape, we investigate the pefoance of diffeent powe ask configuations against the optial case, in which a cental entity optially distibutes powe and esouce blocks aong the uses of the netwok. It is shown that lage diffeences exist between the pefoance of diffeent ask types and the optial case in both, the oveall cell thoughput, as well as the cell-edge use pefoance. 1 Index Tes LTE, OFDMA, soft fequency euse, powe asks, optiization I. INTRODUCTION The Long Te Evolution (LTE) obile boadband syste [1] uses Othogonal Fequency Division Multiple Access (OFDMA) as cobined tansission and ultiple access technique in the downlink. With OFDMA, the syste bandwidth is split into a nube of sub-caies, each featuing a bandwidth salle than the syste s coheence bandwidth, on which data of diffeent uses is tansitted in paallel. While the sub-caie thinness and the esulting lage OFDM sybol tie educes the effect of inte-sybol intefeence (ISI), the othogonality aong the itigates inte-caie intefeence (ICI). By using appopiate cyclic pefixes, ICI and ISI can alost copletely be avoided. OFDMA theefoe is a poising technique fo use in vaious systes and scenaios. When applied to obile cellula systes, a key issue with OFDMA is co-channel intefeence (CCI): Especially teinals located at the cell bode lagely suffe fo the powe adiated by the base station of neighboing cells in thei counication band. Thee ae thee ajo altenatives fo itigating CCI in cellula OFDMA systes: had fequency euse (HFR), factional fequency euse (FFR), and soft fequency euse (SFR). 1 This wok has been suppoted by the Gean Ministy of Education and Science (BMBF) and Eicsson Reseach, Geany, in the context of the poject ScaleNet. Had fequency euse splits the syste bandwidth into a nube of distinct sub-bands accoding to a chosen euse facto and lets neighboing cells tansit on diffeent subbands. Factional fequency euse and soft fequency euse both apply a fequency euse facto of one to teinals located in the cell s cente. Fo teinals close to the cell edge, howeve, a fequency euse facto geate than one applies. Factional fequency euse [2] splits the given bandwidth into an inne and an oute pat. The inne pat is copletely eused by all base stations; the oute pat is divided aong the base stations with a fequency euse facto geate than one. With soft fequency euse [3], the oveall bandwidth is shaed by all base stations (i. e., a euse facto of one is applied), but fo the tansission on each sub-caie the base stations ae esticted to a cetain powe bound. All these appoaches to itigating CCI can be descibed in tes of cell-specific powe asks ove the syste bandwidth. A powe ask pescibes the faction of the axiu tansit powe that the base station ay use depending at the pat of the spectu. In Fig. 1 we assue a scenaio of thee neighboing cells. In the case of had fequency euse with a euse facto of thee (Fig. 1b), the powe asks block all but one thid of the spectu. In ou exaple fo factional fequency euse (Fig. 1c), the powe ask fo the fist half of the spectu is unifo, and the second half coesponds to a condensed vesion of the had euse case. Fig. 1d illustates the soft fequency euse case. The powe asks have a significant ipact on the syste s pefoance. Pevious wok [4] shows that soft fequency euse has a capacity advantage ove the plain had euse. Futheoe, adapting the powe ask used fo soft fequency euse to the cuent taffic situation has ecently been shown to be a geat leve on capacity [5]. Howeve, the question eains, how close this and siila adaptive schees get to optiality. In this pape, we pesent a eans to evaluate powe ask pefoance in cellula OFDMA systes. Ou cental contibution is the foulation of a global knowledge exploiting
powe powe powe powe fequency fequency fequency fequency (a) Unifo (b) Had euse 3 (c) Factional euse 3 (d) Soft euse 3 Fig. 1. Diffeent powe asks non-linea optiization poble and the solving of seveal accoding poble instances in a basic efeence scenaio. We copae soe existing powe ask configuations to the ideal esults, in ode to show how ou odel seves as a basis fo the pefoance evaluation of oe sophisticated static as well as adaptive powe ask configuations. To the best of ou knowledge, this is the fist wok to pesent esults of the non-linea esouce scheduling optiization poble elated to cellula OFDMA netwoks. The eainde of this pape is oganized as follows. In the following section, we descibe esouce scheduling in LTE systes and intoduce ou scheduling goal. Then, in Sec. III we intoduce ou scheduling optiization odel fo the local (Sec. III-A), as well as the global optiization case (Sec. III-B). In Sec. IV, we pesent ou efeence scenaio and the accoding efeence esults. We conclude ou wok and identify topics fo futhe study in Sec. V. II. SYSTEM MODEL In LTE, tie is slotted into tansission tie intevals (TTI) [1] of duation T TTI (in the ode of illiseconds). Duing a single TTI, down-link use data ultiplexing is done in fequency division ultiplexing (FDM) fashion, whee the sallest addessable bandwidth-unit is a esouce block. Following the localized apping schee, a esouce block consists of adjacent sub-caies in the fequency doain. In the tie doain, a esouce block spans all OFDM sybols available fo use data tansission of the espective TTI. Each esouce block is expected to expeience ostly flat fading thoughout a single TTI. A. The schedule Fo each TTI and in each cell, a base station schedule assigns the esouce blocks to the seved teinals. LTE uses adaptive coding and odulation (ACM) pe esouce block, so the schedule deteines also the odulation type and coding, based on available channel state infoation (CSI). In this wok, howeve, we use the theoetical Shannon capacity of a channel [6] instead of efeing to the coding and odulation type cobinations actually consideed fo LTE. Ou ethod is nonetheless also applicable to ealistic coding schees. Shannon s theoe states that fo a channel with bandwidth B and a given signal-to-intefeence-and-noise atio (SINR), thee exists a code that achieves a thoughput of THR = B log 2 (1 + SINR). (1) We assue that the tansit powe is pescibed fo each esouce block by a powe ask. Fo cell i, we will denote the powe ask by p ask i, [0, 1]. This value denotes the faction of the total available output powe p (MAX). On esouce block, cell i thus tansits with a powe of p (MAX) p ask i,. We denote the channel gain in TTI t by γ i,, fo use, base station i, and esouce block, and calculate the cuent SINR as SINR i,, = p (MAX) p ask i, γ i,, j i p(max) p ask j, γ j,, + η. (2) The above denoinato sus up the co-channel intefeence fo concuently tansitting base stations j i and the noise powe η. Note that in a eal syste, the TTIs would not be synchonized aong cells, and the teinal would siply easue the cuent SINR. III. SCHEDULER OPTIMIZATION Scheduling coonly ais at axiizing syste thoughput, but fainess has to be taken into account, too. Solely axiizing the aw syste thoughput can lead to stavation of uses at the cell edge and ovesupply of bandwidth to uses that ae easy to seve. Diffeent kinds of fainess constaints cicuvent this: guaanteeing each use a cetain iniu ate [7], ultiplying each use s thoughput by an individual popotional fai facto [8], o utility-based pe-use thoughput optiization [9]. Utility-based optiization is faiest, but it is highly coplex. A. Local optiization odel Discussing diffeent scheduling and fainess policies is beyond the scope of this pape. We use a siple fainess odel to copae diffeent soft fequency euse scenaios, but ou appoach easily adapts to othe fainess notions. We assue that fo each use thee is a axiu thoughput
THR (MAX), and that any thoughput beyond THR (MAX) is useless. In othe wods, we ty to axiize the syste thoughput while assuing that none of the uses gets oe than a cetain axiu ate. This appoach coesponds to a siple piecewise linea utility function. Foally, we can wite ou scheduling goal as an optiization odel by intoducing the binay use/esouce block assignent vaiable x,, which is 1 if use obtains esouce block, and 0 othewise [10]. The sets of all active uses and of all esouce blocks ae denoted by M and R, espectively. The task of the schedule then is descibed by the following intege linea poga: ax s. t. x, THR ˆ, (3a) x, 1 R (3b) x, THR ˆ, THR (MAX) M (3c) The scheduling objective (3a) is to axiize the total expected thoughput THR ˆ, of all uses on all esouce blocks. Constaint (3b) ensues that each esouce block is assigned to at ost one use at a tie (i. e., exclusively uses at TTI tie t). Constaint (3c) is the utility constaint that guaantees that use does not get oe than the axiu equied thoughput THR (MAX). The expected thoughput THR ˆ, of use on block depends on the expected SINR, which we will denote by SINR ˆ i,,. The expected SINR is deived fo the latest SINR easueent. Accoding to Eq. (1), the expected thoughput is THR ˆ, = f log 2 (1 + SINR ˆ i,,), (4) if is located in cell j out of the set of active cells J. Note that f is the esouce block bandwidth. B. Global optiization odel The global optiization odel ais at scheduling the available syste esouces such that the syste wide thoughput is axiized. We assue that thee is a cental entity equipped with all infoation necessay to achieve this goal. The cental entity not only is in chage of deteining the optial use/esouce block assignents, but also of finding the optial powe levels fo each esouce block in each cell j out of the set of active cells J. Note that in this case, the optiization poble is not subject to powe asking, but to an oveall axiu powe p (MAX) constaint that is allowed to be adiated by each base station (expessed in Constaint 5c). As a consequence, we odify ou local esouce scheduling optiization poble 3 to include the thee-diensional cell/use/esouce block optiization vaiable x j,, : ax s.t. j x j,, THR ˆ j,, (5a) x j,, 1 j, (5b) y j, p(max) j (5c) x j,, THR ˆ j,, THR (MAX) j, (5d) Optiization vaiable y j, is the powe assignent vaiable. The expected use thoughput is coputed following Eq. 4. The expected SINR, howeve, is now coputed as follows: SINR ˆ i,, = y i, γ i,, j i y j, γ j,, + η. (6) Cobining Eqs. 5 and 6, it can easily be seen, that the global esouce scheduling poble is non-linea in natue. Moeove, since the use/esouce block assignent vaiable is binay, wheeas the esouce block/powe assignent is a eal vaiable, the global esouce optiization poble is a nonlinea ixed intege poble, which is known to be exteely had to solve. Still, in the next section we pesent a basic efeence scenaio fo which solving the global esouce allocation poble is possible unde coon optiization poble solving softand hadwae conditions. A. Setup IV. REFERENCE SCENARIO Ou efeence syste and channel odel paaeteization (path loss, shadowing, and fading odel) lagely follows the paaetes fo the UTRA and EUTRA siulation case 1 as pesented in Tables A.2.1.1-1 and A.2.1.1-2 of [4] with an inte-site distance of 500 and uses dopped unifoly in each hexagonal cell. Diffeing paaetes ae shown in Table I. We have consideed two hexagonal cells. The eason fo this is that fo significantly lage scenaios, the global optiization poble is not solvable within easonable tie constaints using egula had- and softwae equipent. Ou LTE syste-level siulato is based on the fee tied discete Paaete Sybol Value Cells in the syste J 2 Uses M 8 Resouce blocks R 24 Resouce block fequency spacing f 180 khz Maxial tansission powe pe cell p ax 43 db TABLE I SIMULATION PARAMETERS.
ean syste thoughput / bps 4.5 x 107 4 3.5 3 2.5 2 1.5 HFR 2 FR 1 SFR 2a [ 1 ; 0.5 ] SFR 2b [ 1 ; 0.1 ] OPTIMUM weakest use thughput ean / bps 5.5 x 106 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 HFR 2 FR 1 SFR 2a [ 1 ; 0.5 ] SFR 2b [ 1 ; 0.1 ] OPTIMUM 1 2 2.5 3 3.5 4 4.5 5 axiu ate pe use theshold / bps x 10 6 (a) Mean syste thoughput (bps), 99 % confidence intevals 0 2 2.5 3 3.5 4 4.5 5 axiu ate pe use theshold / bps x 10 6 (b) Mean thoughput (bps) of weakest use, 99 % confidence intevals Fig. 2. All uses achieve thei axiu equied ate if the esouces ae distibuted optially. In the case of local knowledge based esouce assigneent optiization, case SFR02b, which featues a powe level diffeence between the one of SFR02a and the had fequency euse HFR2 schee achieves the best pefoance, especially in the weakest use pefoance (b). event siulation libay OMNeT++ [11]. The instances of nonlinea global optiization poble (5) have been solved using LINDO s LINGO non-linea optiization poble solve [12]. The local scheduling optiization poble instances (3) have been solved using ILOG s CPLEX linea poble solve [13]. We have siulated 100 diffeent use distibutions. In each un, the instances of the espective global and local scheduling optiization poble wee solved fo each cell. Theeby, we have copaed the pefoance of the global optial scheduling decision to the pefoance of the locally optial schedule featuing the following powe asks: Had Fequency Reuse 2 (HFR2). Each cell ay only use half of the total syste bandwidth. An accoding powe ask fo had fequency euse 3 is depicted in Fig. 1b. Unifo/Fequency Reuse 1 (FR1). The available powe is distibuted evenly acoss all esouce blocks in all cells, cf. Fig. 1a. Soft Reuse 2 (SFR2). Thee ae two diffeent powe levels: high, and low. Each cell uses half of the spectu with each powe level, see Fig. 1d fo the accoding soft euse 3 ask. Thee ae two vesions of soft fequency asks: (a) SFR2a [1; 0.5] and (b) SFR2b [1; 0.1], which eans that in the fist case the the low powe level equals half, and in the latte one tenth of the high powe level. B. Results The esults of ou siulations ae shown in Fig. 2. Moeove, in ode to incease the eadability of the esults, the ean values ae also pesented in Tables II and III. Fig. 2a shows the ean syste thoughput aveaged ove all siulation uns fo the diffeent powe ask schees detailed above. Fig. 2b shows the aveage thoughput obtained by the weakest use, i. e., the individual use that eceived the least thoughput in each of the 100 diffeent use distibution scenaios. In ost cases, this use is closest to the cell-edge (does occasionally Maxiu Rate pe Use Theshold / Mbps Appoach 2 2.5 3 3.5 4 4.5 5 HFR2 14.97 19.12 22.89 26.32 29.43 32.00 34.01 FR1 15.50 19.29 22.95 26.52 30.00 33.35 36.57 SFR2a 15.56 19.37 23.07 26.71 30.19 33.57 36.81 SFR2b 15.76 19.66 23.50 27.25 30.89 34.37 37.71 Optiu 16.00 20.00 24.00 28.00 32.00 36.00 40.00 TABLE II SIMULATION RESULTS: MEAN SYSTEM THROUGHPUT/MBPS. Maxiu Rate pe Use Theshold / Mbps Appoach 2 2.5 3 3.5 4 4.5 5 HFR2 1.346 2.018 2.382 2.521 2.595 2.401 2.039 FR1 1.597 1.916 2.162 2.349 2.479 2.560 2.600 SFR2a 1.651 1.988 2.245 2.466 2.597 2.693 2.745 SFR2b 1.792 2.217 2.591 2.913 3.120 3.259 3.327 Optiu 2.000 2.500 3.000 3.500 4.000 4.500 5.000 TABLE III SIMULATION RESULTS: WEAKEST USER THROUGHPUT/MBPS. not apply unde cetain fading conditions). In addition, the eo bas display confidence intevals with a confidence level of 99 %. Addessing fist the ean syste thoughput in Fig. 2a, the esults show that all powe asks show close to optial pefoance, if the axiu ate pe use is aound 2Mbps. With inceasing axiu ate theshold, howeve, the diffeences in pefoance becoe clea. As expected, the had fequency euse schee achieves the wost pefoance values. This is ainly due to the fact that its bandwidth is liited and its intefeence advantage does not pay off in the highe ax equied ate cases, which favo the uses close to the base station (that ae less susceptible against intefeence). Inteestingly, none of the soft fequency euse cases SFR2a
and SFR2b pefo significantly bette than the equal powe level fequency euse 1 (FR1) case, when it coes to the ean syste thoughput. In tes of weakest use pefoance, howeve, significant diffeences becoe visible when looking at Fig. 2b. Hee, SFR2a achieves an incease of app. 5 % copaed to FR1, wheeas SFR2b even has an app. 25-30 % gain ove FR1. This is an iense gain, consideing the fact that the gain solely stes fo asking the esouce block powe levels. Anothe inteesting effect shows the weakest use thoughput cuve of the had fequency euse case HFR2. Up to a axiu equied ate of 4Mbps, the pefoance of the cell edge uses is bette than in the fequency euse 1 and soft fequency euse SFR2a case. This advantage taces back to the fact that thee is zeo intefeence fo the neighbo cell, and, thus, the channel states of the cell edge uses ae geneally bette than in the fequency euse 1 o the soft fequency euse case. Due to the liited esouces in the had fequency euse HFR2 case, howeve, the weakest uses cannot take advantage of the inceasing axiu ate above that 4Mbps theshold. This is ainly because the cell edge uses hadly get any esouces at all, if the stonge uses ae allowed to consue esouces fo such high ates. Accodingly, thei ean thoughput deceases with the inceasing ax ate afte that tuning point. This is vey likely to happen to the othe schees as well at diffeent points on the ax ate theshold axis. In geneal, none of the locally optiized schees gets close to the optiu in the highe axiu equied ate ange. Note that all uses achieve the axiu equied ate in the consideed ange, if the esouces ae distibuted optially. Even though local optiization stategies ae vey unlikely to get to a pefoance siila to the global optiu, thee is uch space fo ipoveents. Using ou efeence odel, poising candidates can be judged with espect to global optiality. REFERENCES [1] 3GPP; Technical Specification Goup Radio Access Netwok, Physical channels and odulation (elease 8), TS-36.211, Jun. 2007, vesion 1.2.0. [2] M. Stenad, T. Ottoson, A. Ahlén, and A. Svensson, Attaining both coveage and high spectal efficiency with adaptive OFDM downlinks, in Poc. of the 58th IEEE Vehicula Technology Confeence (VTC-Fall 03), vol. 4, Oct. 2003, pp. 2486 2440. [3] 3GPP; Huawei, Soft fequency euse schee fo UTRAN LTE, R1-050507, May 2005. [4], Futhe analysis of soft fequency euse schee, R1-050841, Sep. 2005. [5] K. Dopple, X. He, C. Witjing, and A. Soi, Adaptive soft euse fo elay enhanced cells, in Poc. of the 65th IEEE Vehicula Technology Confeence (VTC-Sping 07), Ap. 2007, pp. 758 762. [6] C. E. Shannon, A atheatical theoy of counication, Bell Syste Tech. J., vol. 27, 1948. [7] I. Ki, H. Lee, B. Ki, and Y. Lee, On the use of linea pogaing fo dynaic subchannel and bit allocation in ultiuse OFDM, in Poc. of the IEEE Global Telecounications Confeence (Globeco 01), Novebe 2001, pp. 3648 3652. [8] Q. Wang, J. Xu, and Z. Bu, Popotional-fai bit and powe adaptation in ulti-use OFDM systes, in Poc. of the IEEE Intenational Syposiu on Pesonal, Indoo and Mobile Radio Counications (PIMRC), Helsinki, Finland, Sep. 2006, pp. 1 4. [9] G. Song and Y. Li, Utility-based joint physical-mac laye optiization in OFDM, in Poc. of the IEEE Global Telecounications Confeence (Globeco 02), vol. 1, Novebe 2002, pp. 671 675. [10] M. Bohge, J. Goss, M. Meye, and A. Wolisz, Dynaic esouce allocation in ofd systes: An oveview of coss-laye optiization pinciples and techniques, IEEE Netwok Magazine, Special Issue: Evolution towad 4G wieless netwoking, vol. 21, no. 1, pp. 53 59, Januay/Febuay 2007. [11] A. Vaga, OMNeT++ Use Manual 3.2. [12] LINDO Systes Inc., LINGO 10 - Use s Guide, Chicago, Illinois, 2008. [13] S. ILOG, ILOG CPLEX 9.0 - Use s Manual, Pais, Fance, 2004. V. CONCLUSION We have pesented a eans to evaluate powe ask pefoance in cellula OFDMA systes. It is based on solving a global knowledge exploiting non-linea optiization poble. We have solved seveal accoding poble instances in a basic OFDMA/LTE efeence scenaio. Theeby, we have shown that thee is a significant gap in pefoance between the application of siple static powe asks in cobination with a locally optial schedule and the global optiu. This is tue especially fo the cell-edge use pefoance. Accoding futue woks include, thus, the developent of oe sophisticated static powe asks, as well as schees fo powe ask adaptation, and a copaison of thei pefoance to the optial case indicated in this pape. Consequently, solving the pesented non-linea optiization odel in a lage efeence odel is also of ajo inteest.