A Location-Based Method for Specifying RF Spectrum Rights

Transcription

1 A Loction-Bsed Method for Specifing RF Spectru Rights John A. Stine, Senior Meber, IEEE Abstrct We provide ethod to specif loction bsed spectru rights tht enbles spectru ngeent with finer resolution in spce nd frequenc. This ethod ccounts for the ttenution of trnsissions fro their source nd so revels the loction bsed opportunities to reuse spectru. The ethod uses concise et fleible dt structure tht hs si prts: signl strength, frequenc, spectru sk, power p, propgtion p, nd scling fctor. Through the use of one or ultiple of these prts ost n tpe of sptil spectru use uthoriztion or protection be defined. The structure llows spectru to be nged s sptil resource nd so subdivided for sptil reuse or for resle. We provide severl eples to deonstrte its verstilit in spectru ngeent. We provide soe observtions nd theores tht re useful in developing lgoriths to verif coplince to the rights nd restrictions conveed in the proposed ethod nd to discern when coeistent spectru use is possible. This ethod provides unified pproch to define spectru use tht cn be used to license spectru, to optiize spectru reuse, to negotite spectru rights, nd to specif spectru polic. It is idell suited for over-the-ir ngeent of spectru use. Inde Ters Dnic spectru ccess networks, spectru rights, spectru regultion, propgtion ps, power ps, fst cond nd control spectru ngeent odel. I I. INTRODUCTION T is envisioned tht net genertion set of wireless counictions devices will dnicll ccess spectru, i.e. oentril ove to unused bnds of spectru for ech couniction. Such wireless devices will hve need to understnd the restrictions plced on their ccess to the spectru bnds the perceive idle. These restrictions re necessr to protect prir users, norll pssive receivers, who not be detectble. The predoinnt philosoph for nging dnic spectru ccess is to equip ech rdio with sensors to detect spectru use nd then rule sets tht define behvior bsed on wht is sensed. This pproch requires priori coitent to the restrictions without certint bout where the devices will be used. Thus, there re two deficiencies. First, in nticiption tht the devices be used in n loction in n dinistrtive region, the rule sets could be overl restrictive in order to nge the worst cse. Second, once rule set is decided upon, use of the devices would be restricted to the specific geogrphic regions covered b the rules. Prir spectru users, dinistrtors, nd device users would still be uncertin whether there is J. A. Stine is with The MITRE Corportion, 7515 Colshire Drive, McLen, VA 2212 (corresponding uthor phone: ; f: ; e-il: jstine@ itre.org). sufficient control of devices to prevent inpproprite interference tht results fro operting the devices outside the regions for which the were configured. As n lterntive, we hve proposed spectru ngeent pproch tht would llow spectru nger to dnicll nge ll tpes of RF eitting devices through network [1]. The dvntges of this lterntive re the rdio does not hve to be configured for region, there is the opportunit for business odel to support secondr rket for spectru, nd there is spectru nger tht cn serve s rbiter of inpproprite or rogue spectru use. This spectru ngeent pproch, however, requires ethod for the requests nd the uthoriztions for spectru use to be rticulted. Since these requests nd uthoriztions re likel to be counicted through the network in cpcit constrined wireless environents, we hve creted concise et ver fleible w to specif spectru rights. In this pper we describe our proposl. Our ethod for specifing spectru rights cptures the sptil use of spectru b including loction nd ccounting for the ttenution of trnsissions s the propgte fro their source. The specifiction of prir right siultneousl conves the conditions under which secondr users cn shre the spectru nd still protect the prir user. The ensuing secondr rights llow ore perissive shring thn possible using spectru sks. These cpbilities ke this pproch to define spectru use suitble for licensing spectru, optiizing spectru reuse, negotiting spectru rights, nd specifing spectru polic to cognitive rdios, thus unified definition of spectru for spectru ngeent. We begin our presenttion with four introductor topics. In the first we review current reserch in the opportunistic use of spectru b cognitive rdios nd the proposed pproches for rticulting spectru use constrints to these rdios. Net we review the concept of fst cond nd control odel. Third, we describe the log distnce pthloss odel. And finll, we describe three dt structures the first propgtion p, the second spectru sk, nd the third power p. After these introductor topics, we describe our ethod for specifing loction bsed spectru rights. We describe severl tpes of spectru rights tht ight be rticulted including brodcster, network, receiver, nd secondr rights. Inherent in the rights given to prir users re the constrints the offer to secondr users. We provide severl observtion nd theores tht could be the foundtion of resoner to deterine if specific use of spectru is

2 coplint with the spectru rights. II. FOUNDATION A. Current Approches Current reserch is seeking cognitive rdio tht will utonoousl ove to nd use unused spectru. As described in the DARPA Net Genertion (XG) vision [2] developent consists of four prts, technologies for sensing nd chrcterizing the environent, lnguge for specifing polic, bstrct behviors tht re governed b the polic, nd finll the protocols of the couniction network. The intent is for the rdios to be polic controlled. Polic is written nd loded into rdio under the theor tht regultor would license equipent tht cn copl with polic nd tht the regultor then nges the polic used b the rdios in their dinistrtive region. The first developent gol ws to deonstrte tht polic bsed control of rdio use of spectru could be written nd tht rdios could be built to copl with tht polic. Within the pst er DARPA eecuted successful eperient deonstrting tht this ws possible [3]. Spectru rights in this rchitecture re provided to rdio in polic lnguge. The XG Polic Lnguge (XGPL) is intended to be declrtive lnguge bsed on fcts nd rules. Policies re encoded s set of fcts nd epressions nd then rule constructs re used to specif the processing logic for policies [4]. A polic rule consists of three fcts, selector description which defines the spectru the rule pplies nd where nd when it pplies, selector description which defines the conditions for king the spectru vilble to the rdio, nd finll usge constrint description tht defines how rdio use the spectru if the selector description is et. The snt of the lnguge provides n ontolog to specif bnds of spectru, geogrphicl regions of pplicbilit (relevnt onl if the rdio hs ens to deterine its loction), tie of pplicbilit, nd power levels. As tpicl in lnguge these cn be cobined in ultiple cobintions to specif usge constrint tht cn vr b n one or ll of these diensions possibl generting ultiple spectru usge sks tht ppl to finite regions during certin tie periods ech d. But in writing polic, polic dinistrtor ust ssess whether the polic protects the spectru rights of n prir user. To protect single user, ultiple policies for different loctions be necessr nd if the loction resolution is iprcticl ver conservtive polic be the onl lterntive. Thus the lnguge supports the specifiction of the spectru rights of the rdio user but the spectru rights of prir users re not defined nd re protected onl b how well the policies re written. Our pproch hs severl distinct differences. Rther thn burdening regultors to crete policies for cognitive rdios tht siultneousl protect prir users our ethod llows regultors to sipl specif the prir rights tht ust be respected with the ipliction tht rdios cn use the se spectru if the confor to those rights. Additionll, loction, direction, nd ttenution, re inherent in our pproch nd so spectru rights cn vr b direction nd distnce fro loction. Spectru ccess does not need preliinr sensing so long s the rdios re loction wre nd cn control their eissions. A third difference is tht our pproch is ent to be used dnicll in wireless network where rights nd restrictions re sent over-the-ir nd so our pproch to conve rights codes infortion nd uses dt structures tht re ver concise. The sentics of these rights re unbiguous. Certinl our pproch could be fitted to n frework or polic lnguge to conve rights; however, we consider our ethods for coding spectru rights into efficient dt structures with well defined sentics n iportnt contribution. B. The Fst Cond nd Control Model (FCCM) There is n ongoing debte bout whether spectru is better nged b using propert odel or coons odel. The propert odel gurntees to the licensee the eclusive use of spectru nd protection fro other users both in-bnd nd out-of-bnd. The coons odel llows free ccess to spectru where users sipl coeist or coopertivel shre the spectru. Dnic spectru ccess offers coproise where polic controlled rdios respect the rights of prir users but will use their spectru if it is idle. However, in the XG odel of dnic spectru ccess, use of spectru is predicted on the sensing condition. (i.e. If the rdio does not her nother spectru user it cn use it.) This pproch hs three deficiencies. First, it is the receivers tht ust be protected nd the offer no signl for n XG rdio to sense. Second, the sensing condition cn occur inppropritel becuse of propgtion effects such s shdowing or fding. Spectru use predicted on these conditions could cuse hrful interference to receivers outside the interference region. These led to the third deficienc tht if n inpproprite use of spectru occurs there is no recourse to fi the proble. The FCCM is intended to fi these deficiencies. The FCCM vision is for spectru ccess to be nged through network. Rther thn spectru polic being written nd loded into rdio, rdios get uthoriztion to use spectru fro spectru nger through network. Rdios would be loded with the logic to confor to the spectru rights the re infored nd so like the XG vision, the rdios cn be licensed without coitent to spectru polic. Unlike the XG vision, rdios do not ct utonoousl but ust connect to network to get spectru use rights nd these spectru rights cn be cncelled b the spectru nger. The eistence of spectru nger nd his bilit to control spectru use provides three significnt cpbilities tht could encourge the vilbilit of spectru for dnic ccess. The spectru nger cn ssess or vlidte whether violtions occur, it cn enforce pproprite spectru use nd so fi probles, nd it cn be the broker in secondr rkets.

3 C. The Log-Distnce Pthloss Model RF eissions ttenute s the propgte fro their source. The quntit of ttenution is function of frequenc, distnce, nd the environent. Precise prediction is usull untenble since totl ttenution cn vr significntl b slight oveents nd subtle chnges in the environent. Attenution trends re ore prcticl to epress. A odel tht is prticulrl suitble is the log-distnce pthloss odel [5]. It is liner odel when pthloss (PL) nd distnce (d) re on logrithic scle, PL( db) = PL( 1) + 1nlog( d), nd cn be n written s PL = PL1 d on liner scle where PL 1, the pthloss of the first eter, nd n, the pthloss eponent, re the odel s two preters. In this odel, pthloss eponent of 2 corresponds to the freespce pthloss odel, i.e. Friis eqution, nd lrger eponents re used in terrestril odels where reflected signl re likel to result in destructive interference. The log distnce odel used to epress spectru rights specifies received signl strength nd so the eqution becoes RP( db) = RP( 1) 1nlog( d), where RP(1) in this odel is the llowed power densit t 1 eter fro the trnsitter, nd RP(dB) is the estited power densit t distnce d, both epressed in decibel units of power, e.g. db/ 2 or dbw/ 2. This odel supports distnce vring spectru use right. Rights be specified to protect trnsissions in which cse signls ttenute w fro the origin or protect receivers in which cse signls ttenute towrd the origin. S the pthloss eponent is n = 2, then the llowed strength t 1 eters fro the protected device would be 4 db beneth tht t 1 eter in trnsitter oriented right nd would be 4 db bove tht t 1 eter fro the 1 eter point in receiveroriented right. The log distnce odel is generll considered to be n unrelible predictor of pthloss due to the wide vrince in pthloss tht occurs due to shdowing nd ultipth fding. Nevertheless, we believe this is the pproprite pthloss odel for spectru rights becuse of its siplicit, pthloss is liner in the log-log plot of signl strength to distnce, nd becuse it is sufficient to cpture the pthloss trend. The vrince in signl strength cused b fding nd shdowing is ccoodted b the protection rgin of the right. D. Propgtion Mps A propgtion p is dt structure tht specifies pthloss eponents b direction. In for, propgtion p is vector of -bit words which support specifing up to 2 pthloss eponents pped to vlues fro soe iniu to soe iu eponent, 2-1 ltitudes (φ) strting fro the verticl up direction nd reching to the verticl down direction (n odd nuber of ltitudes so the iddle ltitude will point to the horizon), nd 2-1 longitudes (θ) reching bout the node on the horizon. (The first nd lst longitudes point in the se direction.) The vector uses two ltitudes to define sphericl nnulus bout node nd then series of eponents nd longitudes tht specif different rnges on tht nnulus b sector. If ll sectors were eplicitl defined b the propgtion p, it would hve the for (,, n, θ 1, n 1, θ 2,, (2 1), φ 1,, n 1, θ 11,, (2 1), φ 2,, n 2,, n lst, (2 1), (2 2)). Since θ =, θ = 2 1, nd φ = 2 2 pper predictbl in the vector, we reduce the vector b deleting the obvious nd we use the ltitude φ =, which is no longer used t the beginning, to deliit the end of the vector. The reduced vector becoes (n, θ 1, n 1, θ 2,, (2 1), φ 1, n 1, θ 11,, (2 1), φ 2, n 2,, n lst, ). Reding the vector, the eponent n pplies to the sector tht reches fro ltitude to φ 1 nd fro longitude to θ 1 nd generll the eponent n pplies to the sector tht reches fro ltitude φ to φ +1 nd fro longitude θ to θ (+1). Figures 1 nd 2 illustrte eples. The reference directions for propgtion ps re bsed on the World Geodetic Sste 1984 (WGS 84) ellipsoid. The horizon of the propgtion p is the plne tngent to the ellipsoid t the propgtion p center. The longitude direction of the propgtion p points in the esterl direction coincident to the WGS 84 ltitude grid nd the 9 longitude points north coincident to the WGS 84 longitude grid. Appendi A provides the conversions fro WGS 84 coordintes to propgtion p coordintes nd directions. The discrete increentl vlues used to specif directions nd eponents in propgtion ps re pped to vlues. In our ipleenttion the longitude directions re evenl spced bout the p with nd 2 1 vlues pointing in the se direction, θ =. 1 The conversion fro p longitude vlue to n ngulr direction is θ 36 θ = It is frequentl desirble to hve greter ltitude resolution ner the horizon thn elsewhere or lterntivel to hve greter resolution ner the il directions. As generl ethod to provide the shifting of resolution we ppl technique where we increentll scle subsequent ltitudes b soe scling fctor oving fro the is to the horizon. Given scling fctor of s the reltion of subsequent vlues re ( φ + 2 φ + 1) = s ( φ + 1 φ ) φ ( φ + 1 φ ) = s ( φ + 2 φ + 1) φ >. where the ltitude φ = ( 2 1) points to horizon. When the scling chieves finer resolution t the horizon, s < 1, the conversion between vlues nd coded vlues re 1 We use the convention tht θ, φ, nd n re the coded vlues of the propgtion p nd tht θ, φ, nd n re the vlues the code.

4 z z z z 9 φ = φ φ ( s ) ( 1 s ) φ 9 ( s ) ( 1 s ) φ ( 1 s ) φ = < φ ln 1 9 φ = φ 9 ln ( s) ( 18 φ )( 1 s ) ln 1 9 φ = < φ 18 ln ( s) When there is no scling, s = 1 φ φ = nd when finer resolution is used t the es, s > φ 1 9 φ = 9 1 φ s 1 1 s φ 1 9 φ = < φ 2 2 s 1 1 s 1 ( 9 φ ) 1 s ln 1 9 φ = φ 9 1 ln s ( φ 9 ) 1 s ln 1 9 φ = < φ 18 1 ln s Eponent vlues re coded such tht subsequent coded vlues estite nerl equidistnt chnge in propgtion rnge fro the lrgest to the sllest eponent vlue. Rnge is the distnce to where ttenution cuses signl to go below threshold, RT, ccording to the odel. The sllest eponent vlue estites the furthest rnge. Given noinl RP(1) nd RT, nd the selected vlues for n low nd n high we cn crete the conversion eqution. First we deterine the iu nd iniu rnge these vlues predict nd the increentl distnce, d inc, we wnt the eponents to epress. E. Spectru Msks A spectru sk specifies the liit on the power over bnd of spectru tht trnsitter eit. It is tpicll presented s piecewise liner grph of power versus fre- TABLE 1. PROPAGATION MAP PARAMETERS (Generl design preters for propgtion p definition) Sbol Description Vlue s =.98 s = 1. s = 1.2 f c Center frequenc 4 MHz Fig. 2. Three illustrtions of the propgtion p (115, 255, 85,, 4, 115, P c = (RP(1)) Miu 1-eter power densit -24 db/ 255, 127, 115, ) using different scling fctors showing the 2 bilit to ffect RT resolution t the Receive horizon power nd t threshold the es. -8 db/ 2 n high Lrgest pthloss eponent 1 n low Sllest pthloss eponent 2 Fig. 1. Illustrtion Nuber of of the bits propgtion per word p (1, 2, 22, 8 6, 125, 15, 6, ) deonstrting the definition of different pthloss eponents b direction. RP( 1) RT 1 n low dlow = 1 RP( 1) RT 1 n high dhigh = 1 dlow dhigh dinc = The conversions between the coded eponents nd the ctul eponent vlues re RP( 1) RT 1 n dlow 1 n = dinc RP RT n = 1log ( 1 ) ( d n d ) Severl eples of propgtion ps re illustrted in Figures 1 nd 2. Tble 1 lists the generl design preters for these illustrtions. The surfce of these propgtion ps identif the rnge fro trnsitter where the signl strength threshold, RT, is reched. Fig. 1 illustrtes propgtion p deonstrting the bilit to specif different eponents b longitude. All vlues in the vector re coded. The ening of the vlues re known b their position. The eponent 1 etends fro the longitude to the longitude 2, the eponent 22 fro the longitudes 2 to 6, the eponent 125 fro the longitudes 6 to 15, nd finll the eponent 6 pplies the rest of the w round the p. There re no ltitude breks in this eple. Fig. 2 illustrtes p with ltitude breks nd the effect of the scling fctor on the ctul ltitude vlues. The eponent 115 etends fro to 255, the lst vlue so ll the w round nd the net vlue in the vector, 85, is the coded vlue of ltitude. In the second nnulus the eponent pplies to the sector fro longitudes to 4 nd then the eponent 115 etends the rest of the w round to 255. Since this is the end of the nnulus the net vector vlue, 127, is ltitude vlue. Finll, the lst nnulus hs the eponent vlue 115. Since follows 115 we know the eponent 115 pplies ll the w round the nnulus nd down to the lst ltitude. The solid ngle projections differ becuse the use different scling fctors. With the scling fctors of.98, 1, nd 1.2, the coded vlue 85 corresponds to the ctul vlues 79.99, 6.24, nd respectivel. The ltitude 127 hppens to be the horizon so it is 9 for ll scling fctors. low inc

5 n, 1 5 Reltive Power (db) nd the reltive chnges fro this power densit re indicted in the se w s the power densit vlues in the spectru sk. The iu power densit of the spectru sk in prticulr direction is the power densit specified for tht direction b the power p. III. METHOD Frequenc s (MHz) n, Fig. 3. Illustrtion of the 8-bit word spectru sk (112, 1, 117, 6, 122,, 132,, 137, 6, 142, 1, 255) with f c = 4 MHz, f i = 5 khz, nd p c = dbw/ 2. quenc where power is the power densit on db scle 2 nd frequenc is either on liner or logrithic scle. Siilr to the propgtion p we specif spectru sk using dt structure consisting of -bit words. The structure lterntes between the frequencies of the inflection points nd their power levels, e.g. (f, p, f 1, p 1,, f, p, 2 ). Three vlues orient the sk, the center frequenc of the sk f c, the iu trnsission power in the sk p c, nd the resolution of the frequenc step f i. There re 2 frequenc levels where ech subsequent vlue is seprted b the specified frequenc step resolution. The frequenc ps to the center frequenc nd the vlue 2 is used just to denote the end of the sk. There re lso 2 power levels where represents the iu power densit level of the sk nd ech coded vlue ps directl to decibel reduction in power fro the iu power. Thus the conversions between the frequenc coded vlues nd their rel vlues re ( 2 1 1) f = fc + fi f + f f f c = + fi The conversions between the power vlues re p = pc p p = pc p where ll vribles use the se decibel power units s p c. It is ssued tht ll eissions fro trnsitter in the bnds outside the spectru sk re ttenuted to below the lowest vlues in the sk. Fig.3 illustrtes n eple sk F. Power Mps In cses where trnsissions re directionl, it be necessr to specif the iu trnsit power densit b direction. In these cses power p be used. A power p is identicl in structure to propgtion p but it uses power densit vlues in plce of pthloss eponents. The highest power densit in n direction, p c, is the reference 2 Our intent is to crete spectru rights tht hve geosptil liit. For such sste to work, the right ust be decoupled fro the ntenn technolog. So trnsit power is defined s the effective power densit t one eter fro the ntenn. Trnsitters with high gin ntenns ust still confor to A. Spectru Rights Model Power in db scle log(d) Pthloss eponent specifies the rte of ttenution w fro the trnsitter The trnsitter given the right log(d) We propose tht spectru rights be rticulted using cobintions of spectru sks, propgtion ps, loctions, nd power ps. These tuples would hve specified or ssued vlues for center frequenc, f c, frequenc resolution, f i, iu power densit, p c or p c, iniu eponent, n low, iu eponent, n high, receive threshold, RT, for scling eponents, nd scling fctor, s, for scling the ltitudes. The spectru sk defines the spectrl nd sptil power densit one eter fro trnsitter or the sptil nd spectrl power densit t receiver. The power p defines how the iu power densit of the spectru sk vries b direction. The propgtion p is odel of ttenution b direction tht is used to ssess the sptil liits of right nd the opportunities for spectru users to coeist. Propgtion ps re not intended to predict pthloss but it is nticipted tht in use tht the conditions will eist for both regultors nd users to cooperte to tune these ps s fesible to tch the ctul pthloss. Although ttenution is function of frequenc, in this regulting ppliction, the propgtion p eponents ppl to ll frequencies of the spectru sk. These spectru sk, propgtion p, loction, power p tuples cn specif right for trnsitter or for receiver. In the cse of trnsitter, the cobintion of the spectru sk nd power p define the iu strength of trnsissions one eter fro the trnsitter. The propgtion p odels the ttenution of the signl w fro the trnsitter. Fig 4 illustrtes n eple. The receiver right works in reverse. The spectru sk nd power p cobintion specif the iu power distnt trnsitter cuse t the receiver. The propgtion p odels how distnt trnsissions ttenute s the propgte towrd tht receiver. Fig. 5 illustrtes tht uthorized secondr users cn trnsit ore power the further the re fro the protected receiver. A receiver right is constrint on distnt trnsitters nd does not grnt trnsission rights. The rights specified b these tuples hve 5 diensions: ori- Fig. these 4. liits A trnsitter in the rights. spectru These right trnsit illustrting powers tht re the equivlent power bound to RP(1) ttenutes the log with distnce distnce pthloss fro the odel. trnsitter given the in right

6 Power in db scle Pthloss eponent specifies the rte of ttenution towrd the receiver tht secondr trnsitters ust ssue to ssess their coplince Signl to interference rgin Trnsitter right s bound on the trnsitter power The receiver being protected log(d) log(d) Fig. 5. A receiver spectru right illustrting tht the power bound ttenutes towrds the receiver being protected gin loction, direction, distnce, power, nd frequenc. The origin loction be point or spce. 3 The sptil etent of rights is function of how users interct with ech other. It is possible to crete rights where secondr users re ble to trnsit in the se spce tht contins prir receivers. It is lso possible to define rights tht restrict secondr users to regions beond where prir receivers re epected to be. It is this fleibilit tht kes our pproch coplete. Although rights cn be de quite cople, in ost cses there will be no need other thn for siple specifiction. B. Specifing Rights Trnsitters ust receive n uthoriztion to trnsit. In the cse of prir user the trnsitter right it is given is sufficient to specif its use of spectru. In the cse of secondr users, its right is iu power constrint on its trnsissions nd then it ust copl with trnsitter nd receiver rights of prir users or other users specified b spectru nger. We now use eples to illustrte how rights ight be specified using these dt structures. 1) Protecting Coercil Brodcsts Currentl, brodcsters re regulted b plcing liits on the ount of power the use in their brodcsts nd controlling where tht brodcst ight originte. In contrst, our lterntive lso iplies geogrphicl liit to the brodcster s right to spectru nd conditions for secondr spectru use. Three different rights tuples re used. First, trnsission right specifies the ount of power the brodcster use in its trnsission. The second is trnsission right underl. This underl specifies rgin tht quntifies the reltive qulit of reception tht receivers ust chieve nd provides opportunit for secondr spectru users to use spectru t uch reduced trnsission power within the brodcster s rights region. This is n optionl prt of the right. The third tuple is receiver right. The receiver right pplies to secondr trnsitters outside the brodcster s rights region. When n underl is used, the receiver right protects receivers t the boundr of trnsitter right where the underl equls the iniu receiver right power. When n underl is not used the iniu receiver right power pplies to ll points in the brodcster s rights region. 3 We do not specif how to define spce fro which receiver rights originte. An ethod be used. Eples could be through the specifiction of solid priitives such s spheres, clinders or cubes originting fro point or defined b series of coordintes on the surfce of the spce. Power in db scle Trnsitter right underl to protect receivers Receiver right underl to epower secondr trnsitters outside the rnge of the prir trnsitter s rights Prir trnsitter s protected rnge The trnsitter given the right log(d) Fig. 6. A brodcster s right specifiction in single direction. A trnsitter rights bound is the constrint on the brodcster s signl strength. The underl specifies the power rgin tht the brodcster cn tr to chieve. The shded re shows the perissible trnsit powers tht secondr users use without violting the brodcster s right. The receiver right ppers to rise quickl on ccount of the log scle for distnce. N A Fig. 7. A brodcster s rights scenrio. The point A rks n ntenn loction for the brodcster nd the shded region rks the service re. The brodcster s rights region cn be rticulted b either n eplicit description of geogrphicl spce or b using specified power threshold coupled to the trnsission right were the liits of the region is the loction where the threshold is pssed. A threshold boundr is theoreticl liit bsed on the power specified in the power p nd the pthloss eponent nd is not ffected b the ntenn gin of possible receivers. All secondr users outside of the brodcster s rights region ust copl with the receiver right of hpotheticl receiver locted where it would be ost restrictive. Fig. 6 illustrtes n eple of such brodcster s right. It onl shows the right in one direction. Different rights cn be specified for other directions. We show tht both the brodcster nd the custoer hve requireent to chieve prticulr perfornce tht tkes dvntge of the right. The brodcster tries to chieve the required power nd the custoer insures his receiver is in position to tke dvntge of tht power. It is envisioned tht over tie the definition of spectru rights for prticulr brodcster cn be refined to ccurtel ccount for the environentl effects tht re ctull present. To deonstrte the fleibilit of the brodcster right consider brodcster tht needs the right in the scenrio illustrted in Fig. 7 but lso needs to llow secondr ccess. Such right ight be specified with the following tuples using 8-bit words in the propgtion ps, power ps nd spectru sks: Trnsitter right bound

7 ), 1, Reltive Power (db) Spectru sk liiting prir trnsitter power Potentil protection rgin Underl restricting secondr trnsitter power Frequenc s1 n,, s2 (MHz) n, Fig. 8. Trnsitter spectru sk with n underl sk Power Densit (dbw/ 2 ) Miu brodcst power Underl power constrint for secondr trnsitters Distnce (log 1 scle ld eters) Point where ttenution odel predicts trnsitter right power reches -8 dbw/ 2 is point where the receiver right rther thn the underl constrins secondr trnsit power. The receiver right power is -12 dbw/ 2 Fig. 9. Miu brodcst trnsitter nd secondr trnsitter powers s function of distnce. Note tht distnce is on logrithic scle. N A Fig. 1. Service re superiposed on top of the spce protected b the cobined propgtion p nd power p deonstrting pproprite coverge. Note tht distnce is on liner scle. Points B, C, nd D re secondr trnsitters which ust copl with the prir rights. Loction: A Spectru Msk: f c = 4 MHz, f i = 1 khz, p c = 2 dbw/ 2 (77, 8, 97, 3, 117,, 147,, 167, 3, 187, 8, 255) Propgtion p: (,) Power p: (15, 255, 5,, 25, 3, 4, 7, 92, 15, 251,, ) Trnsitter underl Spectru Msk: : *f c = 4 MHz, *f i = 1 khz, *p c = 2 dbw/ 2 (97, 2, 12, 4, 152, 4, 157, 2, 255) *Propgtion p: (,) *Power p: (15, 255, 5,, 25, 3, 4, 7, 92, 15, 251,, ) Receiver right Spectru Msk: *f c = 4 MHz, *f i = 1 khz, p c = -8 dbw/ 2, (97, 2, 12, 4, 152, 4, 157, 2, 255) Propgtion p: (,) B C D Ites rked with * re redundnt nd could be dropped Fig. 8 illustrtes the trnsitter right spectru sk nd the underl sk showing the liits on brodcst power, the liits on power tht secondr trnsitter in the se bnd use, nd the rgin tht the brodcster cn tr to chieve. Fig. 1 illustrtes the iu power for these sks s function of distnce in the direction fro the trnsitter where db in the spectru sk is referenced to the brodcster trnsitter power level in Fig 9. We see tht the brodcster hs protected rnge of little over 1 k nd t distnces beond this point the receiver right provides the constrints to secondr trnsitter power. Finll, in Fig. 1, we illustrte the sptil region tht the brodcster cn rech b the specified spectru right nd deonstrte its coverge of the desired service re. In this eple, not onl does the right cover the service re but there is gurd in spce, spectru, nd power to protect the brodcst while still llowing secondr ccess. 2) Protecting Wireless Networks Wireless networks consist of ultiple trnsitters nd receivers nd so the right cnnot be referenced to single point. Spectru rights for wireless networks would specif geogrphic region for the rights, trnsitter right for the networked trnsceivers in the region, nd receiver right tht would be pplied fro the peripher of the region. There would be no underl. Secondr users would onl be ble to use the spectru if the re outside the protected region nd if their trnsissions confor to the ost restrictive receiver right of n rbitrr receiver t the ost constrining loction. 3) Protecting Receiver Potentil receivers needing protection include stellite terinls, rdio strono sites, nd rdrs. The siple receiver right is sufficient to protect these rdios nd their use of spectru. If these tpes of receivers re sttionr, then the receiver right is referenced to point nd if the operte in region then the receiver right would be referenced to geogrphic region. 4) Specifing Secondr Spectru Right Secondr spectru users, whether single trnsitter or group of trnsceivers tht for network, re given rights to use spectru with trnsitter right. However, these trnsitter rights re copliented with the rights definitions of prir users of the se spectru. Secondr devices use the spectru so long s their use confors to the secondr right nd the constrints of the prir users. Fig. 11 illustrtes one of the ver forgiving fetures of secondr spectru rights. Assuing tht the iu power of the secondr user eets the locl requireent, it will becoe ore coplint in directions w fro the trnsitter becuse of the log distnce ttenution of signls. C. Assessing Coplince Rdios tht hve prir rights to spectru copl with

8 ) Power Densit (dbw/ 2 ) 5 Prir, n=2 Secondr t 2 eters, n=2 5 1 Secondr t 1 eters, n= Distnce 1 ld Fig. 11. A coprison of the reltive rte of power ttenution. In the fr field of prir trnsitter, secondr trnsitter s signl will ttenute t uch fster rte on ccount of the log-distnce effect. Secondr trnsitters tht re coplint locll will be coplint t distnces w fro the source in the coincident directions of propgtion. This effect is ore pronounced t greter distnces. Note tht distnce is plotted on logrithic scle., 1, 1, 1, 1 5 Power (db) b s3 n Frequenc,, s2 n,, s4 (MHz) n,, s5 n, Fig. 12. Three signls constrined to different power levels b the se constrining sk the spectru rights specified in the ethod bove b liiting their iu trnsit power to the constrint of the power p nd b ensuring tht the bndwidth of their signl flls within the rights spectru sk. The rnges predicted b the right re not necessril those tht the rdio cn obtin nd re usull chosen to provide dditionl protection to the prir user. Rdios with secondr rights ust do ll of the bove but ust lso insure the eet the constrints of ll prir nd specified secondr spectru users tht cohbit spectru in the trnsitter right spectru sk. The coplince of the rdio to prir constrints is ssessed b whether the rdio s behvior tches the restrictions iposed b the odel, i.e. trnsits t power below tht required b the rights odel, not b whether the result, i.e. signl strength t prticulr point, is correct. In dnicll controlled environent spectru ngers cn chnge rights to protect prir users if the odels prove to be optiistic. D. Concepts nd Theores for Checking Coplince First we consider how to deterine the reltive power constrint tht receiver right spectru sk plces on lower precedence users. Net we consider how sptil power constrints defined using propgtion nd power p structures constrin the trnsit power of lower precedence users. c 1) Spectru Msk Constrints Spectru sks used in this pproch re piecewise liner nd hve the for (f, p, f 1, p 1,, f, p, 2 ) where the pir (f, p ) define inflection point on tht sk. Let there be X inflection points in the constrining sk enuerted fro 1 to X where ech inflection point is lbeled (fc, pc ), 1,2,,X nd Y inflection points in the trnsitter spectru sk of the lower precedence user s signl enuerted fro 1 to Y where ech inflection point is lbeled (f, p ), 1,2,,Y. The vlues pc re esured in db units reltive to the iu power llowed t tht point, i.e. p c, while the vlues p re db units reltive to the iu llowed trnsit power of the lower precedence user. Our gol is to deterine the iniu perissible difference between p c nd the iu trnsit power. Let pd be this difference. The pproch to deterining this difference is to shift the trnsitter spectru sk in power to the point where the constrining sk first restricts the trnsit power. Fig. 12 illustrtes three signls ech constrined to different power level bsed on their frequenc bnd. We observe tht the point of constrint lws occurs t n inflection point, either of the constrining or the trnsitter spectru sk. Thus the rdio cn copute iu trnsit power b identifing the trnsit power llowed b the constrining inflection point. The procedure follows: if ((f 1 > fc X ) or (f Y < fc 1 )) The trnsitter is not constrined else { // Initilize the vribles = 1, = 1, pd = 1, f_ref = fc 1, p_ref = pc 1, fc_constrins = true // Find the first inflection point to check, the lrger of fc 1 nd f 1 while ((f < f_ref) nd ( < Y)) = + 1 if ( > 1) = 1 else { f_ref = f, p_ref = p, fc_constrins = flse while (fc +1 < f_ref) = +1} // Check ll overlpped inflection points nd deterine which constrins while ((f_ref fc X ) nd (f_ref f Y ) nd ( Y) nd ( X)) { if (fc_constrins) f_low = f, f_high = if( < Y, f +1, f ), p_low = p, p_high = if( < Y, p +1, p ) f _ ref f _ low pd _ test = p _ ref ( p _ high p _ low) f _ high f _ low else f_low = fc, f_high = if( < X, fc +1, fc ), p_low = pc, p_high = if( < X, pc +1, pc ) f _ ref f _ low pd _ test = ( p _ high p _ low) p _ ref f _ high f _ low // Choose the sllest power difference s the constrint if (pd_test < pd) pd = pd_test if (fc_constrins) // Check if net prir inflection point constrins if(f_ref < fc X ) // First criteri if(fc +1 < f_high) // Second criteri = + 1, f_ref = fc, p_ref = pc else = + 1, // Secondr inflection point constrins if ( < Y) f_ref = f, p_ref = p, fc_constrins = flse else = + 1, // Secondr inflection point constrins if ( < Y) f_ref = f, p_ref = p, fc_constrins = flse else // Check if net secondr inflection point constrins if(f_ref < f Y ) // First criteri if(f +1 < f_high) // Second criteri = + 1, f_ref = f, p_ref = p else = + 1, // Prir inflection point constrins if ( < X) f_ref = fc, p_ref = pc, fc_constrins = true

9 } } else = + 1, // Prir inflection point constrins if ( < X) f_ref = fc, p_ref = pc, fc_constrins = true The constrining sk in Fig. 12 is (396, -2, 397, -4, 43, - 4, 44, -2). The generic sk for the signls, b, nd c is (f,-6, f+.2, -4, f+.3,, f+.4,, f+.5, -4, f+.7, -6). For signl, f = 396, for signl b, f = 398, nd for signl c, f = The procedure bove deterined power differences of -28 db, -4 db, nd db for signls, b, nd c respectivel. 2) Mp Constrints We ssue tht ll trnsitters re ble to confor their signl to the spectru of their spectru sk nd the directionlit specified in their power p nd their understnding of loction is correct. Our gol is to deterine the constrint cused b prir right to the iu power used in secondr user s trnsissions. 4 A secondr user s signl is coplint to constrining right t point q if the power of the ttenuted secondr signl t q, ps(q) confors to ps( q) pc( q) + pd. where pc(q) is the ttenuted strength of prir signl t q when trnsitted t the iu strength nd pd is the power difference between the pplicble prir underl or receiver right spectru sk nd the secondr trnsitter right spectru sk. Attenution in these ssessents is tht iplied b the propgtion ps of the prir nd secondr rights not ctul esureents. The ssessent of coplince of secondr trnsitter to prir right ust consider the intersections of ll sectors of both rights. The reltive loction of secondr trnsitter to prir right cn be one of three s illustrted in Fig. 1: within the prir rights region like Point C, outside the prir rights region but closest to n underl right like point B, or beond the prir right where receiver right pplies like Point D. For ech pirwise set of sectors of the prir nd secondr rights, we wnt to deterine the points tht ost restrict the secondr trnsit power nd then the ssocited power constrint offered b those points. S such point is q, then the iu llowed trnsit power of secondr trnsitter locted t point s specified b those pirs is ps(, s q) ps() q + 1ns logs q. (1) where s-q is the distnce between the secondr trnsitter nd the constrining point, is the secondr trnsitter s sector contining q, ns is the pthloss eponent of the secondr trnsitter s sector, nd ps(s,q) is the iu llowed trnsit power for sector cused b the conditions t q. Let q i be the set of points in sector tht re considered constrining, then the finl constrint tht pplies is in ps( s, q i ). i Our gol is to find the loctions of potentil constrining 4 We use the words prir nd secondr nd en these to be generl nd to ppl to n constrining nd lower precedence user pir. points in the intersection of prir nd secondr sectors. We strt with soe preliinr definitions nd theores Definition: An equipower surfce (ES) of constrint nchored t node in sector is the surfce where the underl power is the se. Since the pthloss eponent nd iu trnsit power is the se in sector, n ES is surfce equidistnt fro the node. Theore 1: The point on n equipower surfce tht ost constrins secondr trnsitter is the closest point on tht surfce to the secondr trnsitter. Proof. B definition the constrining power is the se t ll points on the ES. Thus b (1) onl the distnce between the points ffects the llowed secondr trnsit power. Allowed power increses with distnce nd so the closest point is ost constrining. Q.E.D. Definition: An ttenution pth is pth fro trnsitter over which signls ttenute t the rte specified b the pthloss eponent. These pths follow lines originting fro the trnsitter. Consider the scenrio in Fig. 13. Let np be the eponent tht pplies to the ttenution long the prir s ttenution pth to point q nd ns be the eponent of the secondr ttenution pth fro point s to point q. We wnt to know which point q on the prir ttenution pth is ost constrining. The vlues nd B re constnts in this scenrio nd b cn be written s function of c using the lw of cosines 2 2 b = + c 2ccosB. The constrining power t point q is pc( q) = p 1np log( c). where p is the iu trnsit power llowed for the prir trnsitter. The iu llowed secondr trnsit power tht is still coplint t q is 2 2 ( ) ( ) ps( s, q) = p 1np log c + pd + 1ns log + c 2c cos B p B c Secondr sector boundries. (2) 5 Definition: A constrining point is point q on segent of prir trnsitter s ttenution pth tht results in 5 We re using the full distnce between the reference point nd ech trnsitter lthough the propgtion odel is referenced to the 1 eter point fro the trnsitters. This works so long s the distnces re uch lrger thn 1 eter. q b s Attenution pth segent Fig. 13. A scenrio used to evlute the constrints cused b points on n ttenution pth. The point p is the loction of prir trnsitter, the point s is the secondr trnsitter, nd q is point on the ttenution pth. The vlues of, b, nd c re the lengths of the respective sides nd B is the ngle fored b the ttenution pth nd the line fro p to s.

10 locl iniu for ps(s,q). Moveents w fro this point re either infesible or llow greter trnsit power. Theore 2. The point qd ost distnt fro the prir trnsitter on n ttenution pth segent is constrining point if it is the closest point to s or if 2 np c c cos B >, 2 2 ns + c 2ccosB where c is the distnce to tht point. Proof. If the qd is the closest point to s then it is ost constrining since the onl fesible oves re towrd the prir trnsitter so pc(q) increses nd the distnce fro s to q increses. Both increse ps(s,q). We now wnt to consider when the end is not the closest point nd deterine if oving towrd p fro q on the ttenution pth will be ore or less constrining. We cn deterine the reltive chnge of ps(s,q) dps ( s, q) with respect to q b finding the derivtive,. dc dps( s, q) 5ns ( c cosb ) 1np =. (3) 2 2 dc ( + c 2ccos B)ln( 1) c ln ( 1) If the derivtive is negtive then the llowed secondr trnsit power increses s c decreses. Using the inequlit <, the eqution dps ( s, q) dc 2 np c c cos B > 2 2 ns + c 2ccosB follows fro (3). Q.E.D. Definition: An interior constrining point is constrining point on n ttenution pth tht occurs prior to the distnt end of segent of n ttenution pth. An interior constrining point eist where dps ( s, q) =. In this cse eqution (3) cn be reduced to dc qudrtic in c nd b using the qudrtic eqution we find tht locl iniu, i.e. constrining point, eist t 2 np np np np 2 2 1cosB+ 2 1 cosb 1 ns ns + ns ns c =. np 21 ns (4) The point is constrining if the rdicl reins positive. There is still point when np = ns nd cn be estited b djusting np = np + ε where ε is sll vlue. Definition: A sector intersection plne is the plne fored b prir sector boundr nd secondr sector. Definition: The closest ttenution pth on sector intersection plne is the ttenution pth through the point closest to s. Theore 3: The interior point of the closest ttenution pth on sector intersection plne is the ost constrining interior constrining point. Proof. Assue n interior constrining point qc eists on the closest ttenution pth. We will prove tht interior constrining points on ll other ttenution pths re less constrining thn this point. The interior constrining point qc cn be one of two tpes, the closest point on the pth segent or locl iniu on the pth segent s deterined b (4). If there is interior constrining point on n lterntive pth then it is either closer, the se distnce, or further fro p thn the constrining point on the closest ttenution pth. If the point is closer, then its constrining power is lrger thn tht t qc nd since its distnce to s is lrger it ust be less constrining. If t the se distnce then it is on n ES with qc nd b Theore 1 qc is the ost constrining. Finll if this point is further w fro p then the ES through this point will intersect the closest ttenution pth further w fro p thn qc. The point t the intersection of the closest ttenution pth nd this ES is ore constrining thn the lterntive point b Theore 1 nd qc is ore constrining thn this point b our initil ssuption. Q.E.D. Theore 4: The ost constrining distnt constrining point is either the furthest point on the closest ttenution pth, the closest point on the prir trnsitter right boundr, or the furthest point fro p on the sector intersection plne. Proof. When secondr sector intersects the boundr of prir sector it will either contin the full prir sector boundr or project rectngle nd crete either qudrilterl plne or qudrilterl plne tht is further cut b the boundries of the prir sector. We will show tht points between the three points, the furthest point on the closest ttenution pth, the closest point on the trnsitter right boundr, nd the furthest constrining point fro p, re not cpble of being ore restrictive. S the furthest point on the closest ttenution pth qd is restrictive, i.e. it eets the requireents of Theore 2. No points closer to p thn the ES through qd cn be ore constrining thn points t the se distnce on the closest ttenution pth. If there is point ore constrining, the constrining point on the closest ttenution pth will not be t the trnsitter boundr nd the ore constrining point ust be t the end of nother ttenution pth further w fro p. The boundr of the ttenution pths is the boundr of the sector intersection plne. This boundr is liner nd so rtes of chnge in the peritted secondr trnsit power will either increse or decrese onotonicll. The end point on this line will be the ost constrining nd it will either end t the trnsitter right boundr or t the furthest constrining point fro p. Q.E.D. Let us now consider the evlution of the scenrios. In the scenrio of Point C, the secondr signl will be strongest t point C nd will hve uch ore rpid ttenution locll becuse of the distnce effect s illustrted in Fig. 12. Thus two points should be checked to deterine coplince, point C nd then the closest point on the ES of the trnsitter right boundr. This point is the intersection of the ES with the ttenution pth tht psses through point C. In the scenrio of point D, the constrining point is the closest point on the trnsitter right boundr. In this eple tht point occurs on the intersection of the ttenution pth tht psses fro A to D nd the trnsitter right boundr. The scenrio of point

11 B is the ore difficult to evlute. Ech of the plnes fored b the intersection of the sectors nd the trnsitter right boundr, if intersected, should be checked. When checking plne, b Theore 3 we should evlute the interior constrining point of the closest ttenution pth tht hs n interior point. B Theore 4 we should check the furthest point on the closest ttenution pth nd the furthest point on the intersection plne boundr tht etends fro the furthest point on the closest ttenution pth. Greenwich Meridin b z Long, λ ν Lt, ϕ h P = X,Y,Z or λ, ϕ,h IV. CONCLUSION In this pper we hve introduced ethod for specifing loction-bsed spectru rights, both of prir nd secondr users. We hve deonstrted the fleibilit of this technique to confor rights to cover sptil regions so tht there be sptil reuse. We hve described how these rights lso provide the criteri for coeistent secondr use of spectru nd then theores nd ethods for verifing coplince with these criteri. This tpe of definition of the sptil RF spectru resource enbles uch finer sptil nd spectrl prtitioning of spectru nd n ttendnt theticl odel for ssessing the interction of users. It could be dded to the ontolog used with XG rdios to define spectru use conditions nd polic. However, it is intended to be the foundtion of dnic spectru ngeent utilit tht would function both s spectru use optiizer nd broker for secondr rkets. With this ethod, the spectru resource cn be defined, subdivided, nged, nd brokered. APPENDIX A The World Geodetic Sste 1984 (WGS 84) defines n erth centric ellipsoid to serve s the reference dtu for loction. It is globl sste nd is the dtu for GPS. Our gol is to tke one WGS-84 coordinte nd ke it the origin of propgtion or power p, crete new coordinte reference t tht point where the horizon is the plne nd the is points north, convert other WGS-84 coordintes to tht reference sste, nd then deterine direction fro the origin to those points. We strt b describing the conversion of ellipsoid coordintes to Crtesin. Net we describe the trnsfortion of the reference sste t point defined b WGS-84 coordintes nd then the conversion of other WGS-84 points to coordintes in tht se reference sste. Finll we provide the equtions for p directions. A. Converting Ellipsoid Coordintes to Crtesin Ellipsoids re fored b rotting n ellipse bout one of its es, the inor is in the cse of geogrphicl reference dtus. An ellipsoid fored b rotting n ellipse bout its inor is hs four esures, the dieter of the seijor is,, the rdius of the seiinor is, b, the flttening, f, nd the eccentricit, e. These esures re relted s follows. b f = (2-1) 2 2 b 2 e= = 2 f f 2 The inor is is coincident with the is of rottion of the erth. For globl dtu reference the center of the coordinte sste is locted t the center of the erth with the z is coincident to the inor is of the spheroid with positive direction towrd the north pole. The is lies on the equtoril plne pointing towrd the eridin pssing through the Greenwich Observtor. The positive direction of the is is chosen to get right hnded coordinte sste. Figure A.1 illustrtes the reltionship between ellipsoidl nd Crtesin coordintes. There re just two preters tht re needed for specifing n ellipsoid, nd b, nd f, or nd e. Norll nd f re given. Conversion between ellipsoidl nd Crtesin coordintes requires n initil clcultion of the rdius of curvture of the prie verticl ν which is function of ltitude. The geodetic ltitude is the ngle between the plne t the equtor nd the geodetic norl to the ellipsoid surfce. Note tht the prie verticl is perpendiculr to the ellipsoid surfce nd etends to the inor is nd not intersect t the,, z origin. This rdius of curvture is deterined b ν = = e sin ϕ 1 2f f sin ϕ ( ) The rdius to the point P is ( ν + h). The WGS 84 Crtesin coordintes follow using the equtions = ( ν + h)cosϕcos λ = ( ν + h)cosϕsin λ Meridin t P Fig. A-1. Coprison of Crtesin nd ellipsoidl coordintes. TABLE A-1. THE WGS-84 ELLIPSOID PARAMETERS Preter Vlue Units eters b eters f e e

12 Fig. A-2. Strting coordinte sste before conversion to propgtion p orienttion is trnslted sste with the point t the origin. Fig. A-3. First step in conversion to propgtion p coordintes is to rotte the sste bout the z is to point the is towrd the ellipsoid is. Fig. A-4. Second step in conversion to propgtion p coordintes is to rotte the sste bout the is to ke the z is coincident with the prie verticl. ( ν ( 2 ) ) z = 1 e + h sinϕ Tble A-1 lists the WGS 84 preters. The conversion fro WGS 84 Crtesin coordintes bck to ellipsoidl coordintes is uch ore involved. See [8] for the vrious pproches. B. Conversion Mtri for the New Crtesin Sste Conversion to propgtion p reference sste centered t point follows directl using the WGS 84 longitude nd ltitude of tht point. Figures A-2 through A-4 show the process. Fig. A-2 shows the new coordinte sste with the WGS 84 reference directions. The first rottion illustrted in Fig. A- 3 is bout the z is to bring the is to the eridin plne tht corresponds to the new sste s origin nd cuses it to point towrd the opposite heisphere. This rottion is (9 + λ). This rottion will bring the is to the tngentil plne pointing esterl. The second rottion illustrted in Fig. A-4 is bout the is nd brings the z is coincident to the prie verticl nd brings the is to the tngentil plne pointing in the desired direction. The ngle of rottion bout the is is (9 - ϕ). The coordinte conversion tri for this new sste is the tri defining these rottions sinϕ cosϕsin λ cosϕcos λ RM = cosϕ sinϕsin λ sinϕcos λ. cosλ sinλ The trnsfortion of other WGS 84 Crtesin coordintes to this new sste is O R M = O. z z z Mp WGS84 O WGS84 where the coordintes O, O, nd z O re the WGS 84 coordintes of the sste origin. C. Deterining Directions Directions fro the origin to point follow directl fro their coordintes in the p sste. Mp longitudes re esured fro the is bout the z is just s in geodetic sstes, however, the ltitudes re esured fro the z is rther thn fro the equtoril plne of the sste. This ltter convention is used to siplif the p construction. The longitude cn be deterined directl fro the,, nd z coordintes in the p reference sste. 1 θ = tn 6 The ltitude is deterined using φ = cos 1 z + + z More detiled discussion of coordinte trnsfortions cn be found in [8]. REFERENCES [1] J. A. Stine, Enbling secondr spectru rkets using d hoc nd esh networking protocols, Acde Publisher J. of Coun., Vol. 1, No. 1, pp April 26. [2] DARPA XG Working Group, The XG Vision. Request for Coents, Version 2., Prepred b BBN Technologies, Cbridge MA, USA, Jnur 24. [3] Shred Spectru Copn News Relese Shred Spectru Copn successfull deonstrtes next Genertion (XG) wireless counictions sste, Septeber content/press/xg_deo_news_relese_6918.pdf [4] DARPA XG Working Group, XG Polic Lnguge Frework. Request for Coents, Version 1., Prepred b BBN Technologies, Cbridge MA, USA, April 24. [5] T. Rppport, Wireless Counictions, Principles nd Prctice, Second Edition, Prentice-Hll, Inc, Upper Sddle River, NJ, 22. [6] DARPA XG Working Group, The XG Architecturl Frework. Request for Coents, Version 1., Prepred b BBN Technologies, Cbridge MA, USA, Jul 23. [7] L. Berlenn, S. Mngold, G. Jiertz, nd B. Wlke, Polic defined spectru shring nd ediu ccess for cognitive rdios, Acde Pub. J. of Coun. Vol. 1 No. 1, pp. 1-12, April 26. [8] J. A. Stine, MITRE Technolog Report Coordinte sstes with trnsfortions for Node Stte Routing, TBP. 6 The brckets bout θ nd ϕ indicte true not coded ngles nd re used to be consistent with our nottion in section II.D.. 6