Controlling Aggregte Interference under Adjcent Chnnel Interference Constrint in TV White Spce Lei Shi, Ki Won Sung, nd Jens Znder KTH Royl Institute of Technology, Wireless@KTH, Stockholm, Sweden E-mil: lshi@kth.se, ngkw@kth.se, jenz@kth.se Abstrct TV White spce, where secondry systems cn be deployed inside the TV coverge re nd utilize the geogrphiclly unoccupied TV chnnels, is considered s promising solution to relieve the spectrum shortge. To utilize this spectrum, the secondry users must enre the protection of TV reception from hrmful interference on both co-chnnel nd djcent chnnels. In this pper, we propose n nlyticl pproch to determining the permissible trnsmit power for short-rnge secondry users under ggregte djcent chnnel interference constrint in TV white spce. This pproch employs sttisticl interference modeling which considers rndom deployment of secondry users, ntenn gin pttern, shdow fding, nd the cumultive effect of interference from multiple djcent chnnels. Numericl relts show tht the proposed scheme permits significntly higher trnsmit power thn the existing deterministic method does, while t the sme time, it keeps the required level of TV protection. Therefore, considerble potentil for the shortrnge secondry ccess to TV white spce is expected with our pproch. Index Terms TV White Spce, ggregte interference, trnsmit power, djcent chnnel, geo-loction dtbse. I. INTRODUCTION With the rpid growth of wireless dt trffic, the limited spectrum hs become the bottleneck for the development of wireless services. Secondry ccess in the VHF/UHF TV bnd, often referred to s TV white spce (TVWS), is considered s one promising solution to this spectrum scrcity problem. It llows secondry users (SUs) to ccess the loclly or temporlly unoccupied TV chnnels, s long s the primry user (PU) is protected from the secondry interference. The bundnce of the potentil vilble spectrum in TVWS nd its fvorble propgtion chrcteristics hve ttrcted wide interests from cdemics nd industry like [1]. The regultors, including FCC in the US [2], CEPT in Europe [3] nd Ofcom in the UK [4], hve tken the inititive to estblish methodologies for estimting the TVWS vilbility, in terms of the permissible secondry trnsmit power t different loctions on different chnnels. To fcilitte the detection of spectrum vilbility, it is recommended to utilize the geo-loction dtbse, which contins informtion ch s TV coverge re, terrin elevtion, popultion density, nd etc. Previous studies in this re hve minly focused on the cochnnel interference cse, where the SUs re locted outside the TV coverge re nd trnsmitting on the sme chnnel used by the TV brodcsting system [5] [6]. These nlysis hve extended the secondry trnsmit power lloction problem to multiple SU cse, with either sttisticl or deterministic interference constrints. Due to the imperfection of the TV receiver filter, however, the TV reception is bjected to not only co-chnnel interference (CCI) but lso djcent chnnel interference (ACI). Thus, even the SUs trnsmitting on non-brodcsting chnnels my still cuse hrmful interference to TV receivers ner by. This is prticulrly true for the WiFi-like or femtocell-like short-rnge SUs tht cn be deployed with high density, s the cumultive effect of ACI over the spectrl domin [7] could cuse significnt deteriortion to the TV reception qulity. However, unlike the CCI cse where the geo-loction dtbse cn be used to estimte the interfering link gin, it is very difficult to determine the ACI link gin between the SU nd the victim TV receiver in its proximity, due to the uncertinty of the TV receiver loction. One deterministic pproch, clled Reference Geometry, ws proposed in ECC report 159 [3] to ddress the ACI ise. Its bsic concept is to define certin fixed ACI link geometries corresponding to the worst cse scenrio for different types of PU/SU deployments. In [8], it is proposed to extend this method to include multiple SUs cse by plcing 3 SUs t the sme reference distnce. While this deterministic method is strightforwrd to implement, its inflexibility lso leds to pessimistic estimtion of the permissible trnsmit power on djcent chnnels [9]. Motivted by these fcts, we propose sttisticl pproch to determine the permissible secondry trnsmit power under ggregte ACI constrint, exploiting the specific fetures of TVWS, ch s the rndom deployment of SUs, TV receiver ntenn directivity [], nd the cumultive effect of ACI. The proposed method utilizes the informtion vilble in the geoloction dtbse to estimte the permissible trnsmit power for different SUs, under PU protection constrint. In the following of this pper, we will strt by briefly explining the system models in Section II. Then the permissible trnsmit power problem is described in Section III. Numericl relts re shown in Section IV. Finlly conclusions re drwn in Section V. A. TV Coverge II. SYSTEM MODEL Let us sme TV trnsmitter brodcsting on set of chnnels, X. The studied re is divided into smll re ele-
Fig. 1: System model for secondry ccess in TVWS. ments ccording to the limited resolution of the geo-loction dtbse, denoted s pixels. In pixel i, ll TV receivers re smed to hve pproximtely the sme received TV signl strength P. i The minimum TV receiver sensitivity level is P min. The mere for TV coverge qulity is the loction probbility, defined s the chnce of ccessful reception of ny TV in tht pixel. Unccessful TV reception is termed outge, either due to the TV signl fding or other interferences. For TV in pixel i, the loction probbility without secondry interference is designted q i 1 q i 1 {P i P min + γ I i }, (1) where, γ is the required minimum rtio between TV signl nd TV self-interference, nd I i is the received TV selfinterference power from other TV trnsmitters. The coverge re is defined by q1 i q, with q being the minimum required loction probbility defined by the regultor. The set of pixels inside the coverge of chnnels x X is denoted s Λ X. B. Interference from Secondry Users To emphsize the cumultive effect of ACI, we consider WiFi-like or femtocell-like short-rnge secondry system deployed inside the TV coverge re following sptil Poisson processes with density λ. The secondry trnsmit power is smed to be limited by the ggregte djcent chnnel interference constrint, due to their close distnce to the potentil victim TV receiver. Inside Λ X, the SUs cn ccess to the unoccupied chnnels, y Y : Y = X c (where X c is the complement of X, with ll the chnnels in VHF/UHF bnd s the universl set). Asming the SU is trnsmitting with power level P y on chnnel y, the interference received by TV on chnnel x in pixel i cn be written s I x = P y g f g θ (θ)g r (d). (2) Here g f is the chnnel fding rndom vrible. g θ (θ) nd g r (d) re the TV receiver ntenn gin nd the distnce dependent pthloss between the SU nd the TV receiver, respectively. Note tht d is generlly unknown nd cn only be Desired to Undesired (D/U) power rtio (db) 4 5 6 7 Adjcent Chnnel Rejection Thresholds on Chnnel 27 (522 MHz) Reference dt[6] D/U rtio for low TV signl strength D/U rtio for high TV signl strength 8 N 6 N 4 N 2 N N+2 N+4 N+6 N+8 N+ N+12 N+14 N+16 N+18 Adjcent Chnnel Fig. 2: Protection rtio s function of frequency offset between TV signl nd interfering signl [7]. estimted bsed on SU density, due to the uncertinty of TV receiver loction. Therefore, ny TV in the sme pixel on the sme chnnel would experience the sme level of interference sttisticlly. C. Cumultive Effect of Multiple Adjcent Chnnels Interferences It hs been reported in [7] tht, the permissible secondry trnsmit power in given djcent chnnel must be reduced, when more djcent chnnels re ccessed by SUs simultneously. It indictes the cumultive effect of interferences from multiple djcent chnnels. To model this effect, we first define n equivlent CCI (I x,) on TV brodcsting chnnel x, tht would cuse the sme level of dmge to the TV reception s the ggregte ACI from interferers on the neighboring chnnels y n Y. It cn be pproximted by the liner mmtion of ACIs, weighted by the protection rtio of ech chnnel respectively I x, = N γ ( f x yn ) I,n x = γ ( ) N γ ( f x yn ) P yn G n, γ ( ) (3) where γ ( f) is the minimum required TV signl to SU interference rtio with frequency offset of f (lso known s protection rtio; see Fig. 2). G n = g f g θ (θ n )g r (d n ) denotes the coupling gin of the n th interfering link from djcent chnnels. N is the totl number of ctive SUs. Without loss of generlity, we cn sme the ggregte interference received by ll TV receivers in the sme pixel hve the sme sttisticl properties. We further sme tht, s the number of ctive SUs increses, the trnsmit power of SUs on different chnnels must be decresed with equl proportion, to stisfy the ggregte interference constrint s defined in the following section. III. PERMISSIBLE TRANSMIT POWER UNDER ADJACENT CHANNEL INTERFERENCE CONSTRAINT The permissible trnsmit power P i,y must be determined per pixel i nd TVWS chnnel y bsed on the informtion
vilble in the geo-loction dtbse, to enre the reduced loction probbility q i,x 2 under secondry interference is no less thn q : { 2 q i,x + y Y P i,x P min + γ I i,x { P i,x P min + γ I i,x γ( f x y ) x X, i Λ X. j Λ y p j,y N y j } + γ ( )Īi,x, G n q, Here N y j is the number of SUs in pixel j on chnnel y. From the geo-loction dtbse s perspective, these SUs shre the sme interference properties, therefore they would be ssigned with the sme permissible trnsmit power level. According to (4), ll SUs trnsmitting on the djcent chnnels y Y, both inside nd outside the coverge re of chnnel x my contribute to the ggregte ACI received by TV in pixel i. In prctices, however, we cn limit our clcultion to few pixels j within the dominnt interference region j Λ i ε, where the mjority, ( ε)%, of the ggregte interference re generted [11]. For instnce, our study hs shown tht, over 99.5% of the ggregte ACI in burbn environment would come from n re with rdius less thn 5 meters. Within this region, the differences in popultion densities nd TV coverge qulities re lmost negligible, thus we cn sme tht P i,y (4) P j,y, j Λ i ε. (5) Denoting the equivlent permissible trnsmit power on chnnel y s P j,x = P j,y γ( f x y ), the constrint in (4) cn be pproximted s 2 Pr P i,x P i,x q i,x P min P min P i,x Zi,x N ε i G n x X, i Λ X, where Z i,x = P i,x + γ I i,x γ I i,x { + P i,x P i,x P i,x N i ε N i ε P min γ I i,x nd G = G n G n } Zi,x G i q, N i ε (6) G n. And Nε i denotes the totl number of ctive SUs trnsmitting on ll djcent chnnels inside Λ i ε. It follows Poisson distribution with density λ i With the simplified constrint in (6), the equivlent permissible trnsmit power P i,x cn be solved for ech pixel i nd ech chnnel x seprtely, s long s we cn find the joint / distribution of Zi G i. A. Cumulnt Bsed Log-norml Approximtion of Secondry Interference Considering tht the SU deployment follows Poisson sptil distribution, their ggregte interference cn be pproximted by different distributions, ch s log-norml, shifted-lognorml or truncted-stble distribution [12] [13]. We choose the log-norml pproximtion, becuse of its esy conversion into logrithmic scle, nd good pproximtion of the upper til of the ggregte interference distribution. By using the first two cumulnts [14] of G i, it cn be pproximted by log-norml rndom vrible Ĝi, with the following probbility distribution function (pdf): f G i (g) fĝi (ĝ) = 1 ĝσĝi 2π exp [ (ln ĝ µĝi 2σ 2 Ĝ i ) 2 ], (7) where µĝi nd σĝi cn be obtined by mtching the cumulnts of Ĝi to tht of G i using the following equtions: [ ] κ 1 (G i ) = exp µĝi + σ 2, (8) Ĝ/2 i [ ] ( ) κ 2 (G i ) = exp(σ 2 1 exp Ĝ) i 2µĜi + σ 2. (9) Ĝ i The cumulnt κ m (G i ) is given by κ m (G i ) = 2πλ i µ m (G f ) µ m (G θ ) Rɛ d g m r,(r)rdr. () where R ε is the rdius of the dominnt interference region. µ m (G f ) nd µ m (G θ ) re the m th rw moments of the distributions of chnnel fding nd ntenn gin, respectively. d is the minimum seprtion distnce between the TV receiver ntenn nd the interfering SU. B. Log-Norml Approximtion of TV Signl nd TV Selfinterference Asming shdow fding in TV signls, Z i,x cn be modeled s the difference between log-norml rndom vribles nd liner constnt. Recll tht q i,x 1 {Z i,x }. Z i,x, thus it cnnot be directly pproximted s log-norml rndom vrible [15]. But if we pply conditionl probbility to (6), it cn be rewritten s cn be negtive with probbility 1 q i,x 1 q {Z i,x Since P i,x Pr{P i,x + Pr{Z i,x < } Pr{P i,x } Pr{P i,x is non-negtive, Pr{P i,x } =. Hence we hve q = + q i,x 1 Pr{P i,x Zi,x G i Z i,x < } Zi,x G i Z i,x }. (11) Zi,x G Z i,x i < } = Zi,x G i Z i,x }, x X, i Λ X. (12)
Now we cn pproximte Z = Z i,x by log norml Z i,x rndom vrible Ẑ LN ( µẑ, σẑ ) by using method of moment [14]. With the bove pproximtion, we cn now convert the constrint (12) into db domin q i,x 2 q i,x 1 Pr{P i,x (dbm) Z (dbm) Ĝi (db) } q. (13) Noting tht both Z (dbm) nd Ĝi (db) follow norml distribution, we cn solve the equivlent permissible trnsmit power s P i,x (dbm) = µẑ (dbm) µ Ĝ i (db) [ ( 2erfc 1 2 1 q q 1 )] σ 2 Ẑ (db) + σ2 Ĝ i (db), (14) where erfc 1 ( ) is the inverse complementry error function. One SU trnsmitting chnnel, y, cn be djcent to different TV brodcsting chnnels, nd hve different constrints. But the permissible power is lwys limited by the TV chnnel most vulnerble to ACI. Thus the permissible trnsmit power for ech unoccupied chnnel y is then given by P i,y = min x X ( P i,x ). (15) γ( f x y ) It is worth mentioning tht, the permissible trnsmit power cn be decided by ech SU independently following the proposed procedure, requiring only the knowledge bout the secondry user density, deployment scenrio nd the TV coverge qulity t its own loction. It is not necessry to know the exct loctions of TV receivers. IV. NUMERICAL RESULTS In this section we first look into test scenrio to verify the proposed pproch ginst simultions. Lter, we pplied the proposed procedure to obtin the sptil distribution of the permissible trnsmit power in rel-world environment for short-rnge secondry system. A. Verifiction of the Proposed Approch In the test scenrio, we focus on single pixel i locted t D km wy from the TV trnsmitter. The SUs re deployed in the pixel i nd its rroundings, following Poisson sptil distribution with density λ i. Here we sme the studied pixel hs.99 loction probbility without secondry interference. In order to hve fir comprison with the reference geometry (Ref Geo) pproch for multiple secondry trnsmitters described in [8], here we lso considered burbn environment with outdoor SU nd rooftop TV ntenn. Propgtion model ITU Recommendtion P.1411 [16] for burbn re over rooftop link is dopted for the distnce bsed pthloss g r (r). It follows the free-spce pthloss for line-of-sight distnce up to d LoS, nd chnges to higher pthloss exponent fter certin brekpoint. This brekpoint distnce is set to be lrger thn the reference distnce, d ref, used in [8], so tht the secondry interference is not underestimted in our model. The minimum seprtion distnce d between the SU trnsmitter nd PU receiver is only limited by the physicl difference in their ntenn heights. On the other hnd, we lso modified the pthloss model ch tht g r (d) = g r (d ref ), for d d ref, becuse it is smed in [8] tht the highest interfering link gin is chieved t d ref. The prmeters for the test scenrio re mmrized in Tble I. Only shdow fding is considered in this pper, s the widebnd orthogonl frequency division multiplexing (OFDM) signl, used by the TV system nd prembly lso by the secondry system, is less prone to severe fst fding. TABLE I: Simultion Prmeter 5 m for ε =.5 Prmeter Vlue TV signl stndrd devition 4.65 db TV SINR requirement 17.4 db TV receiver sensitivity -8.6 dbm TV receiver ntenn height m t rooftop TV receiver ntenn directivity Defined by ITU-R BT419-3 [] Cluster height m Loction Probbility Threshold q.95 SU Trnsmitter height 1.5 m SU Trnsmitter ntenn gin dbi Secondry interference stndrd 3 db for d d LoS nd 6 db for devition d d LoS Dominnt interference region rdius R ε Line of Sight distnce in ITU- 5 m P1411 d LoS Reference distnce d ref 22 m Minimum seprtion distnce d 8.5 m Geo-loction dtbse resolution 25 m 25m A pir of the verifiction relts re shown in Fig.3 nd Fig.4, where Monte Crlo simultion is performed to djust the mximum SU trnsmit power itertively until the protection requirement is stisfied. As we cn see from Fig.3, the proposed method slightly underestimte the permissible trnsmit power when the SU density is low. On the other hnd, the estimted power level mtches closely with the simultion relt t higher SU density. The proposed method cn lwys provide fficient PU protection s seen in Fig.4. In comprison, the reference geometry method is overly pessimistic, even in the cse with very high SU density. B. A Cse Study: Permissible Trnsmit Power in Stockholm Are Hving verified the pproximtions, we now pply this method to rel environment, utilizing the popultion density [17] nd terrin elevtion informtion [18]. The initil study is focused on the Stockholm re (Fig.5). Here we sme the ctive SU density is one tenth of the popultion density nd the SUs cn select ll the unoccupied TV chnnels with equl probbility. There re one mjor TV trnsmitter (Tower A) with 28 meters height mst nd 8 dbm equivlent isotropiclly rdited power (EIRP), nd smller repeter sttion (Tower B) with 9 meters height nd 55 dbm EIRP. Both trnsmitters re brodcsting on the sme set of chnnels: chnnel 23, 42, 5, 53, 55, 56 nd 59 [19]. Here conservtive smption is mde tht, the cluster height nd TV receiver ntenn deployment throughout the
Permissible SU trnsmit power (dbm) 5 4 Ref Geo @ N+1 Proposed Approch @ N+1 Simultion @ N+1 Ref Geo @ N+5 Proposed Approch @ N+5 Simultion @ N+5 4 6 8 1 14 16 SU density per km 2 Fig. 3: Permissible trnsmit power with different SU densities λ. q 1 =.99, q =.95. () Mp of Stockholm re.1.9.8 Ref Geo Proposed Approch Simultion 1 q 1 5 45 4 Received TV Signl Strength (dbm) Urbn Are Outge probbility ((1 q 2 ).7.6.5.4.3.2 1 q* y coordintes (km) 35 25 15 5 Tower B Tower A 4 5 6 7 8.1 4 6 8 1 14 16 SU density per km 2 Fig. 4: TV outge probbility with different SU densities λ. q 1 =.99, q =.95. studied re re the sme s the burbn cse defined in IV-A, in order to void ny discontinuity my be cused by using different propgtion models t different loctions. The TV coverge (Fig.5b) is obtined by using ITU Recommendtion P.1546 []. Fig.6 depicts the permissible trnsmit power per SU in Stockholm re on chnnel 51 (the first djcent chnnel to chnnel 5, which is occupied by the TV brodcsting system in this re). We cn see tht most re in Stockholm permit more thn dbm SU trnsmit power, except frction of the dense urbn re where the permissible trnsmit power is reduced to round dbm. Similr clcultion cn be repeted for other djcent chnnels s well, which ully permit higher secondry trnsmit power thn the first djcent chnnel. 5 15 25 35 4 45 5 x coordintes (km) (b) Medin received TV signl strength (dbm)on chnnel 5 Fig. 5: Studied re in Stockholm. V. CONCLUSION In this pper, we investigted the djcent chnnel interference problem in secondry ccess to TV white spce. A sttisticl pproch bsed on geo-loction dtbse is proposed to determine the permissible secondry trnsmit power under ggregte djcent chnnel interference constrint. The proposed pproch considers mny spects of the secondry interference, ch s, shdow fding, TV receiver ntenn directivity, the rndom deployment of secondry users nd the cumultive effect of interferences from multiple djcent chnnels. The complexity for computing the permissible secondry trnsmit power is, however, reduced considerbly by the log-norml pproximtion of the secondry interference. The numericl relts show tht, this sttisticl pproch 9
y coordintes (km) 5 45 4 35 25 15 5 Permissble Secondry Trnsmit Power (dbm) Tower B Urbn Are Tower A 5 15 25 35 4 45 5 x coordintes (km) Fig. 6: Permissible trnsmit power on the first djcent chnnel to brodcsting chnnel in Stockholm re with q =.95. predictes much higher permissible trnsmit power thn the existing deterministic frmework, while providing relible primry user protection. Furthermore, this pproch cn be esily pplied to the rel-world scenrios. A smple nlysis for Stockholm re indictes considerble potentil for shortrnge secondry ccess in TV white spce. In the future study, we will consider the effect of externl co-chnnel secondry interference nd the possible wys to combine different propgtion models used for different environments, so tht we cn provide comprehensive nlysis of the TV white spce vilbility. ACKNOWLEDGMENT The reserch leding to these relts hs received prtil funding from the Europen Union s Seventh Frmework Progrmme FP7/7-13 under grnt greement n 2483 (QUASAR). The uthors lso would like to cknowledge the VINNOVA project MODyS for providing prtil funding. 5 4 [7] E. Obregon, L. Shi, J. Ferrer, nd J. Znder, A model for Aggregte Adjcent Chnnel Interference in TV White Spce, in IEEE 73rd Vehiculr Technology Conference (VTC), My 11. [8] Europen Brodcsting Union, The Cumultive Effect of Multiple WSD Interference, Sept. 11, [Online]. Avilble: http://www.cept.org/meeting-documents. [9] H. Krimi, Geoloction Dtbses for White Spce Devices in the UHF TV Bnds: Specifiction of Mximum Permitted Emission Levels, in IEEE Symposium on New Frontiers in Dynmic Spectrum Access Networks (DySPAN), My 11. [] Directivity nd Polriztion Discrimintion of Antenns in the Reception of Television Brodcsting, ITU-R Recommendtion BT.419-3. [11] M. Aljuid nd H. Ynikomeroglu, Identifying Boundries of Dominnt Regions Dictting Spectrum Shring Opportunities for Lrge Secondry Networks, in IEEE 21st Interntionl Symposium on Personl Indoor nd Mobile Rdio Communictions (PIMRC),, Sept.. [12] A. Ghsemi nd E. Sous, Interference Aggregtion in Spectrum- Sensing Cognitive Wireless Networks, IEEE Journl of Selected Topics in Signl Processing,, vol. 2, no. 1, pp. 41 56, Feb. 8. [13] M. Aljuid nd H. Ynikomeroglu, A Cumulnt-Bsed Chrcteriztion of the Aggregte Interference Power in Wireless Networks, in IEEE 71st Vehiculr Technology Conference (VTC), My. [14] K. W. Sung, M. Tercero, nd J. Znder, Aggregte Interference in Secondry Access with Interference Protection, IEEE Communictions Letters, vol. 15, no. 6, pp. 629 631, June 11. [15] SE43 Meeting Document, On the Permissible Trnsmit Power for WSDs in TV White Spce, Sept. 11, [Online]. Avilble: http://www.cept.org/meeting-documents. [16] Propgtion Dt nd Prediction Methods for the Plnning of Short- Rnge Outdoor Rdio Communiction Systems nd Rdio Locl Are Networks in the Frequency Rnge MHz to GHz, ITU Recommendtion P.1411. [17] Center for Interntionl Erth Science Informtion Network (CIESIN), Columbi University, nd Centro Interncionl de Agricultur Tropicl (CIAT), Gridded Popultion of the World, version 3, Nov. 11, [Online]. Avilble: http://sedc.ciesin.columbi.edu/gpw. [18] Centro Interncionl de Agricultur Tropicl (CIAT), SRTM Digitl Elevtion Dtbse, Nov. 11, [Online]. Avilble: http://srtm.csi.cgir.org. [19] Post och Telestyrelsen, Tillst?dsdt Digitl TV Mrs 8 Version A, Mr. 8, [Online]. Avilble: http://www.pts.se/sv/dokument/. [] Method for Point-to-Are Predictions for Terrestril Services in the Frequency Rnge MHz to 3 MHz, ITU Recommendtion P.1546-4. REFERENCES [1] M. Nekovee, Quntifying the Avilbility of TV White Spces for Cognitive Rdio Opertion in the UK, in IEEE Interntionl Conference on Communictions Workshops, June 9. [2] Federl Communictions Commission, In the Mtter of Unlicensed Opertion in the TV Brodcst Bnds: Second Memorndum Opinion nd Order, Sept.. [Online] Avilble: http://www.fcc.gov, [3] ECC Report 159, Technicl nd Opertionl Requirements for the Possible opertion of Coginitive Rdio Systems in the White Spces of the Frequency Bnd 47-79mhz. Jn. 11, [Online]. Avilble: http://www.ero.dk. [4] Ofcom, Digitl Dividend: Geoloction for Cognitive Access, Nov. 9, [Online]. Avilble: http://stkeholders.ofcom.org.uk/conlttions/cogccess/. [5] K. Ruttik, K. Koufos, nd R. Jäntti, Modeling of the Secondry System s Generted Interference nd Studying of Its Impct on the Secondry System Design, Rdio Engineering, vol. 18, no. 7, pp. 1271 1278, Dec.. [6] Y. Selén, J. Kronnder Optimizing Power Limits for White Spce Devices under Probbility Constrint on Aggregted Inteference, bmitted to IEEE Interntionl Symposium on Dynmic Spectrum Access Networks (DySPAN), 12.