Secondary Spectrum Access in TV-Bands with Combined Co-Channel and Adjacent Channel Interference Constraints

Secondary Spectrum Access n TV-Bands wth Combned Co-Channel and Adjacent Channel Interference Constrants Le Sh, K Won Sung, and Jens Zander KTH Royal Insttute of Technology, Wreless@KTH, Stocholm, Sweden E-mal: lsh@th.se, sungw@th.se, jenz@th.se Abstract The potental of VHF/UHF band as a canddate for secondary spectrum access, so called TV whte spaces, has been ntensvely nvestgated n recent years. However, the mpact of the accumulated nterference from multple secondary users on dfferent adjacent channels has not been well studed thus far, let alone the effect of combned nterference from both co-channel and adjacent channels. Ths paper presents a framewor for assessng secondary spectrum reuse opportuntes for portable and moble devces that comply wth geo-locaton database concepts. The opportunty s evaluated n terms of the maxmal number of secondary users that can access the TV whte space smultaneously. Partcular emphass s gven to the protecton of TV recever from harmful aggregate nterference orgnated from not only the secondary users outsde the TV coverage on the same channel but also those close to the TV recevers operatng on dfferent adjacent TV channels. An optmzaton problem s solved to maxmze the number of secondary users admtted to the avalable TV channels at dfferent locatons. Through n-depth analyss of the nterference characterstcs of the optmal soluton, t s dentfed that the cumulatve effect of adjacent channel nterferences has the domnant mpact on TV recepton, partcularly for the case of secondary devces wth lmted transmt power. Ths suggests the possblty to acheve near-optmal explotaton of TV-bands for secondary reuse wthout explct coordnaton of co-channel nterference from the secondary users deployed over a wde geographcal area. Index Terms TV Whte Space, secondary spectrum reuse, optmzaton, aggregate nterference, adjacent channel nterference, geo-locaton database. I. INTRODUCTION The rapdly growng demand for wreless servces has drven the wreless ndustry to search for new rado spectrum to accommodate the enormous moble data traffc. As a promsng alternatve to the lengthy spectrum reallocaton process, secondary access to the locally or temporally underutlzed lcensed spectrum has attracted wde nterests from ndustry and academc ale. Among the potental spectrum for secondary access, the VHF/UHF TV band s consdered as the most promsng canddate, thans to ts well defned prmary usage and the favorable propagaton characterstcs for wde coverage and ndoor penetaton [1] [2]. The regulators have taen the ntatve to establsh regulatory framewor for secondary access n TV whte space (TVWS) [3] [4] [5]. These wors have ntroduced the gudelne for the secondary user (SU) to detect avalable TV channels and control ts nterference to the prmary user (PU), usng geo-locaton database or spectrum sensng. However, the dscussons wthn the regulatory framewor on secondary access n TV-bands has been prmarly lmted to sngle secondary user case so far. Recent researches have extended the study to multple- SU case, developng both heurstc algorthm [7] [8] and optmzed solutons [9] [10] for the secondary transmt power allocaton. These studes have clearly demonstrated the mpact of aggregate nterference from multple SUs on the secondary spectrum reuse opportunty, but ther focus has been on the co-channel nterference (CCI) from the SUs located outsde the TV coverage area wth long ln-dstance. On the other hand, the TV recever can be very vulnerable to adjacent channel nterferences (ACI) as well, especally when the SUs are transmttng n the proxmty of the vctm recever [11]. In [12], t has been shown that the ACI s the lmtng factor for the secondary transmt power allocaton wth the method proposed n ECC report 159 [5]. In multple- SU scenaro, partcularly wth dense deployment of portable or moble secondary devces, the mpact of ACI on TV recepton s further sgnfed by the cumulatve effect of nterferences from multple channels [13]. A stochastc model for the accumulated ACI from multple short range SUs transmttng on dfferent channels has been proposed n [14], where the results also strengthened the mportance of ACI n TV whte space (TVWS) analyss. The method to combne these two types of nterferences nto a sngle constrant, however, s stll lacng. The exstng framewors [5] [9] [14] have so far consdered CCI and ACI separately, whch could potentally lead to ether neffcent secondary spectrum utlzaton, or overestmaton of the spectrum reuse opportunty and cause excessve nterference to the TV recevers. The am of ths paper, therefore, s to propose a new framewor for assessng the spectrum reuse opportunty n TV-bands for multple portable/moble secondary devces n complance wth the combned nterference constrant. More specfcally, we wll optmze the number of admtted SUs on each avalable TV channel at dfferent locatons such that the total number of the actve SUs s maxmzed. To our best nowledge, t s the frst framewor for the optmal

(a) Case A: ndoor SU and set top TV recepton antenna (b) Case B: outdoor SU and set top TV recepton antenna (c) Case C: ndoor SU and roof top TV recepton antenna (d) Case D: outdoor SU and roof top TV recepton antenna Fg. 1: Secondary access scenaros TVWS utlzaton wth a comprehensve nterference model that combnes CCI from SUs outsde the TV coverage and ACI from SUs close to the TV recevers. The optmal solutons are analyzed to dentfy whether ACI or CCI has the domnant damagng mpact on the TV recepton, so that we can provde more nsghts to mprove the effcency of the regulatory rule for secondary access n TV-bands. In the followng of ths paper, we wll start wth a bref descrpton of the studed scenaro n Secton II. The system model s explaned n Secton III. Then the optmzaton problem s formulated n Secton IV, followed by numercal results and dscussons n Secton V. Fnally conclusons are drawn n Secton VI. A. Prmary System II. SECONDARY ACCESS SCENARIO In terrestral TV broadcastng networ, a TV staton can cover an area wth radus of 30-50 m. The TV receves the sgnal through ether a rooftop antenna or an ndoor set-top antenna. In order to avod mutual nterferences and to provde regonal content, neghborng TV statons (or neghborng sngle frequency networs) typcally transmt on dfferent subsets of TV channels. Therefore, certan TV channels are locally unoccuped by the prmary servce and potentally avalable for secondary reuse. B. Secondary System As ponted out n [15], the commercal sweet pont for secondary reuse of TVWS les n the scenaro wth dense deployed short-range or ndoor wreless system. Thus, the secondary system consdered n our study s the portable or moble devces, wth lmted transmt power and below clutter antennas. These devces could be regarded as the access pont/user equpment n a WF-le or Femtocellle secondary system. The SU s assumed to be randomly deployed ether ndoor or outdoor, and transmttng wth fxed power, p su, on one of the locally unoccuped TV channels. C. Coexstence Deployment Scenaros Wth the above mentoned prmary and secondary systems, dfferent combnatons of the coexstence scenaros are llustrated n Fg.1. In both case A and case B, the TV recever s connected to an ndoor set-top antenna. It can be expected that the mpact of ACI on TV recepton s stronger n case A, as both the SU and the TV recever are deployed ndoor. In case C, the TV recever s connected to a roof-top antenna whle the SUs are deployed outdoor. Both lns are free from wall penetraton loss. The CCI ln s an over-the-rooftop ln, and wll suffer less propagaton loss as compared to the CCI ln n case B, where both TV antenna and SU are below clutter heght. In contrast, the ACI ln s relatvely weaer n case C, because the closest SU s most lely to be outsde the man lobe of the drectonal rooftop antenna ponted horzontally or even slghtly upwards. Case D s smlar to case C, as both lns are subject to wall penetraton loss. Hence, f we can dentfy that ACI has domnant effect n ether case C or case D, then the same concluson can be readly appled to all the other cases. In the followng of the study, we wll focus on Case C, wth rooftop drectonal antenna and outdoor SUs, as t s more comparable wth one of the reference geometres descrbed n [5]. III. SYSTEM MODEL A. Secondary Access usng Geo-locaton Database Followng the suggeston by ECC [5], we adopts the geolocaton database approach to regulate the secondary access to TV-bands, and protect the TV recepton from harmful nterference. Gven the lmted resoluton of the database and locaton detecton capablty of the SU, t s mpossble to estmate the recepton qualty of each ndvdual TV recever. Thus, the studed area s dscretzed nto small area elements, denoted as pxel. The geo-locaton database stores nformaton for

each area elements, such as the TV coverage qualty, terran elevaton, populaton densty, etc. For notaton purpose, we defne the set of pxels over the entre studed regon as A := {a 1,..., a m }. The set of TV channels s defned by F := {f 1,..., f n }. The TV sgnal power level on channel f at pxel a s denoted S. Wth shadow fadng assumpton, S follows log-normal dstrbuton wth parameters µ S and σ S. Then, pxel a s regarded as nsde the coverage of channel f, f { } S q1, = Pr γ 0 q N 1, (1) tv where N tv s the TV recever nose power plus TV selfnterference. γ 0 s the mnmum sgnal-to-nterference-andnose rato for successful TV recepton. q1 s the mnmum requred locaton probablty wthout secondary nterference, defned by the regulator as the measure for the prmary system qualty of servce requrement. A channel s regarded as occuped at a pxel f that pxel s nsde ts coverage, otherwse t s consdered as avalable for local secondary access. The set of occuped TV channels n pxel a s parameterzed by an ndex set K,.e., F := {f K }. Smlarly, the set of avalable TV channels n pxel a s defned as F := {f l l L }. We also defne the ndex sets for the pxels nsde and outsde the coverage area of channel f as I and J, respectvely. An occuped TV channel must be protected from harmful secondary nterference, wth the followng requrement: { } S q2, = Pr N tv + I γ 0 q2, (2) where I s the receved secondary nterference and q2 s the mnmum locaton probablty under secondary nterference defned by the regulator. Otherwse, the TV recepton on that channel s deemed as beng volated. All the TVs n the same pxel a recevng on the same channel f, are assumed to experence statstcally the same level of TV sgnal power S and secondary nterference poweri. B. Aggregate Interference Model Due to the mperfecton of the TV recever flter characterstc, the nterferences from SUs that are smultaneously actve on both co-channel and dfferent adjacent channels would cause cumulatve damagng effect on the TV recepton. Ths cumulatve effect of nterferences from multple channels can be modeled by the weghted summaton of the nterferences from dfferent channels [13] (smlar to the Nusance Feld defnton n [5]). Lettng Ieff, denotes the effectve aggregate nterference, we can defne t as I eff, = N t=1 γ,lt γ 0 p su g d (d t )g θ (θ t )g f. (3) Here N s the total number of actve SUs. γ,l s the mnmum requred TV sgnal to SU nterference rato between channel Desred to Undesred (D/U) power rato (db) 30 20 10 0 10 20 30 40 50 60 70 Adjacent Channel Rejecton Thresholds on Channel 27 (522 MHz) Reference data[6] D/U rato for low TV sgnal strength D/U rato for hgh TV sgnal strength 80 N 6 N 4 N 2 N N+2 N+4 N+6 N+8 N+10 N+12 N+14 N+16 N+18 Adjacent Channel Fg. 2: Protecton rato as a functon of frequency offset between TV sgnal and nterferng sgnal [13]. f and channel f l (also nown as protecton rato [6]; see Fg. 2). g d (d) s the dstance based attenuaton. g θ (θ) s the recever antenna gan, wth ncdent angle θ. And g f s the channel fadng gan. Ths aggregate nterference model ncorporates CCI and ACI from dfferent channels. Nevertheless, n order to capture the dstngushng characterstcs between the ln geometres of ACI and CCI, we re-wrte (3) as I eff, = CCI + ACI, (4) where CCI represents the aggregate co-channel nterference, and ACI the effectve adjacent channel nterferences. 1) Co-Channels Interferences: The CCI from a sngle actve SU n pxel a to the vctm TV n pxel a j on the same channel f s defned as cc,j = p su g d (d,j )g θ (θ,j )g f, (5) where d,j s typcally much larger than the pxel sze. So t can be approxmated by the dstance between the center of the two pxels. Wth slow fadng assumpton, cc,j can be modeled as a log-normal random varable (RV). We can express ts frst two cumulants [16] as ( ) [ ] κ 1 cc,j = exp µ cc,j + σ 2 cc /2, (6),j ( ) ( ) ] ( ) κ 2 cc,j = [exp σ 2 cc 1 exp 2µ,j cc,j + σ 2 cc,,j (7) where the locaton parameter, µ cc,j, can be drectly estmated from the geo-locaton database µ cc,j = E [ ln ( cc,j)] = ln (psu g d (d,j )g θ (θ,j )), (8) and the scale parameter, σ 2, s the shadow fadng varance cc,j n natural logarthmc scale. In multple-su case, all CCI lns between pxel a and pxel a j are assumed to have the same dstance and hghly

correlated shadow fadng. Assumng the number of admtted SUs on channel f n pxel a j beng x j, the aggregate CCI can be wrtten as CCI x j cc,j. (9) j J Thus the mth cummulants of CCI are gven as ( ) κ m CCI = x ( ) j κ m cc,j. (10) j J 2) Adjacent Channels Interferences: Contrary to the CCI case, the SUs nterferng on channels adjacent to the broadcastng TV channels are located n the proxmty of the TV recever, and the aggregate ACI s manly domnated by a few SUs close by. Thus, we can lmt the area of nterference aggregaton to the domnant nterference regon [17], from where (100 ε)% of the aggregate nterference are orgnated. Denotng Ω l as the set of actve SUs on channel f l nsde the domnant nterference regon concentrc to pxel a, we can express the aggregate ACI from SUs on dfferent locally avalable TV channels, L, as ACI l L γ,l γ 0 p su g d (d t )g θ (θ t )g f. (11) t Ω l Accordng to our study [14] and the numercal results n [17], the radus of the domnant nterference regon s around 500 meters for ɛ = 0.5 n suburban envronment. Consderng the lmted resoluton of the geo-locaton database, we can assume the admtted SUs are unformly dstrbuted wth constant densty nsde the domnant nterference regon. Thus, we have λ Ω l λ l = xl a, (12) where a s the sze of pxel a. Gven the varance of the shadow fadng and the user dstrbuton densty, the aggregate ACI can also be approxmated by a log-normal RV [18]. Its frst two cumulants can be obtaned by cumulants matchng [14]: κ m (ACI ) = x l a 2π µ m(g f ) µ m (g θ )p m su l L = ( ) x l κ m ac,l, l L ( γ,l γ 0 ) m Rɛ gd m (r)r dr (13) where µ m (G f ) and µ m (G θ ) are the mth raw moments of the dstrbutons of channel fadng and antenna gan, respectvely. d 0 s the mnmum separaton dstance between ( ) the TV recever antenna and the nterferng SU. κ m ac,l s equvalent the cumulant of nterference from a sngle adjacent channel wth SU densty equal to 1/ a. d 0 IV. OPTIMAL EXPLOITATION OF SECONDARY OPPORTUNITY From the perspectve of the regulator or the operator of the TVWS geo-locaton database, one way to promote effcent explotaton of spectrum reuse n TV-bands s to admt as many SUs as the aggregated nterference constrant would allow. Because the resource sharng among the SUs s typcally beyond ther control. To capture the tradeoff between the optmal explotaton of TVWS, the nterference constrant and the prescrbed locaton probablty, we employ Chance Constraned Programmng (CCP) [19] to formulate the optmzaton problem. The CCP formulaton can be expressed as follow: max x s.t. m x l =1 l L Pr { N tv + I eff, S γ 0 0 l L x l c, 0 x l c, f F, a A. } q2, (14) Here, the objectve s to maxmze the total number of admtted SUs over all channels n all pxels. Ieff, s a functon of the decson varable x as defned n the prevous secton. c s the maxmum number of SUs n pxel a, whch depends on the populaton densty, traffc load, etc. c set the lmt on the number of admtted SUs n each channel. A. Determnstc Equvalent for Interference Constrant By Symonds theorem [20], the probablstc constrant n (14) can be replaced by a determnstc equvalent, whch s generally non-lnear and dependent on the dstrbuton of the random coeffcents n the constrants. As dscussed earler, Ieff, s a sum of log-normal RVs. By applyng Fenton-Wcnson method [21], we can approxmate the sum of the aggregate nterference and the TV recever nose (a lnear constant) as a sngle log-normal RV, denoted as IN. Its frst two cumulants are gven as κ 1 (IN ) = N tv + x ( ) j κ 1 cc,j + x l κ 1 (ac,l ), j J l L (15) κ 2 (IN ) = x ( ) j κ 2 cc x,j + x l κ 2 (ac,l ). (16) j J l L Its dstrbutonal parameters, µ IN and σ 2, can be obtaned IN by [16] [ ] ( ) µ IN = ln κ 1 (IN ) 1 2 ln 1 + κ 2(IN ) (κ 1 (IN, (17) )) 2 σ 2 IN = ln [ ] 1 + κ 2(IN ) (κ 1 (IN. (18) )) 2

Together wth the log-normal approxmaton of the TV sgnal, the probablstc constrant n (14) can be replaced by a determnstc equvalent as { } { S q Pr 10 log10 S } IN γ 0 = Pr 10 log 10 IN 10 log 10 γ 0 = Q 10 log 10(γ 0 ) + µ IN,dB µ S,dB σ 2 +, IN,dB σ2 S,dB (19) Here the decson varable x s ncluded n µ IN,dB and σ 2 IN,dB through (15) - (18). And µ db = 10 ln 10 µ, σ db = 10 ln 10 σ. B. Lnear Approxmaton of Optmzaton Problem For the large scale scenaros we are typcally facng n TVWS, solvng the optmzaton problem formulated above drectly can be very computatonally demandng, as the decson varables are ntegers and the equvalent determnstc constrant s non-lnear. To smplfy the computaton, we frst approxmate the nteger decson varable x by a contnuous one, ˆx. It s a reasonable approxmaton because x can be up to a few thousands n the dense deployment scenaros. In [19] [22] and [23], several unformly tghter approxmatons have been developed to replace the non-lnear constrant by a set of lnear nequaltes. However, these methods are only suted to problems wth a small number of random coeffcents. Hence, we adopted a smpler approach that has been proven to ft well wth typcal TVWS scenaros n [9] to lnearze the constrant n (19). Frst, we rewrte the determnstc constrant (19) by nvertng the Q-functon µ IN,dB Q 1 (q2) σ 2 + IN,dB σ2 S,dB (20) µ S,dB 10 log 10 (γ 0 ). Notng that the non-lnearty les n σ IN,dB, we rewrte (21) as 10 ( ) [ ln 10 κ 1 IN exp Q 1 (q2) σ 2 + IN,dB σ2 S,dB + 1 ] (21) 2 σ2 IN,dB + µ S,dB 10 log 10 (γ 0 ). Here, the left hand sde of the nequalty s a lnear combnaton of ˆx as n (15). And the rght hand sde, denoted b, contans the non-lnear terms, whch we approxmate by a lnear constant ˆb : b ˆb [ ] = exp Q 1 (q2)σ S,dB + µ S,dB 10 log 10 (γ 0 ). (22) Although the last lnear approxmaton s not unformly tghter than the orgnal constrant, t s shown n Fg.3 that the approxmaton error s wthn ±1 db for practcal settngs. Also, t wll be further llustrated n the result secton that only few TV channels n a lmted area (less than 2% of total) are around 0.5% short from the locaton probablty b/ˆb [db] 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 Avg TV sgnal strength = 45dBm Avg TV sgnal strength = 55dBm Avg TV sgnal strength = 65dBm 1 1 2 3 4 5 6 7 8 9 σ IN [db] Fg. 3: Rato between actual constrant and ts lnear approxmaton. requrement due to the approxmaton error. Thus, t can be easly compensated by applyng a small fxed margn to ˆb f necessary. C. Lnear Program Formulaton Wth some manpulaton n the subscrpts, we can fnally formulate the orgnal optmzaton problem by the followng lnear program max 1X X s.t. AX B, (23) 0 HX C, 0 X c. Here X s the contnuous decson varable vector ˆx 1 ˆx 2 X =.. (24) ˆx β. Its cardnalty s the sum of the number of avalable channels n all the pxels,.e. X = m =1 L = n =1 J. Assumng the ndex of pxel a s the ζ th elements n the ndex set I and the η th elements n the ndex set J, then ˆx s mapped to ˆx β by settng β = 1 t=0 J t + η (Note: J 0 = ). The matrx A s the sum ( of ) two matrxes, G cc and G ac, correspondng to the κ 1 cc,j and κ1 (ac,l ) respectvely. G cc s gven by g1,1 cc g1,2 cc g cc 1,β g cc... 2,1 G cc =...., (25) gα,1 cc gα,β cc....

where gα,β cc = ( ) κ 1 cc,j f I and j J, α = 1 t=0 It + ζ and β = 1 t=0 J + ηj ; 0, otherwse. (26) G ac has smlar structure wth ts elements gα,β ac gven by ( ) κ 1 ac,l, f I J l, gα,β ac = α = 1 t=0 It + ζ, and β = (27) l 1 t=0 J t + η l; 0, otherwse. The bnary matrx H s used to sum up the number of admtted SUs on all avalable channels for each pxel. Its elements s gven by { l 1 1, α =, and β = h α,β = t=0 J t + η l, l L ; 0, otherwse. (28) The constrant vector B and C s gven by. and b α = ˆb, wth α = 1 t=0 It + ζ, K ; (29) c α = c, wth α =. (30) Once matrxes are constructed, t s straghtforward to solve the optmzaton problem wth standard lnear program technque, such as, smplex method [25]. V. NUMERICAL RESULTS We use the lnprog functon wth smplex method n Matlab 2011a [26] to solve the optmzaton problem formulated above. Then we nvestgate the relatve mpact of ACI and CCI on the optmal soluton and the TV recepton volaton. A. Sample Study For numercal llustraton, we consder four dentcal TV towers regularly deployed n a square area, each broadcastng on a dfferent groups of 10 TV channels out of 40 total TV channels. Wrap around technque [27] s appled to elmnate any border effect (as seen n Fg.4). The TV statons are transmttng wth 43 dbw equvalent sotropcally radated power (EIRP) and the mast heghts are 200 meters. The TV recever antenna heght s 10 meters, the same as the average surroundng clutter heght. The drectonal rooftop antenna follows specfcaton defned n [28], and s assumed to be pontng towards the closest TV staton. Wth coverage requrement q 1 = 0.95, the radus of the coverage s approxmately 40 lometers. For smplcty, the protecton rato of the TV recever s assumed to be flat on all adjacent channels, and s equal to -45 db (around the average value of the neghborng 10 channels protecton ratos as defned n Fg.2). The secondary transmtter heght s 1.5 meters. The mnmum separaton dstance between the TV antenna and the SU s only lmted by ther heght dfference. The secondary user transmt power s 30 dbm. The maxmum densty of SUs s 4000 SUs Fg. 4: Illustraton of TV tower deployment wth wrap around. per m 2 throughout the studed area, and no more 150 SUs per m 2 can be admtted to the same channel. Wth secondary nterference, the mnmum locaton probablty requrement s q 2 = 0.94. Propagaton model ITU-R P1546 [29] s used for TV coverage and CCI ln pathloss calculaton. Propagaton model ITU-R P1411 [30] for over-the-rooftop path s used for ACI ln pathloss calculaton. The shadow fadng standard devatons are 4.65 db for TV sgnal ln and 6 db for both CCI and ACI lns. The optmal secondary user admsson s presented n Fg.5 as a functon of dstance from the TV staton. As can be expected, the optmal soluton s acheved by admttng as many SUs as possble n pxels close to the TV staton, whle only a lmted number of SUs are allowed to access TV-bands at the coverage boundary. For comparson, we also plot the results when ether only CCI constrant or ACI constrant s appled. Clearly, ACI constrant s the lmtng factor at the area not very far from the TV coverage boundary, as the number of admtted SUs wth only ACI constrant matches closely to that under both constrants. However, the spectrum reuse opportunty s overestmated n the regon between 10-20 m away from the TV staton f only ACI constrant s appled. On the other hand, wth only CCI constrant, 100% admsson rate s reached only at area close to the TV staton, but more users are admtted n the mddle range of the coverage area than the other two cases. Monte Carlo smulaton s performed to exam the actual TV recepton qualty wth the optmzed SU admsson. Fg.6 depcts the dstrbuton of the resultng locaton probabltes of all TV channels n all pxels. The sold lne represents the case when the SU admsson s optmzed over the aggregate nterference constrant (21). The protecton requrement, q 2

Percentage of admtted SUs (%) 100 90 80 70 60 50 40 30 20 10 0 Constrant on both ACI and CCI Constrant on only ACI Constrant on only CCI 3 6 9 12 15 18 21 24 27 30 33 36 39 42 Dstance from the TV staton [m] Fg. 5: Percentage of admtted SU at dfferent dstance from the TV staton. F(x) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Emprcal CDF q2 wth contr. on both ACI and CCI q2 wth contr. on only ACI q2 wth contr. on only CCI q1 0 0.9 0.92 0.94 0.96 0.98 1 Locaton Probablty Fg. 6: Locaton probablty dstrbuton over all TV channels n all pxels. 94%, s satsfed n almost all pxels. A very small porton of the avalable channels n several pxels experence a locaton probablty slghtly lower than the requred 94% due to the approxmaton error of the nterference constrant. If the SU admsson obtaned wth only CCI constrant s appled nto the smulaton, the TV recepton s severely volated n more than half of the pxels. In comparson, the deteroraton n the locaton probabltes s much less f only ACI constrant s consdered. It s evdent that the effectve nterference that causes damage to the TV recepton s domnated by ACI. B. Senstvty Analyss To draw a wder mplcaton, we nvestgate the effects of two ey parameters: the secondary transmt power and the TV recever protecton rato. 1) Secondary Transmt Power: The optmzaton problem s solved for three dfferent levels of secondary transmt power: 20 dbm, 30 dbm and 40 dbm, whle the rest of the parameters reman the same as n the prevous analyss. Fg.7a, shows the average admsson rato n the studed area,.e., m =1 l L x l / m =1 c. No matter whch constrant s appled, less secondary users are admtted as ther transmt power ncreases. Fg.7b shows the average percentage of volated TV channels n all pxels,.e. m =1 K / m =1 K, where K denotes the ndex set for the set of volated TV channels n pxel a. Interestngly enough, wth optmal SU admsson under only CCI constrant, the volaton to TV recepton actually becomes more severe as the secondary transmt power decreases. At the same tme, optmzng over only ACI constrant can acheve a much lower percentage of volated TV channels. In fact, when secondary transmt power s less than 20 dbm, the results obtaned by optmzng over only ACI constrant are farly close to that wth both constrants. However, f the SU transmt wth 40 dbm power, applyng ether types of constrant would lead to a comparable level of volaton. These results agan support our argument that ACI has domnant mpact on TV recepton volaton for the case of dense deployed SUs wth lmted transmt power. Thus control over ACI alone could acheve near-optmal TV whte spaces explotaton f such a secondary system s envsaged. In other cases, however, the aggregate nterference constrant must tae nto account both ACI and CCI to ensure the protecton of TV recepton. 2) Protecton Rato: The value of protecton rato used n the prevous analyss s based on the average of measurement results from dfferent TV recevers wth LTE user equpment beng the secondary transmtter. Whle t s wdely used as a reference, the actual protecton rato can vary sgnfcantly wth dfferent TV recevers and secondary nterference sgnal modulatons. Fg.8 depcts the mpact of the dfferent protecton rato values on the secondary reuse opportunty. A low-end TV recever wth poor ACI rejecton capablty s represented by an average protecton rato as hgh as -35 db [13]. Apparently, the poor TV recever qualty greatly reduced the opportunty for secondary spectrum reuse due to the strong ACI nfluence on TV recepton. For better TV recevers that are commercally avalable, the protecton rato can reach an average value of -55 db. The number of admtted SUs s more than doubled as compare to the case wth low-end TVs. Whle ACI stll has a stronger nfluence over the TV recepton n ths case, the damagng effect of CCI begns to surface and controllng only ACI s no longer suffcent for TV protecton (Fg.8b). In fact, CCI could domnate the aggregate nterference f the ACI rejecton capablty of TV recever contnues to mprove. For nstance, assumng a next-generaton TV has an average protecton rato as low as -75 db, the number of admtted SUs greatly ncreases and suffcent protecton of the TV recepton can be provded by consderng CCI constrant only.

(a) Percentage of admtted SUs n all pxels (%), (a) Percentage of admtted SUs n all pxels (%), (b) Percentage of volated TV channels n all pxels (%), Fg. 7: Effect of dfferent secondary transmt power p su (γ,l = 45 db). (b) Percentage of volated TV channels n all pxels (%), Fg. 8: Effect of dfferent protecton rato γ,l (p su = 30 dbm). VI. CONCLUSION In ths wor, we have nvestgated the TV whte spaces opportunty for portable or moble secondary devces. A new framewor for assessng the potental of secondary spectrum reuse n TV-bands s proposed, whch to the best of our nowledge s the frst framewor wth combned co-channel and adjacent channel nterference constrants. The spectrum reuse opportunty has been assessed n terms of the number of secondary users admtted to each avalable channel at dfferent locatons, by solvng an optmzaton problem wth probablstc nterference constrant. Wth n-depth analyss of the nterference characterstc of the optmal soluton, we have dentfed the domnant mpact of the aggregate adjacent channel nterference on TV recepton qualty. In partcular, for densely deployed portable/moble secondary devces wth a lmted transmt power, near-optmal explotaton of the spectrum reuse opportunty can be acheved by controllng only adjacent channel nterferences from nearby SUs. Therefore, t s possble to sgnfcantly reduce the complexty of the geo-locaton database by avodng explct coordnaton of cochannel nterferences from SUs over a large geographcal area. At the same tme, we have also showed the defcency of exstng framewors consderng only co-channel nterference constrant. It has been proven to provde nsuffcent protecton for the TV recepton, unless the adjacent channel nterference rejecton performance of the TV recever can be drastcally mproved. Overall, we have demonstrated the necessty of ncorporatng co-channel and adjacent channel nterference n the assessment of TV whte spaces and establshed the methodology for that. To extend the framewor, we wll refne the lnear approxmaton and apply t to evaluate the potental of TV whte spaces n a real envronment wth nhomogeneous user demand dstrbuton and non-flat protecton ratos. Another possble drecton of extensons s to nclude multple secondary systems.

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