Joint Adaptive Modulation and Power Allocation in Cognitive Radio Networks

Transcription

1 I. J. Communcatons, etwork and System Scences, 8, 3, 7-83 Publshed Onlne August 8 n ScRes ( Jont Adaptve Modulaton and Power Allocaton n Cogntve Rado etworks Dong LI, Xanhua DAI, Han ZHAG School of Informaton and Scence Technology, Sun Yat-Sen Unversty, Guangzhou, Chna E-mal: ld3@mal.sysu.edu.cn Receved on May 4, 8; revsed and accepted on August 5, 8 Abstract Lnk adaptaton s an mportant ssue n the desgn of cogntve rado networks, whch ams at makng effcent use of system resources. In ths paper, we propose and nvestgate a jont adaptve modulaton and power allocaton algorthm n cogntve rado networks. Specfcally, the modulaton scheme and transmt power are adjusted adaptvely accordng to channel condtons, nterference lmt and target sgnal-tonterference-plus-nose rato (SIR). As such the total power consumpton of cogntve users (CUs) s mnmzed whle keepng both the target SIR of CUs and nterference to prmary user (PU) at an acceptable level. Smulaton results are provded to show that the proposed algorthm acheves a sgnfcant gan n power savng. Keywords: Adaptve Modulaton, Power Allocaton, Cogntve Rado. Introducton Wth the ncreasng number of varous bandwdthconsumng wreless servces, spectrum for avalable bands becomes more and more scarce. Moreover, these bands are not occuped or underutlzed by lcensed users most of tme, whch leads to the waste of bandwdth resources and low spectral effcency. One soluton to ths problem s that cogntve (unlcensed) users (CUs) are allowed to have opportunstc access to these dle bands or to the actve ones wthout causng harmful nterference to the prmary (lcensed) user (PU), n order to mprove the bandwdth utlzaton. Ths technology s called cogntve rado [,]. The major advantage of cogntve rado technology s ts ablty to search for avalable spectrums n ts surroundng envronment and adjust ts transmt parameters accordngly to enhance the system performance. The transmt parameters, for example, nclude modulaton scheme, beamformng vector, center frequency, transmt power and so on. The whole process can be summarzed as sense-cognton-adaptaton. In wreless network, a fundamental characterstc s the nterference ntroduced by mult-user or co-channel transmsson at the same tme or over the same frequency rado channel. It s well-known that power allocaton [3,4] s an effectve way to mtgate nterference by means of updatng transmt powers accordng to the target SIR. Besdes, the effectve use of transmt power can not only mnmze the nterference ntroduced by other transmt nodes to enhance the capacty, but also conserve energy to prolong battery lfe. In [3], the author proposed a smple dstrbuted power allocaton algorthm, n whch the power level at next teraton only depends on target and actual SIR as well as current power level. The goal s to mnmze the total power consumpton subject to the target SIR requrement. Further studes are shown n [5 8]. In [5], the jont optmzaton of beamformng and power control s studed n the downlnk of a cogntve rado network. The objectve of the proposed algorthm s to mnmze the total transmt power whle satsfyng the target SIR constrant of CUs and maxmum tolerable nterference to PU. However, ths work can not be extended to the energy-constraned wreless networks, n whch there s a constrant of maxmum transmt power for each CU. Lterature [6] proposes a cross-layer framework for jont schedulng and power control combned wth adaptve modulaton n ad hoc networks, whch can be vewed as the stuaton where only CUs share the same frequency band wth the absence of PU. Therefore, the proposed algorthm can not be applcable to the case of the co-exstence of PU and CUs n the same Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83

2 JOIT ADAPTIVE MODULATIO AD POWER ALLOCATIO I COGITIVE RADIO ETWORKS 9 frequency band, snce t does not consder the nterference ntroduced to PU caused by CUs. Whle lterature [7] and [8] only consder the problem of adaptve modulaton and power control of a sngle CU n the presence of PU. In contrast to prevous work n [5 8], we consder the scenaro where one PU and multple CUs share the same frequency band n wreless networks. So far as we know, lttle attenton has been pad to the topc of jont adaptve modulaton and power allocaton n cogntve rado networks, n whch the protecton of PU and the qualty of servce (QoS) of CUs are assured. In ths contrbuton, our goal s, therefore, to jontly optmze the modulaton schemes as well as transmt powers n order to mnmze the total power consumpton whle keepng both the nterference to PU and target SIR of CUs at an acceptable level. More specfcally, we perform a twostage power allocaton processng for the proposed algorthm: Frst, transmt powers are allocated to all CUs wth the same modulaton scheme, under the constrant of target SIR of CUs and a gven nterference lmt to PU; Second, each CU wth adaptve modulaton scheme adjusts ts transmt power based on the frst allocated power, n order to reduce the total power consumpton. The rest of ths paper s organzed as follows: Secton descrbes the system model and basc assumptons. In Sectons 3, we develop the proposed algorthm for jont adaptve modulaton and power allocaton n cogntve rado networks. Performance analyss of the proposed algorthm s nvestgated n Secton 4. Secton 5 concludes ths paper. otaton: All vectors and matrces are denoted n bold letters. I stands for dentty matrx. A (, j) denotes the (, j) th element of the matrx A. The operators ( ), ( ) and ( ) T represent pseudo nverse, nverse and transpose, respectvely. Fgure. System model wth one PU n dashed lne and CUs n sold lne.. System Model The cogntve rado network under consderaton s composed of one PU and CUs, whch are modeled as a collecton of separate (+) transmt-receve pars wth a sngle channel, as llustrated n Fgure. All CUs are allowed to transmt at the same tme and share the same frequency band by adoptng code dvson multplexng access (CDMA). The transmsson mode for each CU s half-duplex n order to avod self-nterference [9] caused by one node smultaneously transmttng and recevng. The channel propagaton model s characterzed by path loss, whch s gven by [] d PL( d) PL( d ) log ( ) db = + α d d d where d and d are the reference and transmtterrecever (T-R) dstance, respectvely. α denotes path loss exponent, whch depends on propagaton crcumstance. Then, the actual SIR for th CU can be expressed as G P SIR = Gj Pj + G P + η K j=, j where P and P denote power level of th CU and prmary user, respectvely. G s the channel gan over CU, G j and G represent the channel gan between CU j transmtter, prmary user s transmtter and CU recever, respectvely. η s the background nose power and K denotes the spreadng gan. s the target SIR for all CUs and the constrant SIR () guarantee the QoS for th CU. On the other hand, the total nterference ntroduced to PU s gven by ξ = G P ξ (3) = where G j represents the channel gan between CU j transmtter and PU s recever and ξ denotes the maxmum tolerable nterference for PU. Throughout ths paper, we make the followng assumptons: ) The system conssts of an access pont (AP) [] for dalogues wth CUs through a dedcated control channel, and the global nformaton of channel gans s assumed to be avalable at AP. ) The local nformaton of channel gans and SIR measurements at the recevers of all CUs are sent to ther respectve transmtters va a dedcated feedback channel. 3) All CUs are well synchronzed, and are assumed to be mmoble or move slowly so that the correspondng channel gan remans constant durng the convergence of transmt power. Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83

3 3 D. LI ET AL. 3. Jont Adaptve Modulaton And Power Allocaton The objectve of ths algorthm s to assgn constraned transmt powers and avalable modulaton schemes to all CUs, n order to mnmze the total power consumpton whle satsfyng the target SIR constrant of CUs. Besdes, we should also consder mantanng the nterference ntroduced to the prmary user wthn a gven nterference lmt, snce CUs coexst wth the PU n the same frequency band. Therefore, we can formulate the followng constraned optmzaton problem: subject to where SIR mnmze P (4) = (5) ξ P [, Pmax ] and max ξ (6) P s the maxmum transmt power. In what follows, transmt powers whch satsfy both the constrant (5) and (6) are calculated by AP and sent to all CUs, n whch the modulaton scheme s the same and chosen to guarantee the exstence of postve powers. Then, the modulaton scheme (or equvalently, target SIR) s modfed based on the ntal SIR for each CU, n order to mantan a certan BER requrement. It wll be shown that, based on the modfed target SIR for each CU, the total power consumpton s greatly reduced by teratvely updatng transmt power of each CU, whle both the QoS and nterference constrant can also be satsfed. 3.. Frst Power Allocaton The constrant (5) can be expressed n the followng way P G ( G P + η) j Pj (7) j=, j KG G ote that the target s the same for all CUs n ths stage. Let P = ( p, p, L, p ) T, rewrte (7) wth equalty n the matrx form, we can obtan ( I F ) P = U (8) where F and U are gven by n the followng Gj F (, j) = KG,, j, j =,, L, = j ( G P + η) ( G P + η) ( G P + η) U = L G G G (,,, ) T Meanwhle, we can also rewrte constrant (6) wth equalty n the matrx form as β F P = U (9) where F = ( G, G, L, G ) s a vector and U = ξ. ote that, n equaton (9), β s a constant, and the nterference constrant of PU can be easly satsfed by ncreasng the value of β, because the powers allocated to all CUs are kept at a low level. However, t does not mean that large β wll satsfy the target SIR requrement for all CUs. Combne (8) and (9), the constrants (5) and (6) can be fnally expressed n the matrx form as follows I - F U β P = F { U 443 F U where F s a ( + ) matrx and U s a ( + ) column vector. ote that the equaton has a feasble soluton,.e., there exsts a postve power vector P, f the followng condton holds < λ ( ) max F () where λ ( ) max F stands for the maxmum egenvalue of matrx F. Otherwse, no CUs can be admtted to share ths frequency band wth PU. As for the value of, we wll gve detals n the next secton. Once F and U are determned, the powers frst allocated to CUs are gven by P = mn( Pmax, F U ) () P = ( p, p, L, p ) T s a column where max max max max T T vector and F = ( F F) F. Remarks: ) Equaton s overdetermned, and () s ts least square (LS) soluton to the optmzaton problem of (4) wth constrants (5) and (6). ) The frst allocated transmt powers P and fxed modulaton scheme (or ) are obtaned at AP, and ths nformaton s sent from AP to the transmtter of correspondng CU through the dedcated control channel. Table. Constellaton sze and correspondng mnmum 3 requred SIR for target BER = [6]. Constellaton sze (M) SIR Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83

4 JOIT ADAPTIVE MODULATIO AD POWER ALLOCATIO I COGITIVE RADIO ETWORKS 3 It should be noted that the protecton of PU and QoS of CUs are both met wthout the maxmum power constrant. However, due to the fact of power-constraned CUs, the target SIR constrant of all CUs may not be satsfed. In the followng, we wll address ths ssue n detal. 3.. Adaptve Modulaton Adaptve modulaton enables the system to support hgh data rate by varyng the number of bts per symbol n accordance wth the nstantaneous SIR, whle keepng a target BER requrement. The transmsson rate of th CU for M-ary quadrature ampltude modulaton (M-QAM) s gven by [6] where R = log ( + k SIR ) (3).5 k = ln(5 BER ) and BER s the target BER requrement. ote that transmsson rate obtaned n equaton (3) s contguous and should be quantzed to a fnte number of nteger values n practcal stuaton. The mnmum requred SIR correspondng to the target BER for M-QAM can be obtaned by [6] I + J BER log M M erfc ( ), rectangular QAM 3 M ( I + J) SIR = ( M ) BER M log M erfc ( ), square QAM 3 M (4) where I = M and M J =. As a result, the mnmum 3 requred SIRs correspondng to BER = for M =, 4, 6, 8, 6, 3 and 64 can be calculated and the results are shown n Table. Accordng to Table, s determned n such a way that the maxmum SIR s chosen from avalable ones whch satsfy the condton (), n order to acheve hgh data rate. However, the actual SIR based on the ntal allocated power for each CU can not satsfy the mnmum requred SIR for certan BER at the same tme. Therefore, the modulaton scheme,.e. target SIR, should be modfed for each CU. To be specfc, assumng that the set Ω s composed of SIRs n Table whch are no more than, then the modfed target SIR for each CU denoted as, s chosen n such a way that the correspondng requred SIR n Ω s no more than ts actual SIR. In the worst case, f the actual SIR falls below 4.77, the correspondng CU wll abort transmsson. For nstance, f = 9.55 and the CUs actual SIRs based on the frst allocated powers are, 5 and 3, respectvely, then Ω = [4.77, 9.55], and therefore = 9.55, = 4.77 and 3 = (no transmsson), respectvely. ote that, n ths case, the constrant (5) s changed nto SIR. Therefore, the modfed target SIR constrant of all CUs can be satsfed Second Power Allocaton Snce both the QoS and nterference constrant are satsfed as dscussed before, we consder reducng the total power consumpton for all CUs. Let = dag(,, L, ) be a dagonal matrx of sze, then the equaton (8) can be rewrtten n the followng form as P k = F P k U (5) ( + ) ( ) + where P ( k + ) and P ( k) denote power level at next and current teraton, respectvely. Then, the optmal transmt power can be obtaned by teraton of [3] P ( k + ) = mn( Pmax, P ( k)) (6) SIR ( k) ote that the above algorthm termnate wth convergent power f P ( k + ) P ( k) ζ, where ζ > s a neglgbly small error. Based on P and, t can be known that the total power consumpton wll be reduced after second power allocaton usng equaton (6), n whch the ntalzed power s P. The followng theorem supports our concluson. Theorem: Gven P and correspondng SIR whch satsfy SIR, =,, L,, then there exsts a steady-state that () P P = = () P to acheve such whle satsfyng both the QoS and nterference constrant. Proof: It can be known from equaton (6) that, f SIR for each CU satsfes the condton SIR ( k), then we have Table. Smulaton parameters. umber of CUs () 9 ose varance (η ) eglgble error ( ζ ) Reference dstance ( d ) Path-loss factor ( α ) m Processng gan (K) 8 Maxmum power ( P max ) W Constant ( β ) Maxmum tolerable nterference ( ξ ) W Maxmum number of teraton Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83

5 3 D. LI ET AL. P ( k + ) = mn( P, P ( k)) = P ( k) < P ( k) max SIR ( k) SIR ( k) () The teraton wll termnate f SIR = SIR ( k) =, so the QoS constrant of CUs s satsfed. That s to say that there s no neglgble change n P ( k ) such that P ( ) P ( ) power k + k ζ. Therefore, the convergent P = P ( k) P = P. As a result, we have () () P P = =, and the nterference constrant of PU s. = = ( ) ( ) also satsfed wth ξ = G P ξ = G P ξ 4. Smulaton Results In ths secton, we provde numercal results to demonstrate the effectveness of the proposed algorthm 5 n reducton of the total power consumpton whle satsfyng both the QoS constrant of CUs and nterference constrant of PU. Besdes, we analyze the effect of dfferent P on the proposed algorthm. In our smulaton, we consder the cogntve rado network placed n a m m square area, n whch transmt nodes are located unformly and the correspondng receve nodes are random placed wthn 6m 6m square area centered around them. The specfc parameters used n ths smulaton are lsted n Table, n 4 whch the channel gan can be expressed as G = d, where d j s the dstance between jth CU s transmtter and th CU s recever. 4.. Performance Analyss Frst, we examne the performance of proposed algorthm wth respect to power savng. Fgure (a) shows the convergence property of transmt power for each CU n the second power allocaton stage wth P = 5W, n j j 5 5 Power(dB) 5 3 Power(dB) SIR(dB) Iteraton (a) Iteraton (b) Fgure. Convergence of transmt power and actual SIR for each CU n the second power allocaton stage, where P = 5W. (a) Transmt Power (db). (b) Actual SIR (db) Iteraton SIR(dB) (a) Iteraton (b) Fgure 3. Convergence of transmt power and actual SIR for each CU n the second power allocaton stage, where P = W. (a) Transmt power (db). (b) Actual SIR (db). Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83

6 JOIT ADAPTIVE MODULATIO AD POWER ALLOCATIO I COGITIVE RADIO ETWORKS 33 whch the ntal powers are P = (,,.6,.773,,.96,,,.65) n W accordng to equaton, () and the convergent powers are P = (.879,.538,.,.86,,.66,.789,,.5) n W. From Fgure (a), we can fnd that the total power consumpton s greatly reduced after second power allocaton wth adaptve target SIR. Then, we nvestgate the SIR performance of the proposed algorthm. Based on P, the actual SIRs for all CUs are SIR = (5.653, 8.599, , ,.6, , ,.398, 4.498). s set to be 9.55 so that the constrant () s satsfed, and Ω = (4.77, 9.55). Therefore, the adjusted target SIRs for all CUs n the second power allocaton stage are set to be = (4.77, 4.77, 9.55, 9.55,, 9.55, 4.77,, 9.55). We notce that the target SIRs of two CUs are equal to, whch means that the correspondng CU wll not transmt. Fgure (b) shows the convergence property of the actual SIR for each CU, n whch the actual SIRs for the admtted CUs converge to 4.77 and 9.55, respectvely. In other words, the constellaton sze M s chosen to be and 4, accordngly. Fnally, we examne the performance of the proposed algorthm n terms of the nterference constrant of PU. Accordng to equaton (3), the actual nterferences ntroduced to PU n the frst and second power allocaton stage are 8.8 mw and 4.8 mw, respectvely, whch are far less than the nterference lmt ξ = W. Ths s manly due to the maxmum transmt power lmt for each CU. 4.. Impact of Dfferent P In our prevous study, a constant P s chosen for all smulatons. To be more practcal, we study the mpact of dfferent P on the system performance. umber of Admtted CUs P (W) Fgure 4. umber of admtted CUs versus P. As expected, wth the ncreasng value of P, the nterference ntroduced to all CUs wll ncrease accordngly. Ths means the frst allocated power P wll be ncreased for each CU n order to satsfy the target SIR constrant. For nstance n Fgure 3(a), P = (,,.8,.3,,,,,.8) n W. Besdes, the () convergent powers are P = (,.383,.3,.53,,.99,,,.48) n W. Meanwhle, the ncreased nterference caused by PU wll certanly affect the SIR performance for each CU. In ths case, the SIR constrant of some CUs wll be volated. Therefore, the ntal SIRs of these CUs decrease and correspondng target SIRs should be adjusted accordngly, whch can be seen from Fgure 3(b). In Fgure 3(b), we can fnd that two CUs target SIRs are reduced from 4.77 to compared wth Fgure (b). That s to say these CUs abort transmsson. Specfcally n Fgure 3(b), the actual SIRs for all CUs are SIR = (.976, 6.743, 5.586, 9.,.538, 9.73, 3.364,.4, 6.346), = 9.55 and Ω = (4.77, 9.55). Therefore, the adjusted target SIRs for all CUs n the second power allocaton stage are = (, 4.77, 9.55, 9.55,, 9.55,,, 9.55). Furthermore, A close observaton of Fgure and Fgure 3 shows that the convergence of transmt power and actual SIR for each CU requres only several teratons wth dfferent P, whch s qute acceptable. As mentoned before, some CUs are turned off n the second power allocaton stage, n whch ther QoS can not be guaranteed due to the nterference from PU. It would be also nterestng to study the relatonshp between the number of admtted CUs and P. As can be seen from Fgure 4, the number of accepted CUs decreases wth the ncreasng value of P n general. Ths s because more CUs QoS requrements can not be satsfed and swtched off accordngly. In ths case, the total power consumpton after second power allocaton decreases roughly wth the decreasng number of admtted CUs. However, we also notce that the number of admtted CUs remans the same for P = 5 and W, whch means more power consumpton s needed when P = W than the case of P = 5W. It can be known that, when P s large enough, there s no CUs that can be admtted by the system. 5. Conclusons In ths paper, we have proposed and nvestgated a jont adaptve modulaton and power control algorthm n cogntve rado networks. Our goal s to mnmze the total power consumpton whle keepng the nterference ntroduced to PU below a gven lmt and satsfyng the SIR constrant of CUs. Specfcally, the proposed algorthm s mplemented n a two-stage power allocaton Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83

7 34 D. LI ET AL. processng wth fxed and adaptve modulaton, respectvely, whch has been proved to greatly mprove the power effcency. Smulaton results are shown to confrm the effectveness of the proposed algorthm. 6. Acknowledgement Ths work s supported by the atonal Scence Foundaton of Chna (SFC), Grant 6773, and the jont foundaton of atonal Scence Foundaton of Chna (SFC) and Guangdong Provnce U6353, and also supported by the Scence & Technology Project of Guangdong Provnce, Grant 7B References [] S. Haykn, Cogntve rado: bran-empowered wreless communcatons, IEEE Journal on Selected Areas n Communcatons, Vol. 3, o., pp., February 5. [] J. Mtola, Cogntve rado: an ntegrated agent archtecture for software defned rado, Tekn. Dr. dssertaton, Royal Insttute of Technology (KTH), Stockholm, Sweden,. [3] G. J. Foschn and Z. Mljanc, A smple dstrbuted autonomous power control algorthm and ts convergence, IEEE Transactons on Vehcular Technology, Vol. 4, o. 4, pp , ovember 993. [4] J. Huang, R. A. Berry, and M. L. Hong, Dstrbuted nterference compensaton for wreless networks, IEEE Journal on Selected Areas n Communcatons, Vol. 4, o. 5, pp , May 6. [5] M. H. Islam, Y. C. Langand, and A. T. Hoang, Jont beamformng and power control n the downlnk of cogntve rado networks, n Proceedngs IEEE Wreless Communcatons and etwork Conference, pp. 6, March 7. [6] W. L. Huang and K. B. Letaef, Cross-layer schedulng and power control combned wth adaptve modulaton for wreless ad hoc networks, IEEE Transactons on Communcatons, Vol. 55, o. 4, pp , Aprl 7. [7] M. Hong, J. Km, H. Km, and Y. Shn, An adaptve transmsson scheme for cogntve rado systems based on nterference temperature model, n Proceedngs IEEE Consumer Communcatons and etworkng Conference, pp , January 8. [8] L. Guo, P. Wu, and S. Cu, Power and rate control wth dynamc programmng for cogntve rados, n Proceedngs IEEE Global Telecommuncatons Conference, pp , ovember 7. [9] T. ElBatt and A. Ephremdes, Jont schedulng and power control for wreless ad hoc networks, IEEE Transactons on Wreless. Communcatons, Vol. 3, o., pp , Januray 4. [] T. S. Rappaport, Wreless communcatons prncples and practce, Prentce Hall Inc [] IEEE 8. Workng Group on Wreless Regonal Area etworks, Copyrght 8 ScRes. I. J. Communcatons, etwork and System Scences, 8, 3, 7-83