Relay Based Cooperative Spectrum Sensing in Cognitive Radio Networks

Transcription

1 Relay Base Cooperatve Spectrum Sensng n Cogntve Rao Networks Saman Atapattu, Chntha Tellambura, an Ha Jang Department of Electrcal an Computer Engneerng, Unversty of Alberta, Emonton, AB, Canaa Emal: {atapattu, chntha, ha.jang}@ece.ualberta.ca Abstract In ths paper, we explot cooperatve spectrum sensng technque for applcatons n a relay base cogntve rao network. Relays are assgne n cogntve rao networks to transmt the prmary user s sgnal to a cogntve coornator. Ths research s focuse on the etecton of prmary user n sngle or multple cogntve relay scenaros. The performance of energy etector s analyze for nepenent Raylegh fang channels. False alarm an etecton probabltes are erve theoretcally wth or wthout rect communcaton between the prmary user an the cogntve coornator. An upper boun s also gven for etecton probablty. Our analyss s valate by numercal an smulaton results. Inex Terms Cogntve rao, cooperatve spectrum sensng, energy etecton, relay. I. INTRODUCTION Rao spectrum s an expensve an lmte resource n wreless communcatons. Surprsngly t turns out that lcense users terme prmary users rarely utlze all the assgne frequency bans at all the tme. Consequently, spectrum holes exst, whch are frequency bans not occupe by prmary users at a certan tme an a certan locaton. The resultng spectral neffcency has motvate cogntve rao technology, an emergng novel concept n wreless access. Cogntve rao represents a much broaer paragm where many aspects of communcaton systems can be mprove va cognton. The key features of a cogntve transcever are rao envronment awareness an spectrum ntellgence []. Intellgence can be acheve through learnng the spectrum envronment an aaptng transmsson parameters. For nstance, unlcense users terme seconary users or cogntve users can frst etect the actvtes of prmary users, an get access to the spectrum f no prmary actvtes are etecte. So ynamc spectrum access [], [3], [4], [5] can be acheve. In cogntve rao networks, the prmary users shoul be protecte as much as possble. Ths task s usually fulflle through spectrum sensng. Thus sensng accuracy s mportant for avong nterference to prmary users. Tratonally three methos can be use to perform spectrum sensng [6]: energy etector non-coherent etecton through receve energy, matche flter coherent etecton through maxmzaton of the sgnal-to-nose rato, an cyclostatonary feature etecton explotaton of the nherent perocty of prmary sgnals. Among them, the energy etector s the most popular metho. Ths research was supporte by the Gangwon-Alberta Research Collaboraton Fun an the Natural Scence an Engneerng Research Councl NSERC of Canaa. To mprove the spectrum sensng accuracy, cooperatve sensng can help, beneftng from nformaton exchange among seconary users. In [7], an optmal spectrum sensng framework s ntrouce by conserng both spectrum effcency an nterference avoance. The benefts of sensng cooperaton n cogntve rao are llustrate n [8], [9] for both two-user an multple-user networks. Reucton of etecton tme an ncrease of overall aglty are observe. In ths paper, we propose a relay base cooperatve spectrum sensng n cogntve rao networks. The ea s to utlze relay noes to convey the sgnal transmtte from the prmary user to a cogntve coornator, whch wll make estmaton of the presence or absence of prmary actvtes. The cogntve coornator uses an energy etector to make estmaton. Cogntve relays are operate n an amplfy-an-forwar moe wth varable-gan []. Note that nstantaneous channel gan nformaton s avalable for the channel from the prmary user to each relay, an from each relay to the cogntve coornator. II. SYSTEM MODEL A. Channel Moel The wreless network s assume to operate over nepenent an not necessarly entcally strbute Raylegh fang channels. h xy s the fang coeffcent for the X Y lnk, an the magntue of h xy s wth the probablty ensty functon pf gven [] by f hxy t =te t,t, where E h xy =.HereE represents mathematcal expectaton. Atve whte Gaussan nose AWGN, enote w x at noe X, s assume, whch s a crcularly symmetrc complex Gaussan ranom varable wth mean zero an varance N.e., w x CN,N. B. Cooperatve Scheme We conser a relay-base spectrum sensng. A number, n, of cogntve relays name r,r,..., r n are ae n the cogntve rao network, as shown n Fg.. As the prmary user starts usng the ban, cogntve raos receve the sgnal of the prmary user. Therefore n the frst phase, all cogntve relays lsten to the prmary user sgnal. Instea of makng nvual har ecson about the presence of the prmary user, relay-base cogntve raos smply amplfy an retransmt the nosy verson of the receve sgnals to the cogntve coornator n the secon phase. Each communcaton between cogntve relay an cogntve coornator occurs n orthogonal channels to avo the nter-channel nterference. In orthogonal Ths full text paper was peer revewe at the recton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 9 proceengs /9/$5. 9 Authorze lcense use lmte to: UNIVERSITY OF ALBERTA. Downloae on May 8, at :3: UTC from IEEE Xplore. Restrctons apply.

2 Fg.. P h sr n r h pr h r h pr h sr Relay lnk Drect lnk r h p r r n h r h r h r n p: Prmary user r : -th Cogntve relay : Cogntve coornator Illustraton of a cooperatve network wth cogntve relays. channels, the cogntve coornator receves nepenent sgnals from the prmary user an cogntve relays base on tme vson multple access TDMA. The cogntve coornator s equppe wth the energy etector whch compares the receve sgnal strength wth a pre-efne threshol. Base on the ecson, the cogntve coornator nforms the cogntve raos of the presence or absence of prmary user s actvtes. It s assume that the prmary user s not affecte by cogntve rao transmsson. In ths research, we conser a ual-hop topology. Although a mult-hop scheme can cover a larger area, t takes longer tme to relay the prmary user s sgnal to the cogntve coornator. Therefore, etecton tme woul be ncrease. Further, errors coul be propagate from one hop to another. In the followng, the cases wth a sngle cogntve relay an multple cogntve relays are scusse, respectvely. C. Sngle Cogntve Relay In the case wth a sngle relay enote r, we have three noes,.e., the prmary user, the cogntve relay, an the cogntve coornator. The cogntve relay contnuously montors the sgnal receve from the prmary user. The receve sgnal by the cogntve relay, enote y pr, s gven by y pr = θxh pr +w r, where θ enotes the prmary actvty ncator, whch s equal to at the presence of prmary actvty, or equal to otherwse, x s the transmtte sgnal from the prmary user, h pr s the channel gan between the prmary user an relay, an w r s the nose sgnal at the cogntve relay. The cogntve relay acts as a varable gan amplfy-an-forwar relay AF, whch s more practcal than ecoe-an-forwar or bln/sem-bln relay operaton. The cogntve relay has a transmsson power constrant E r. Therefore, the amplfcaton factor, β r s gven by β r E = r θ E p h pr +N, where E p s transmtte sgnal power from the prmary user. Thus, the receve sgnal at the cogntve coornator, enote y r, s gven by y r = β r y pr h r + w = θ β r h pr h r x + β r h r w r + w = θhx + w, where h r s the channel gan between the relay an the cogntve coornator, w s the nose sgnal at the cogntve coornator, h = β r h pr h r, an w = β r h r w r +w s the total effectve nose at the cogntve coornator, whch can be moele as w hpr,h r CN, β r h r +N. The receve sgnal at the cogntve coornator follows a bnary hypothess: { w : H θ =, y r = hx + w : H θ =. As escrbe n [], [3], the receve sgnal s frst prefltere by an eal banpass flter wth center frequency f c an banwth W n orer to normalze the nose varance. The output of ths flter s then square an ntegrate over a tme nterval T to fnally prouce a measure of the energy of the receve waveform. The output of the ntegrator, enote Y, acts as the test statstc. The pf of Y s gven [3] by { f Y y = u Γu yu e y : H y γ u e γ+y I u γy : H where Γ s the gamma functon, I v s the v th orer mofe Bessel functon of the frst kn, an u = TW where T an W are chosen to restrct u to an nteger value. The total en-to-en sgnal-to-nose rao SNR, enote γ, s gven [] by γ pr γ r γ = γ pr + γ r +, 3 where γ pr = h pr E p /N an γ r = h r E r /N are SNRs of the lnks from the prmary user to the cogntve relay an from the cogntve relay to the cogntve coornator, respectvely. D. Multple Cogntve Relays In the case wth multple cogntve relays, we have n cogntve relays between the prmary user an the cogntve coornator, as shown n Fg.. h pr, h p an h r enote the channel gans between the prmary user an the th cogntve relay r, between the prmary user an the cogntve coornator, an between the th cogntve relay r an the cogntve coornator, respectvely. All cogntve relays smultaneously receve prmary user s sgnal through nepenent fang channels. Each cogntve relay say relay r amplfes the receve prmary sgnal by an amplfcaton factor β r gven as β r E = r θ E p h pr +N an forwars to the cogntve coornator. All the cogntve relays use mutually orthogonal channels to forwar the receve prmary sgnal. Such orthogonal channels can be realze by usng TDMA technology. The receve sgnals at the cogntve coornator can then be consere as nepenent copes through orthogonal channels. Therefore, the maxmal rato combnng MRC at the cogntve coornator can be mplemente, an after an ntegrator, the fnal test statstc Y s obtane. The total en-to-en SNR s gven by γ = n γ pr γ r γ pr +γ r + where γ pr an γ r are SNRs of the lnks from the prmary user to the cogntve relay r an from the cogntve relay r to the cogntve coornator, respectvely. Ths full text paper was peer revewe at the recton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 9 proceengs /9/$5. 9 Authorze lcense use lmte to: UNIVERSITY OF ALBERTA. Downloae on May 8, at :3: UTC from IEEE Xplore. Restrctons apply.

3 A. Energy Detector III. DETECTION ANALYSIS At the cogntve coornator, the test statstc Y s compare wth the preefne threshol value λ. The probabltes of etecton P an false alarm P f can be generally evaluate by PrY > λ H an PrY > λ H respectvely to yel [3] an P f = Γu, λ Γu 4 P = Q u γ, λ, 5 where Q u, s the generalze Marcum-Q functon an Γ, s the upper ncomplete gamma functon whch s efne by the ntegral form Γa, x = x ta e t t an Γa, = Γa. Probablty of false alarm P f can easly be calculate usng 4. B. Average Detecton Probablty Generalze Marcum-Q functon can be wrtten as a crcular contour ntegral wthn the contour raus r [,. Therefore 5 can be re-wrtten [4] as P = e λ jπ C e z γ+ λ z z u z, 6 z where Δ s a crcular contour of raus r [,. The moment generatng functon MGF of γ s M γ s =Ee sγ. Thus, the average etecton probablty s gven by P = e λ M γ e λ z jπ C z z u z. 7 z Therefore, t s mportant to know the MGF of γ. Base on the close-form MGF for Nakagam-m fang [5], we can erve the MGF of γ n 3, enote M γ s, wth a sngle relay over Raylegh fang as M γ s = s Γ, t Γ k= k k k 4 t γpr γ r, t+ 4 t γpr γ r [ e 3t/ t k γ pr γ r ] t=s+ γpr +γ r γpr γ r 8 A close-form soluton for the exact P seems analytcally ntractable. However, effcent numercal algorthms are avalable to evaluate a crcular contour ntegral. We use Mathematca software that proves aaptve algorthms to recursvely partton the ntegraton regon. Wth a hgh precson level, the numercal algorthm can prove an effcent an accurate soluton for 7.. C. Upper Boun of P Now we procee to erve an upper boun for the average etecton probablty. The total SNR γ can be upper boune by γ up as γ γ up = γ mn, 9 where γ mn = mnγ pr,γ r. Therefore, MGF of γ up can be wrtten as M γup s = M γ mns, for nepenent lnks. M γup s can be erve as γ pr + γ r M γup s =, γ pr γ r s + γpr + γ r γ pr γ r where γ pr = E hpr E p N an γ r = E h r E r N are average SNRs for lnks from the prmary user to cogntve relay r an from cogntve relay r to the cogntve coornator, respectvely. We refer reaers to the Appenx for the etals. Substtutng to 7, can be re-wrtten as = e λ gzz, jπ where e gz = λ z n Δ γ z u n z z Δ, wth Δ = pr γ r γ pr +γ r +γ pr γ. r Snce the Resue Theorem [6] n complex analyss s a powerful tool to evaluate lne ntegrals of functons over close curves an can often be use to compute real ntegrals as well, t s use n ths research to evaluate the ntegral n. Two cases nee to be consere. When u>n: There are u n poles at orgn an n poles for Δ s =,.., n n raus r [,. Therefore, can be erve as = e λ C Res g;+ Res g;δ 3 where Res g; an Res g;δ enote the resue of the functon gz at orgn an Δ, respectvely. When u n: There are n poles at Δ s =,.., n n raus r [,. Therefore, can be erve as = e λ Res g;δ. 4 We refer reaers to the Appenx for the etals of the ervaton of Resg;. D. Incorporaton wth the Drect Lnk In preceng subsectons, the cogntve coornator receves only sgnals comng from cogntve relays. Actually t can also receve the sgnal of the prmary user when the prmary user starts to utlze ts ban. The etecton of prmary actvtes becomes relable f the cogntve coornator s close to the Ths full text paper was peer revewe at the recton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 9 proceengs /9/$5. 9 Authorze lcense use lmte to: UNIVERSITY OF ALBERTA. Downloae on May 8, at :3: UTC from IEEE Xplore. Restrctons apply.

4 P n =.4 n = n = 3.3 n = 4. n = wth rect lnk n = wth rect lnk. n = 3 wth rect lnk n = 4 wth rect lnk..4.8 P f P n = n = n = 3 n = 4 n = wth rect lnk n = wth rect lnk n = 3 wth rect lnk n = 4 wth rect lnk λ Fg.. Varaton of P wth P f for fferent number of cogntve relays. Fg. 3. Varaton of P wth λ for fferent number of cogntve relays. prmary user, beneftng from the strong rect lnk. Then the total SNR at the cogntve coornator can be gven as γ = γ + γ r, 5 where γ = h p E p N s the rect path SNR, an γ r = γ r γ pr γ r +γ pr + s the relaye path SNR from relay r. Therefore corresponng MGF of γ, assumng nepenent fang channels, can be wrtten as M γ s =M γ s n M γ r s where M γ s s gven by + γ s, γ = Eγ, an M γr s s from 8. As n preceng subsectons, we can fn accurate average etecton probablty usng numercal ntegraton. In ths case, gz n can be wrtten as n gz = e λ z z u n z Δ z Δ Δ z Δ. 6 where Δ= γ + γ. When u>n+, there are u n poles at orgn, one pole at Δ an n poles for Δ s =,.., n n raus r [,. Further, a tght upper boun of the etecton probablty, enote P,up, can be erve n close-form as P,up = e λ Res g;+res g;δ+ Res g;δ. 7 Where Res g;δenotes the resue at Δ of the functon gz n 6. For gz gven n 6, Res g; an Res g;δ can be calculate as prevous. Calculaton of Res g;δs gven n the Appenx. When u n+, there are one pole at Δ an n poles for Δ s =,.., n n raus r [,. Smlarly, P,up can be erve n close-form for ths case. IV. NUMERICAL AND SIMULATION RESULTS Ths secton proves analytcal an smulaton results. Note that n all fgures n ths secton, numercal results are repre- sente by curves, whle smulaton results are represente by screte marks on the curves. For smulatons, the lnks from the prmary user to cogntve relays an from cogntve relays to the cogntve coornator are nepenent an entcally Raylegh fae wth average SNR beng 5 B. The etecton threshol λ vares from to 5. The value of u s set to be. Fg. shows the numercal an smulaton results regarng how the etecton probablty P changes wth the false alarm probablty P f. For the numercal results, the ntegral formula 7 s use for fferent cases. Clearly, the numercal results match perfectly wth ther smulaton counterparts, confrmng the accuracy of the analyss. As the number of cogntve relays ncreases, the etecton probablty also ncreases. Fg. also shows that a rect path gves a major mpact on the etecton probablty. Fg. 3 shows the mpact of the etecton threshol λ on the etecton probablty P. When the etecton threshol λ s at a small regon e.g., from to n Fg. 3, the etecton probablty P ramatcally ecreases when λ ncreases. Smlar to the observaton n Fg., more cogntve relays or a rect path tens to ncrease the etecton probablty. Fg. 4 shows the upper boun of etecton probablty erve n Secton III. C. It can be seen that the upper boun s not tght when there s a sngle cogntve relay. The upper boun s much tghter when a strong rect path can be utlze. Ths s because, n the upper boun ervaton for γ gven n 5, the approxmaton s only for the relay paths, not for the strong rect path. V. CONCLUSION We have stue the relay base spectrum sensng wth an energy etector for a cogntve rao network wth Raylegh fang channels. The analyss covers the etecton probablty an the false alarm probablty. The MGF of receve SNR of the prmary user s sgnal s utlze to analyze the etecton Ths full text paper was peer revewe at the recton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 9 proceengs /9/$5. 9 Authorze lcense use lmte to: UNIVERSITY OF ALBERTA. Downloae on May 8, at :3: UTC from IEEE Xplore. Restrctons apply.

5 P Boun n =.4 Boun n = wth rect lnk Boun n = 3 wth rect lnk.3 Boun n = 4 wth rect lnk. Exact n = Exact n = wth rect lnk. Exact n = 3 wth rect lnk Exact n = 4 wth rect lnk..4.8 P f Fg. 4. Upper boun an exact plot between P an P f for fferent number of cogntve relays. probablty. It s shown that the etecton probablty ncreases when the number of cogntve relays ncreases. Furthermore, rect path communcaton between the prmary user an the cogntve coornator has a major mpact on the etecton probablty by ntroucng spatal versty. A close-form upper boun expresson of the etecton probablty s erve. Ths boun becomes tght when there s a strong rect path between the prmary user an the cogntve coornator. A. MGF of γ mn APPENDIX The cumulatve strbuton functon cf of γ mn = mnγ pr,γ r s gven by F γ mnt = Prγ pr >t,γ r >t = F γpr t+f t F γr γ pr,γ r = e γ pr + γ r γpr γ r t t, t 8 where F γpr t an F t are the cf of γ γr pr an γ r, an F γpr,γ t, t s the jont cf of γ r pr an γ r. By the frst-orer ervatve of F γ mnt, the pf of γ mn s gven by f γ mnt = γpr + γ r γ pr γ r Therefore, the MGF of γ mn by M γ mns =, M γ mn γpr + γ r γ pr γ r e γ pr + γ r γpr γ r t. 9 s =Ee γmn s s gven s + γpr + γ r γ pr γ r. B. Calculaton of Resue Resg; If gz has the Laurent seres representaton,.e., gz = = a nz z n for all z, the coeffcent a of z z s the resue of gz at z [6]. In eq. 3, Res g; can be evaluate as Res g;= u n e λ z Δ u n! z u n z z Δ. z= Smlarly, Res g;δ j n eq. 3 can be evaluate as e λ Δ Δ j Res g;δ = Δ u n Δ Δ Δ j. j=, j Res g;δ n eq. 7 can be evaluate as e λ Δ Δ Res g;δ= Δ u n. Δ Δ Δ REFERENCES [] S. Haykn, Cogntve rao: Bran-empowere wreless communcatons, IEEE Journal on Selecte Areas n Communcatons, vol. 3, no., pp., Feb. 5. [] H. Jang, L. La, R. Fan, an H. V. Poor, Optmal selecton of channel sensng orer n cogntve rao, IEEE Transactons on Wreless Communcatons, vol. 8, no., pp , Jan. 9. [3] Q. Zhao, L. Tong, A. Swam, an Y. Chen, Decentralze cogntve MAC for opportunstc spectrum access n a hoc networks: A POMDP framework, IEEE Journal on Selecte Areas n Communcatons, vol. 5, no. 3, pp , Apr. 7. [4] R. Fan an H. Jang, Channel sensng orer settng n cogntve rao networks: A two-user case, IEEE Transactons on Vehcular Technology, accepte. [5] Z. Han, R. Fan, an H. Jang, Replacement of spectrum sensng n cogntve rao, IEEE Transactons on Wreless Communcatons, vol. 8, no. 6, pp , June 9. [6] D. Cabrc, S. M. Mshra, an R. W. Broersen, Implementaton ssues n spectrum sensng for cogntve raos, n Proc. Aslomar Conference on Sgnals, Systems an Computers, Nov. 4, pp [7] W.-Y. Lee an I. Akylz, Optmal spectrum sensng framework for cogntve rao networks, IEEE Transactons on Wreless Communcatons, vol. 7, no., pp , Oct. 8. [8] G. Ganesan an Y. L, Cooperatve spectrum sensng n cogntve rao, part I: Two user networks, IEEE Transactons on Wreless Communcatons, vol. 6, no. 6, pp. 4 3, June 7. [9] G. Ganesan an Y. L, Cooperatve spectrum sensng n cogntve rao, part II: Multuser networks, IEEE Transactons on Wreless Communcatons, vol. 6, no. 6, pp. 4, June 7. [] J. N. Laneman, D. N. C. Tse, an G. W. Wornell, Cooperatve versty n wreless networks: Effcent protocols an outage behavor, IEEE Transactons on Informaton Theory, vol. 5, no., pp , Dec. 4. [] M. K. Smon an M.-S. Aloun, Dgtal Communcaton over Fang Channels, n E. New York: Wley, 5. [] H. Urkowtz, Energy etecton of unknown etermnstc sgnals, Proceengs of the IEEE, vol. 55, no. 4, pp , Apr [3] F. F. Dgham, M.-S. Aloun, an M. K. Smon, On the energy etecton of unknown sgnals over fang channels, IEEE Transactons on Communcatons, vol. 55, no., pp. -4, Jan. 7. [4] C. Tellambura, A. Annamala, an V. K. Bhargava, Close form an nfnte seres solutons for the MGF of a ual-versty selecton combner output n bvarate Nakagam fang, IEEE Transactons on Communcatons, vol. 5, no. 4, pp , Apr. 3. [5] D. Senaratne an C. Tellambura, Unfe exact performance analyss of two hop amplfy an forwar relayng n Nakagam fang, IEEE Transactons on Vehcular Technology, July 9, submtte. [6] S. G. Krantz, Hanbook of Complex Varables, st E. Brkhuser Boston, 999. Ths full text paper was peer revewe at the recton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 9 proceengs /9/$5. 9 Authorze lcense use lmte to: UNIVERSITY OF ALBERTA. Downloae on May 8, at :3: UTC from IEEE Xplore. Restrctons apply.