22nd IEEE Personl Indoor Mobile Rdio Communictions Aggregte Interference from Secondry Users with Heterogeneous Density Miurel Tercero, Ki Won Sung, nd Jens Znder Wireless@KTH, Royl Institute of Technology(KTH), SE-164 40 Kist, Sweden Emil: {mitv, sungkw, enz}@kth.se Abstrct This pper presents n nlyticl model to pproximte the probbility distribution function of the ggregte interference tht primry user receives from multiple secondry trnsmitters. In prticulr, we consider heterogeneity in sptil distribution of secondry users such tht there re severl sites with densely populted secondry users in the whole re. The concentrtion of secondry users is modeled s n nnulus sector with higher user density, which is termed hot zone. The mthemticl frmework presented in this pper cn redily be dpted to vrious existing interference models. It is observed tht the heterogenous user distribution hs considerble impct on the ggregte interference if the hot zone is ner the primry receiver, while hot zones over certin distnce is well pproximted by homogeneous secondry user distribution. The ggregte interferencelso dependson the shpe of thehot zone nd the interference eshold imposed on the secondry users. Index Terms Aggregte interference, secondry spectrum ccess, heterogeneous density, hot zone model I. INTRODUCTION Rdio spectrum hs become fundmentl resource for wireless communiction services with the drmtic increse in the wireless trffic. The trditionl wy to mnge spectrum hs been ssigning fixed nd exclusive frequency bnds to different systems for long periods of time. Problem tht hs emerged under the fixed spectrum lloction is tht there is not enough spectrum vilble for the incresing demnd of wireless services. On the other hnd, mesurement results indicte tht the llocted spectrum is being under-utilized[1]. A possible solution to utilize the llocted spectrum more efficiently is secondry spectrum ccess which is envisioned by cognitive rdio[2]. This llows secondry users to ccess the spectrum tht hs lredy been ssigned to primry users. Thebsicideisthtthesecondryusersshouldbecpble of detecting opportunities for using the llocted spectrum without cusing hrmful interference to the primry users. The protection of the primry users from interference is crucil for llowing the secondry users to ccess the spectrum. Accurte modeling of the ggregte interference is of importnce in ddressing the impct of multiple interfering secondry users. Mthemticl models for the probbility distribution of ggregte interference in secondry ccess hve recently been investigted in [3] [7]. The models in [3] [6] considered n exclusion region of circle with fixed rdius inordertooffertheprotectiontotheprimryuserfromdetrimentl interference. Homogeneous Poisson point process ws employed to spred the secondry users outside the exclusion region. In [7], secondry users re uniformly distributed in lrge circle nd the trnsmissions of secondry users re regulted by n individul interference eshold under the ssumption tht the secondry users know the propgtion loss to the primryuser. The modelin [7] hs been pplied to prcticl secondry ccess scenrios where meteorologicl rdrs nd eronuticl equipments re considered to be the potentil primry users[8],[9]. In spite of the extensive reserch, the existing work hs limittion tht the secondry users re ssumed to be distributed in homogeneous mnner. In prcticl environments, it is usul tht the secondry users hve heterogeneity in sptil user distribution. For exmple, let us consider low power secondry users such s WLAN devices. The towns or cities will hve higher concentrtion of secondry users thn the rurl res. In this regrd, the following reserch question should be ddressed: How is the ggregte interference ffected if heterogeneous densities of secondry users re considered? Inthispper,weimtnsweringthequestion.Ourmin contribution is to propose mthemticl frmework to derive the probbility distribution function (pdf) of the ggregte interference generted by multiple secondry users but including heterogeneous density. We consider sitution tht there re severl zones with different levels of concentrtion in the whole re of homogeneous or uniform bckground user density. Ech zone is modeled s n nnulus sector, whichistermedhotzone.weobtinthepdfoftheggregte interference bsed on our previous work [7]. Note tht the frmework presented in this work cn lso be esily pplied to other existing models, e.g.[3] [6]. Our hot zone model hs n dvntge tht vrious shpes of hot zones cn be considered by dusting the prmeters of the nnulus sector. We investigte the impct of shping prmeters of the hot zone such s the distnce from the primry receiver, density difference from the bckground, nd sizeofthehotzone. The rest of the pper is orgnized s follows. Section II detils the system model, the bsic ssumptions, nd the hot zone model. Section III presents the nlytic model for the ggregte interference. Section IV shows the numericl results obtined from mthemticl nlysis nd simultion. Finlly, weclosewiththeconclusioninsectionv. 978-1-4577-1347-7/11/$26.00 2011 IEEE 428
II. SYSTEM MODEL A. Modeling of secondry spectrum ccess We consider reference scenrio tht primry receiver is interfered by multiple secondry trnsmitters spreding in lrge re. Secondry ccess to 5.6 GHz rdr spectrum cn be regrded s prcticl exmple of our scenrio[8]. However, we do not tke into ccount rdr specific fetures such s the rdr ntenn pttern. Insted, we focus on developing mthemticl frmework to reflect the heterogeneous user density. A mechnism to protect the primry user is considered tht resembles dynmic frequency selection (DFS) specified in the IEEE 802.11h stndrd [10]. Ech secondry user is llowed to trnsmit if its individul interference to the primry user is less thn certin eshold. We ssume tht the secondry users cn hve n ccurte estimte of the propgtion loss to the primry receiver. This ssumption is resonble if the primry user is the rdr or the secondry users re ssisted by becon signl from the primry receiver. Detiled description of the considered interference protection schemecnbefoundin[7]. Let ξ betheinterferencethttheprimryuserwillreceive from the trnsmission of secondry user. Since the trnsmission of is regulted by the interference protection mechnism, the user stops trnsmission if it cuses interference greter thn the eshold I. Thus,the ctul interference fromuser,nmely I,isgivenby: { ξ, if ξ I = I, (1) 0, otherwise. The interference eshold I is ssumed to be predetermined. We consider n instntneous moment tht N secondryusersinthesystemdesiretotrnsmit.letusdefine I s the ggregte interference t the primry user cused from thesecondryusers.then, I iscomputedsthesumofthe individul interference of N secondry users. I = N I. (2) =1 B. Modeling of the heterogeneous secondry user density Modeling of heterogeneity in the sptil distribution of secondry users should be done first in order to obtin the pdf of I. There would be vrious models to describe the heterogeneity depending on specific geogrphicl loctions nd the types of primry nd secondry systems. Note tht we consider lrge re consisting of cities, towns, nd rurl res.itisusulthtthepopultiondensityofcityortown ismuchhigherthnthtofrurlre.itislsoresonbleto consider tht the number of secondry users is proportionl to the popultion density. We further ssume tht the secondry users re homogeneously distributed within ech city or town with it own density. Then, n nnulus sector, nmely hot zone, is employed to describe the crowded region s depicted in Fig. 1. For the rest of the pper, we focus on one hot zone for brevity nd for better investigtion of its impct on θ H r H 2 r H RB -> Primry receiver -> Secondry trnsmi er Fig. 1. Representtion of the scenrio with the hot zone model. the ggregte interference. Extending our work to severl hot zones with different densities is trivil. The use of nnulus sector in the modeling of the hot zone is inspired by recent work in the field of secondry spectrum ccess. In [11], non-circulr re is described by the ggregtion of infinitesiml nnulus sectors. In [12], the impct of secondry field size is investigted by ssuming the nnulus sector re. The nnulus sector hs n dvntge tht it cn be molded to vrious shpes ccording to the ee shping prmeters: r H, rh, nd θ H. As illustrted in Fig. 1, r H is the distnce between the center of the hot zone nd the primryuser,thelengthofthehotzone(depth)is 2 rh,nd thecentrlngle(width)isgivenby θ H. The distnce, depth, nd width chrcterize the hot zone long with the density of the zone. We ssume tht N B secondry users re homogeneously distributed in circle of rdius R B (bckground) nd N H secondry users re homogeneouslydistributedwithinhotzone.let ρ B nd ρ H denote the densities of secondry users in the bckground nd thehotzone,respectively(ρ H > ρ B ).Theprimryreceiveris locted t the middle of the bckground circle. The hot zone model is roughly demonstrted in ner Stockholm re s illustrted in Fig. 2 where meteorologicl rdr is considered to be the primry receiver. The primry user is bout 35 Km wy from the Stockholm city where popultion density is significntly higher thn surrounding res. III. PROBABILITY DISTRIBUTION OF AGGREGATE INTERFERENCE A. Distribution of the secondry users Letusconsidernnnulussectorwithinnerrdius R 1,outer rdius R 2,ndcentrlngle θ c.acirclecnberegrdeds specil cse of the nnulus sector. Thus, it cn represent both the bckground re nd the hot zone. For the cse of the bckgroundre,thefollowingprmetersrepplied: R 1 = 0, R 2 = R B,nd θ c = 2π.Asforthehotzone,theprmeters re R 1 = r H rh, R 2 = r H + rh, nd θ c = θ H. Note thttheprimryuserisloctedttheoriginofthebckground circle. 429
Primry receiver (Meteorologicl rdr in Arlnd Airport) where f ξ (z) = h(z, R 2 ) h(z, R 1 ), (7) Secondry trnsmi ers r H θ H r H Fig.2. Anppliction ofthehotzonemodeltostockholm re.themp is cptured from http://www.eniro.se/. Theloctionofnrbitrrysecondryuser isdenotedby (r, θ ), where the rndom vrible (RV) r is the distnce from the primry user to the user, nd the RV θ is the its ngle. Since the user is ssumed to hve the uniform distribution, the pdf the loction is given by: f r,θ (y, θ) = 2y (R 2 2 R2 1 )θ, R 1 < y R 2, 0 θ θ c. (3) By ssuming the primry nd secondry users hve omnidirectionl ntenns,(3) cn be simplified s f r (y) = 2y (R 2 2 R2 1 ), R 1 < y R 2. (4) Noticethtwedefined(3)tomodel N B + N H secondry usersheterogeneouslydistributedwithinnreofrdius R B. However the sme distribution cn lso model N B + N H secondry users homogeneously distributed if the hot spot is not considered. B. Interference from n rbitrry secondry user Notetht ξ isdefinedstheinterferencethttheprimry user will receive from the trnsmission of secondry user. Then, ξ isgivenby: ξ = GP t L(r )X, (5) where P t denotes the trnsmit power of the secondry user, X isrndomvriblemodelingfdingeffect,nd L(r )is the distnce depend pth loss model defined s: L(r ) = Cr α, (6) where C nd α re the pth loss constnt nd exponent, respectively. The other gin nd losses re ccounted by G. Weconsiderlog-normlshdowfdingfor X ndssume tht X isindependentof r.from theresultof[7] ndthe pdfofthesecondryuser in(4),itisstrightforwrdtoshow thtthepdfof ξ, f ξ (z),isderivedsfollows: h(z, y) = Ωz 2 α 1 ( ln 1 +erf z GP tl(y) 2σ 2 X ) 2σ2 X α. (8) In(8), σx db denotethestndrddevitionoftheshdowingin dbscle,ndtheconstnt Ωisgivenby: Ω = 1 (R 2 2 R2 1 )α ( 1 GP t C ) 2 α exp ( 2σ 2 X /α 2). (9) In order to obtin the pdf of I from f ξ (z), we follow the steps in [7]. When I is pplied to user, it stops trnsmissionif ξ exceeds I sdepictedin(1).thismens tht portion of secondry users hve zero trnsmission power. Thtportionofusersisgivens 1 F ξ (I )where F ξ (.) denotedecumultivedistributionfunction(cdf)of ξ.thus, thepdfof I issfollows: 1 F ξ (I ), if z = 0 f I (z) = f ξ (z), 0 < z I (10) 0, otherwise. The derived f I (z) cn be directly pplied to both the bckground nd the hot zone secondry users by dusting theprmeters R 1 nd R 2 sdiscussediniii-a. C. pdf of the ggregte interference Let us define I B nd Ii H s the interference from the secondry user in the bckground nd the secondry user i in the hot zone, respectively. The pdf of I B nd Ii H re given in (10). Since we ssume tht N B secondry users re uniformly distributed within the bckground re nd N H uniform secondry users re within the hot zone, the totl interference received t the primry user from the ll secondryusers I T iscomputedsthesumoftheggregte interference from the users in the bckground I B nd the ggregteinterferencefromtheusersinthehotzone I H. N B N H I T = I B + I H = I B + Ii H, (11) =1 i=1 We employ cumulnt-bsed pproch to pproximte the pdfof I T.Notethtthecumulntshventtrctiveproperty thtthe m th cumulntofthesumofindependentrvsisequl tothesumoftheindividul m th cumulnts [6].Also,thefirst nd second cumulnts of RV correspond to the men nd vrince.let k I B (m)nd k I H (m)denotethe m th cumulnt of I B nd IH,respectively.Then, k I T (m) = k I B (m) + k I H (m) (12) N B N H = k I B (m) + k I H i (m). =1 i=1 430
TABLE I SIMULATION PARAMETER VALUES Prmeters Vlues 1. Primry receiver(meteorologicl rdr) Frequency bnd[mhz] 5600 Antenn height[meter] 30 Trnsmission power[kw] 250 Bndwidth[MHz] 4 Antenn Gin[dBi] 40 2. Secondry trnsmitters(wlan) Antenn height[meter] 1.5 Trnsmissionpower[P t inw] 0.2 Bndwidth[MHz] 20 Antenn gin[dbi] 0 Rdiusofbckgroundre[R B inkm] 150 Shdowingstndrddevition[σX db indb] 8 From the cumulnts of the I T, the pdf of IT cn be pproximted s known distribution by employing the method of moments. We use log-norml distribution to pproximte thepdfof I T sin(13). ( ) 1 ln(z) µi T f I T (z) = exp z 2πσI 2 2σ 2. (13) T I T Theprmeters µ I T nd σi 2 ofthepdfcnbeobtinedfrom T the first nd second cumulnt computtions s: k I T (1) = E[I T ] = exp[µ I T + σi 2 /2], (14) T k I T (2) = V r[i T ] = (exp[σ 2 I ] 1)exp[2µ T I T + σ2 I ]. (15) T IV. NUMERICAL RESULTS In this section, we present the results of the numericl experiments. The primry nd secondry systems re modeled with the prmeter vlues summrized in Tble I. The bsic propgtion loss model used in this study is the C1-Suburbn WINNERmodelwhichisproposedfor5GHzbndbyWIN- NER proect in[13]. The prmeters of the propgtion model indbsclere: L(d) = 41.2036 + 3.5225 log 10 (d[meter]). (16) Notice tht in section III, we introduced generl mthemtic frmework to clculte the ggregte interference, nevertheless when it comes to the experimentl prt we need to define specific primry receiver nd secondry users. Thus, we hve set meteorologicl rdr s primry receiver nd WLANs s secondry trnsmitters. However, we ssume tht the primry receiver or the rdr hs n omnidirectionl ntenn. This is becuse we do not compute the ggregte interference by snpshots(when the rdr is fcing portion of the totl re), but the contrry. This ssumption leds to obtin conservtive results. The CDF of the totl ggregteinterference I T with heterogeneous secondry users density is presented in Fig. 3. We cn notice good mtch with the Monte Crlo simultion. Twodifferent I represented,onewithlowerrequirement ofinterferenceprotection I =-100dBmwhichcretehigher ggregte interference becuse 99.97% of the secondry users re llowed to trnsmit. The second with higher requirement of interference protection I =-160dBm which induce less ggregte interference to the primry receiver becuse only 52.61% of the secondry users cn trnsmit. The next two experiment presented in Fig. 4 nd Fig. 5 hve the purpose to show the impct of the hot zone s prmeters (r H, nd rh ) on the ggregte interference. In Fig.4wevry thedistncebetween theprimryreceiver nd the center of the hot zone r H, for the two mentioned interference protection requirement. It is observed tht there is n intersection point or vlue for r H from where considering the distribution of secondry users s homogeneous (uniform) or heterogeneous led to the sme result in term of ggregteinterference.thisvlueof r H dependsonthe I requirements.also,itisfoundthttsomepointof r H nd high I consideringhomogeneousdistributionofsecondry trnsmitters overestimtes the ggregte interference. InFig.5weexperimentwithdifferentvluesforthedepth of the hot zone but keeping r H fixed. This shows how the distributionof dispersionin thehotzone, r H rh < y r H + rh, ffects the ggregteinterferencewhen different I re required. If the center of the hot zone is 80 Km wy from the primry receiver, vrition in rh is not ffecting the ggregte interference. The contrry cse hppens whenthecenterofthehotzoneisonly30kmwyfromthe primry user. Then, the ggregte interference is incresing or decresing(ccording I )withtheincrementof rh.this suggests tht the impct on the ggregte interference will dependonthegiven I, r H nd rh. Cumultive Distribution Function(CDF) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Simultion I = 100dBm Anlysis I = 100dBm Simultion I = 160dBm Anlysis I = 160dBm 120 115 110 105 100 95 90 85 Aggregteinterference powerfromsecondryusers I T [dbm] Fig. 3. CDF of I T with heterogeneous users density, with one hot zone with prmeters I = 80dBm nd 140dBm, r H =15Km, rh =5Km, θ H =10, ρ B =1/Km 2,nd ρ H =20/Km 2. V. CONCLUSION In this pper we proposed mthemticl model to consider the heterogeneous distribution of secondry users nd investigted the impct of this heterogeneity on the ggregte 431
P 95 [I T ]indbm 65 70 75 80 85 90 95 100 Heterogeneous cse I = 80dBm Homogeneous cse I = 80dBm Heterogeneous cse I = 140dBm Homogeneous cse I = 140dBm depthofhotzone,i.e.theverticllengthofthennulussector, nd the interference eshold imposed on the secondry users re key prmeters to determine the behvior of the ggregte interference. Severl importnt issues remin s further reserch. First, the hot zone model should be exmined in prcticl geogrphicl regions to know how well it reflects the rel environment. Second, the impct of multiple hot zones should be investigted. Third, more prcticl primry nd secondry system chrcteristics should be considered such s the directionl ntenn. 105 5 10 15 20 25 30 35 Fig. 4. Impct of the distnce between the center of the hot zone nd the primry user r H in I T, with the hot zone prmeters r H =5Km, Are H =78.5Km 2, ρ B =1/Km 2, nd ρ H =20/Km 2. The opertor P 95 [I T ] denotesthe95thpercentile of I T. P 95 [I T ]indbm 74.7 74.8 74.9 75 75.1 75.2 104.1 104.15 104.2 104.25 104.3 104.35 104.4 Heterogeneous cse r H =30Km Heterogeneous cse r H =80Km Homogeneous cse rh I = 80dBm 5 10 15 20 25 30 Heterogeneous cse r H =30Km Heterogeneous cse r H =80Km Homogeneous cse rh in[km] I = 140dBm 5 10 15 20 25 30 rh in[km] Fig.5. Impctofthevritionof rh on I T,when N H=1,500users,nd ρ B =1/Km 2.Theopertor P 95 [I T ]denotesthe95thpercentile of IT. interference to the primry user. We ssume lrge re which is mixture of cities, towns, nd rurl res. The regions with higher secondry user densities re termed hot zone, nd modeled s nnulus sectors on circle of bckground user density. In order to obtin the pdf of the ggregte interference, first we derived the pdf of n rbitrry secondry user in either hot zone or bckground.then, the method of moments is employed to pproximte the pdf of the ggregte interference s log-norml distribution. Comprison of the nlytic pdf with Monte Crlo simultion shows good greement. This suggests tht the derived pdf cn obvite the need for complicted nd time-consuming simultion. Our hot zonemodellso hsndvntgethtitcnhvevrious shpeswithinthefrmeofthennulussector.theimpctof shping prmeters ws evluted. Bsed on the numericl experiments, our findings re s follows: the ggregte interference is ffected considerbly by the heterogeneous density or concentrtion of secondry users when the hot zone is close to the primry receiver. On the other hnd,if the hotzoneis fr wy,we cn simplify the model by not considering secondry user heterogeneity. The ACKNOWLEDGMENT The reserch leding to these results hs received prtil funding from the Europen Union s Seventh Frmework Progrmme FP7/2007-2013 under grnt greement n 248303 (QUASAR). The uthors lso would like to cknowledge the VINNOVA proect MODyS for providing prtil funding. REFERENCES [1] D. Cbric, I. O Donnell, M.-W. Chen, nd R. Brodersen, Spectrum Shring Rdios, IEEE Circuits nd Systems Mgzine, vol. 6, no. 2, pp. 30 45, 2006. [2] J. Mitol III nd G. Q. Mguire Jr, Cognitive Rdio: Mking Softwre Rdios More Personl, IEEE Personl Communictions, vol. 6, no. 4, pp. 13 18, Aug. 1999. [3] A. Ghsemi nd E. S. Sous, Interference Aggregtion in Spectrum- Sensing Cognitive Wireless Networks, IEEE Journl of Selected Topics insignlprocessing,vol.2,no.1,pp.41 56,Feb.2008. [4] A. Ghsemi, Interference Chrcteristics in Power-Controlled Cognitive Rdio Networks, in Proc. 5th Interntionl Conference on Cognitive Rdio Oriented Wireless Networks nd Communictions (CrownCom), Cnnes, Jun. 9-11 2010. [5] X. Hong, C.-X. Wng, nd J. Thompson, Interference Modeling of Cognitive Rdio Networks, in Proc. 67th IEEE Vehiculr Technology Conference(VTC), Singpore, My 11-14 2008, pp. 1851 1855. [6] M. Aluid nd H. Ynikomeroglu, A Cumulnt-Bsed Chrcteriztion of the Aggregte Interference Power in Wireless Networks, in Proc. 71st IEEE Vehiculr Technology Conference(VTC), Tipei, My 16-19 2010. [7] K. W. Sung, M. Tercero, nd J. Znder, Aggregte Interference in Secondry Access with Interference Protection, IEEE Communictions Letters, 2011, ccepted for publiction, temporriliy vilble t http://dl.dropbox.com/u/18150297/sung.pdf. [8] M. Tercero, K. W. Sung, nd J. Znder, Impct of Aggregte Interference on Meteorologicl Rdr from Secondry Users, in Proc. IEEE WCNC, Cncun, Mr. 28 31 2011. [9] K. W. Sung, E. Obregon, nd J. Znder, On the Requirements of Secondry Access to 960-1215 MHz Aeronuticl Spectrum, in Proc. IEEE DySPAN, Achen, My 3 6 2011. [10] IEEE Std 802.11h-2003, Spectrum nd Trnsmit Power Mngement Extensionsinthe5GHzbndinEurope, Oct.2003. [11] A. Rbbchin, T. Quek, M. Win, nd H. Shin, Cognitive Network Interference, IEEE Journl on Selected Ares in Communictions, vol.29,no.2,pp.480 493,2011. [12] M. Aluid nd H. Ynikomeroglu, Impct of Secondry Users Field Size on Spectrum Shring Opportunities, in proc. IEEE WCNC, Sydney, Apr. 18 21 2010. [13] IST-4-027756 WINNER II, D1.1.2 v1.2 WINNER II Chnnel Models, [Online]. Avilble: https://www.ist-winner.org/winner2- Deliverbles/. 432