The Spectrum Sharing in Cognitive Radio Networks Based on Competitive Price Game

Transcription

1 8 Y. B. LI, R. YAG, Y. LI, F. YE, THE SPECTRUM SHARIG I COGITIVE RADIO ETWORKS BASED O COMPETITIVE The Spectrum Sharng n Cogntve Rado etworks Based on Compettve Prce Game Y-bng LI, Ru YAG., Yun LI, Fang YE Dept. of Informaton and Communcaton Engneerng, Harbn Engneerng Unversty, Harbn,, Chna lybng@hrbeu.edu.cn, yangru@hrbeu.edu.cn, lnyun@hrbeu.edu.cn, yefang@hrbeu.edu.cn Abstract. The compettve prce game model s used to analyze the spectrum sharng n the cogntve rado networks. Ths paper focuses on the mproved spectrum sharng problem wth constrants of avalable spectrum resource from prmary users. The constraned spectrum sharng model based on compettve prce game s establshed. In order to acheve the spectrum sharng strategy that satsfes the constrants from prmary users, the Rockafeller multpler method s appled to deal wth the constrants of avalable lcensed spectrum resource, and the mproved proft functon s acheved, whch can be used to measure the mpact of shared spectrum prce strateges on the system proft. However, n the compettve prce game based spectrum sharng problem of practcal cogntve rado network, prmary users have to determne the shared spectrum prce wthout the acknowledgement of the other prmary user s prce strateges smultaneously. Thus a fast gradent teratve calculaton method of equlbrum prce s proposed, only wth acknowledgement of the shared spectrum prce strateges durng last cycle. Through the adaptve teraton at the drecton wth largest gradent of mproved proft functon, the equlbrum prce strateges can be acheved rapdly. It can also avod the predefnton of the adjustment factor accordng to the parameters of communcaton system n conventonal lnear teraton method. Smulaton results show that the proposed compettve prce game based spectrum sharng model can be appled n the cogntve rado networks wth constrants of avalable lcensed spectrum resource, and t has better convergence performance. Keywords Cogntve rado, spectrum sharng, game theory, compettve prce model.. Introducton Cogntve rado s vewed as an effectve approach for mprovng the utlzaton of the rado spectrum [], []. The cogntve transcevers have flexble spectrum sensng ablty, and can adjust transmsson parameters adaptvely accordng to the ambent envronment. The spare spectrum of lcensed users (prmary user) can be accessed by the cogntve users (secondary user) dynamcally wthout causng harmful nterference. As the behavors of the prmary users and secondary users nteract wth each other, game theory, whch s vewed as an effectve tool for the analyss of nteractve decson makng, s appled n the spectrum sharng problem of cogntve rado networks [], []. Dust yato ntroduced the compettve prce model to the spectrum sharng problem n cogntve rado networks, and dscussed the ash equlbrum prce strateges that mze the profts of prmary users. As the prce strateges of other prmary users are usually not avalable smultaneously, the teratve equlbrum prce calculaton was further analyzed [], [6]. The spectrum sharng problem wth prce strateges offered smultaneously and sequentally s also dscussed n [7]. Xuezh Tan dscussed the selecton of adjustment factor n the calculaton of the equlbrum prce [8]. The calculaton of the equlbrum shared spectrum prce s analyzed n [9]. But only the spectrum sharng problem wth the assumpton that the spectrum demand of the cogntve users could be satsfed was dscussed n the research above. In order to guarantee the communcaton qualty of the prmary users n the practcal applcaton, the spectrum sharng problem wth the constrants of mum avalable spectrum resource s more unversal. In ths paper, we develop an mproved spectrum sharng model based on compettve prce game wth the consderaton of lmted spectrum resources from prmary users, and dscuss the teratve calculaton of the equlbrum shared spectrum prce. We proposed a fast gradent teratve method based equlbrum prce calculaton scheme, whch can avod the predefnton of the adjustment factor, and acheve the equlbrum prce teratvely wth better convergence performance. The rest of ths paper s organzed as follows. In secton, we descrbe the system model of spectrum sharng n cogntve rado networks. In secton, the spectrum sharng problem based on compettve prce game s analyzed, wth the consderaton of constrants of avalable spectrum resource from the prmary users. In secton, the calculaton of the equlbrum prce wthout acknowledgement of the prce strateges from other prmary users s further analyzed. Secton presents the smulaton results, and secton 6 concludes the paper.

2 RADIOEGIEERIG, VOL., O., SEPTEMBER 8. System Model Consderng a wreless system wth multple prmary users, the communcaton of secondary users s served by a secondary servce for smplcty. The spectrum sharng problem between the multple prmary users and secondary users can be equvalent wth the spectrum sharng problem between multple prmary users and sngle secondary user servce. Assumng prmary users wthn the cogntve rado network, prmary user tends to share porton of ts spare spectrum wth secondary user at prce p. The communcaton requrements of secondary user should be satsfed wth assurance of prmary users communcaton qualtes, and certan economc revenue s obtaned by the prmary users through spectrum sharng. The demanded spectrum sze of secondary user here s determned by ts transmsson effcency and the shared spectrum prce that provded by prmary users. The transmsson effcency of secondary user s related to the modulaton and channel qualtes, whch can be expressed as follows []: k log ( K ) () where γ s the sgnal to nose rato of the secondary recever, K =./[ln(./ber tar )], BER tar s the requred bt error performance of the secondary user. The prmary users tend to mze ther profts compettvely by controllng prce strateges of the shared spectrum, whch s defned as Bertrand prce model n economcs, and t s used to analyze the spectrum sharng problem n cogntve rado networks. The prmary users provde the prce strateges of shared spectrum, and the demanded spectrum sze of the secondary user s determned from ts utlty functon, whch s relevant to the prce strateges provded by prmary users. The spectrum sharng profts of prmary user depend on the economc revenue and the cost due to spectrum sharng. Here, the cost of spectrum sharng s defned as the degradaton of the qualty of servce (QoS). The prmary users constantly adjust the prce strateges of shared spectrum to acheve the ma of ther own profts.. Constraned Spectrum Sharng Model Based on Compettve Prce Game The demanded spectrum sze of secondary user can be calculated through the quadratc utlty functon that s descrbed as follows []: U( b ) bk b v bb j pb () j where b s the set of the shared spectrum sze from dfferent prmary users, b={b, b,,b }; p s the prce strategy of shared spectrum from prmary user, p={p, p,,p }; k (s) s the spectrum effcency of secondary user that can be acheved by occupyng the spectrum resource from prmary user ; v s the spectrum substtutablty factor, and v [,]. When v =, the spectrum resource of dfferent prmary users can t be substtuted, whle v =, the spectrum resource of dfferent prmary users can be substtuted freely. The demanded spectrum sze by secondary users can be get by U ( b). () b j j Thus we can get k b v b p. () The sze of shared spectrum can be rewrtten as the lnear equatons accordng to () b vb vb vb k p vb b vb vb k p vbvb vb b k p The demanded spectrum sze of the secondary user can be expressed as D=[b b b ] T, F=[k (s) -p k (s) - p k (s) -p ] T, and A s the coeffcents matrx. The sze of demanded spectrum can be obtaned by where () D A F (6) v v v v v v A v v v v v v The elements n the nverse of A matrx can be acheved by elementary transform. ( ) v j ( v)( ( ) v) a j (7) v j ( v)( ( ) v) Wth the acknowledgement of shared spectrum prce strateges p, the sze of demanded spectrum can be expressed as follows: ( k p)( v( ) ) v ( kj pj) j D ( p ). (8) ( v)( v( ) ) The cost of spectrum sharng n ths paper s defned by the QoS degradaton of prmary users. The revenue functon R and cost functon C for the prmary user that provdes certan sze of shared spectrum are defned as follows respectvely[]. R cm, (9)

3 8 Y. B. LI, R. YAG, Y. LI, F. YE, THE SPECTRUM SHARIG I COGITIVE RADIO ETWORKS BASED O COMPETITIVE W b C b c M B k () req ( p) ( ) ( ) M where c, c are constants that denote the weghts between revenue functon and cost functon, B req s the bandwdth requrement of prmary user, W s the total sze of avalable spectrum, M s the number of prmary connectons, and k s the transmsson effcency of prmary users. Thus, the proft functon of prmary user can be expressed as P( p ) bp RC( b). () In Bertrand prce model, the players of the game are the prmary users, the strateges of the players are prces of shared spectrum,.e. {p }, and the utlty functon s the acheved proft,.e. {P }. If the spectrum demand of cogntve user can be satsfed by the prmary users,.e. the avalable spectrum resource of the prmary users are larger than the spectrum demand D of the secondary user, the proft functon of prmary users s gven by [] req ( p) W D( p) P( p) pd ( p ) cm cmb k. () M However, n practcal spectrum sharng model for cogntve rado networks, the spectrum resources of the prmary users are usually restrcted. The spectrum demand of the secondary users wll not be defntely satsfed by the prmary users. Thus, t needs to consder the constrants of the shared spectrum sze. B s the mum shared spectrum sze of prmary user, and the compettve prce game based spectrum sharng model wth constrants of shared spectrum for cogntve rado networks can be formulated as (),.e. determne the prce strategy p * satsfes p * arg p st.. D ( p),,,, D B ( p),,,, P p () where p * s also defned as the ash equlbrum prce of the compettve prce game. In order to acheve the p * that satsfes (), the relaxaton varables y, y are appled. There must exst specfc varable y j equvalent wth D. Thus the mproved proft functon can be obtaned ( p) P ( p) D( p) y D( p) y B D( p) y B D( p) y () where σ, ω, ω are constant varables, wth further smplfcaton of (), we can obtan ( p) ( p) ( p) P D y B D( p) y () The value of y, y s determned wth the objectve of mzng the mproved proft functon, whch can be gven by y, D( ), y, B D( ) p p. (6) Substtute (6) nto (), we can get ( p) P( p), D( p) (7), B D( p) The above functon can be seen as a stage functon, and at the stage ponts, the left lmt equals the rght lmt, thus functon (7) s dervatve. In order to acheve the equlbrum prce strategy p *, we can have ( p ),, (8) p where ( p) P( p) D( p) p p p, D ( p) D( p), D( p) B p. Iteratve Calculaton of the Shared Spectrum Prce In practcal cogntve rado networks, the prce strateges of other prmary users cannot be acheved smultaneously, the ash equlbrum prce strategy of the compettve prce model cannot be acheved through the lnear equatons formed by (8). Thus, t s needed to further dscuss the teratve prce calculaton method wthout acknowledgement of prce strateges from other prmary users smultaneously []. Assume the prce strateges of other prmary users cannot be acheved smultaneously, but the shared spectrum prce strateges of prmary users durng last cycle s avalable. The ash equlbrum prce that mzes the system profts of the prmary users can be acheved teratvely.. The Lnear Iteratve Method The lnear gradent descent algorthm s one of the effectve tools to calculate the mum and mnmum value of contnuous target functon durng the optmzaton problems. For the prmary users, the proft functon s convex wth the varaton of shared spectrum prce. At the k th teraton, p k s the shared spectrum prce of prmary user, P k s the proft of prmary user, and φ k s the

4 RADIOEGIEERIG, VOL., O., SEPTEMBER 8 mproved system proft functon. If the avalable spectrum resource of the prmary users s larger than the spectrum demand of the secondary user and φ/ p k s postve, the value of the mproved system proft functon of prmary users wll ncrease teratvely wth the ncrease of p k untl the mum of the mproved system proft functon s obtaned or the spectrum constrants of the prmary users cannot be satsfed. When the avalable spectrum resource constrants can be satsfed and φ/ p k s negatve, wth the lnear teraton as (9), the value of the mproved system proft functon wll decrease untl the equlbrum shared spectrum prce s acheved. It s due to the cogntve user tends to demand less spectrum resource when the prce of the shared spectrum s too hgh. Besdes, when the spectrum demand of the secondary user can not be satsfed by the avalable spectrum resource of prmary users,.e. the cogntve user tends to apply for more spectrum resource than spectrum constrants, the value of the mproved proft functon wll also decreases. Thus the equlbrum prce of the shared spectrum that mzes the mproved system proft functon and satsfes the constrants of avalable spectrum resource can be acheved teratvely. k k ( ) p p a p (9) k p where a s the nonnegatve adjustment factor. Wth approprate value of adjustment factor, the shared spectrum prce that mzes the mproved system proft functon can be acheved teratvely. The value of adjustment factor s very mportant for the calculaton of the equlbrum shared spectrum prce. If the adjustment factor s too large, strong fluctuatons wll exst n the calculaton of shared spectrum prce, or even the equlbrum shared spectrum prce can t be acheved. On the contrary, f the value of the adjustment factor s too small, the varaton of calculated prce changes slowly, and more teratons are also needed to acheve the equlbrum shared spectrum prce. Thus the approprate adjustment value s necessary for teratve method to acheve the equlbrum prce of the compettve prce game based spectrum sharng model.. The Fast Gradent Iteratve Method Based on the above research, a fast gradent teratve method s proposed to obtan the equlbrum prce of shared spectrum. It does not need the predefnton of the adjustment factor accordng to the transmsson parameters of the cogntve rado networks, and t can acheve the equlbrum prce of the shared spectrum wth less teratons. The steepest gradent descend algorthm, whch s frstly proposed by the French mathematcan Cauchy, s one of the mportant optmzaton methods. The teratons n the steepest descent drecton of the target functon are appled to acheve the mnmum value of the target functon. Ths paper apples prncple of the steepest gradent descend algorthm, and uses the drecton wth the fast varaton of the mproved system proft functon to calculate the equlbrum prce of shared spectrum teratvely. The adjustment factor of the fast gradent method s adjusted to guarantee the shared spectrum prce teratons n the gradent drecton of the mproved system proft functon. The target functon here s defned as f ( p) arg ( p ). () The drectonal gradent of the target functon d k at the prce strategy p k can be defned as k ( p) d p P( p) D( p) (), D ( p) p p D( p), D( p) B p Wth one-dmensonal nvestgaton along the drecton d k, and the value of the adjustment factor λ s updated to guarantee the drecton wth fast varaton. k k k ( p d ). () Thus P( pd) D( pd), D ( pd) D( pd), D( pd) B () where P( pd) D( pd) dd ( pd) p d ( p) req ( p) W D( pd) D( pd) ck B k M D ( ) (( ) ) pd v d j j v d ( v)(( ) v) The prce strategy of shared spectrum s calculated accordng to (), untl the varaton of the prce strategy can satsfy the precson requrement. p p d. () k k k k. Smulaton Results We consder the cogntve rado networks wth two prmary users and one secondary servce, the total spectrum bandwdth of each prmary user s MHz, and the prmary connectons are set as M = and M = respectvely. The requred communcaton bandwdth of prmary users B req s MHz. The weghts of the revenue and cost functon c = c =. The target BER performance s -,

5 86 Y. B. LI, R. YAG, Y. LI, F. YE, THE SPECTRUM SHARIG I COGITIVE RADIO ETWORKS BASED O COMPETITIVE and the SR s db, the spectrum substtutablty factor v =.. The ntal value of the shared spectrum prce s set to be n the teratve method to calculate the ash equlbrum prce. Fg. shows the system proft of prmary users wth varable shared spectrum prce when suffcent spectrum resource can be provded by prmary users. It can be concluded from Fg. that the system proft s convex wth the varaton of shared spectrum prce, the mum system proft can be acheved at certan prce strategy. System proft p Fg.. The total revenue of prmary users wth varaton of shared spectrum prce. Fg. shows the smulaton results of shared spectrum sze under dfferent spectrum constrants of prmary users, among whch the avalable spectrum constrant of prmary users B s fxed as MHz and the avalable spectrum constrants of prmary users B s set to be vared from restrcted to suffcent respectvely. It can be concluded from Fg. that, when the avalable spectrum resource from prmary user restrcted, the secondary user tends to demand the remanng shared spectrum from prmary user. Wth the ncrease of B, the shared spectrum sze from prmary user s ncreased, and the shared spectrum sze from prmary user s decreased accordngly. When the avalable spectrum of prmary user s larger than the demanded spectrum sze of secondary user, the shared spectrum sze from prmary user wll not ncrease wth the ncrease of B, and the secondary user tends to demand the reasonable spectrum sze that mzes ts own utlty functon. D p D B D B.. B Fg.. The calculaton of ash equlbrum prce by lnear equatons Fg. shows the calculaton of the ash equlbrum prce by the lnear teratve method under dfferent adjustment factors. It can be concluded from Fg. that the value of the adjustment factor has sgnfcant mpact on the teratve calculaton of the ash equlbrum prce. When the adjustment factor s small, the prce of shared spectrum vares slghtly, and the convergence speed n calculaton of the shared spectrum prce s slow; when the adjustment factor s large, although the prce of the shared spectrum vares sgnfcantly, t may also affect the convergence speed of the lnear gradent method due to strong fluctuatons. Prce of shared spectrum..... a=. prmary user a=. prmary user a=. prmary user a=. prmary user Iteratons (a) wth restrcted prmary resource, B = and B = Prce of shared spectrum..... a=. prmary user a=. prmary user a=. prmary user a=. prmary user Iteratons (b) wth suffcent prmary resource, B = and B = Fg.. The teratve calculaton of ash equlbrum prce under dfferent adjustment factor. Fg. shows smulaton result of lnear teratve method wth nadequate adjustment factor. It can be concluded from Fg. that nadequate adjustment factor may lead to unstable shared spectrum prce strategy, and the value of adjustment factor has sgnfcant mpact on the convergence of the lnear teratve method. Fg. shows the smulaton results of equlbrum prce by fast gradent teratve method proposed n ths paper, t s consstent wth the acheved shared spectrum prce n Fg.. The fast gradent method also does not need the prce strateges of other prmary users smultaneously. It can adjust the prce strateges n the drecton wth the fastest varatons of the system proft functon, and t can acheve the equlbrum prce strategy that satsfes the avalable spectrum resource constrants from the prmary users.

6 RADIOEGIEERIG, VOL., O., SEPTEMBER 87 Prce of shared spectrum prmary user prmary user Iteraton Fg.. The calculaton of ash equlbrum prce wth nadequate adjustment factor. Prce of shared spectrum..... B = prmary user B = prmary user B = prmary user B = prmary user Iteratons Fg.. The calculaton of ash equlbrum prce through fast gradent teratve scheme. Fg. 6 shows the smulaton results of the convergence performance of the fast gradent method and the conventonal lnear gradent method. It can be concluded from Fg. 6 that the fast gradent teratve method has better convergence speed n the calculaton of the equlbrum prce, and t can also avod the predefnton of the adjustment factor accordng to the communcaton parameters n the cogntve rado networks. Convergence Iteratons lnear gradent method fast gradent method n ths paper Adjustment factor a Fg. 6. The convergence speed of lnear teratve scheme and fast gradent teratve scheme. 6. Conclusons The compettve prce game model s appled to analyze the spectrum sharng problem n cogntve rado networks. The prmary users can obtan economc revenue by sharng porton of ther spare spectrum, and the prmary users provde prce strateges of the shared spectrum compettvely, and the secondary users determne the demanded spectrum sze accordng to the prce of shared spectrum and ts own communcaton parameters. The prmary users tend to select the shared spectrum prce that mzes ther system proft. The spectrum sharng problem wth constrants based on compettve prce game model s further analyzed n ths paper. The mproved system proft functon s formed by the Rockafeller multpler algorthm, and the shared spectrum prce strategy that mzes the system proft and satsfes the constrants of the avalable spectrum resource from the prmary users can be acheved. A fast gradent algorthm based teratve method s proposed to calculate the shared spectrum prce. It can acheve the shared spectrum prce that satsfes the avalable spectrum constrants wthout the dependence on the prce strateges from other prmary users smultaneously, and has better convergence performance. Acknowledgements Ths paper s supported by the Fundamental Research Funds for the Central Unverstes o. HEUCFZ9 and o. HEUCF8. References [] HAYKI, S. Cogntve rado: Bran-empowered wreless communcatons. IEEE Journal on Selected Areas n Communcatons,, vol., no., p. -. [] AKYILDIZ, I. F., LEE, W. Y., VURA, M. C., MOHATY, S. A survey on spectrum management n cogntve rado networks. IEEE Communcatons Magazne, 8, vol. 6, no., p [] FETTE, B. A. Cogntve Rado Technology. ewnes, USA, 6. [] JI, Z., LIU, K.J. R. Cogntve rados for dynamc spectrum access - Dynamc spectrum sharng: A game theoretcal overvew. IEEE Communcatons Magazne, 7, vol., no., p [] IYATO, D., HOSSAI, E. Compettve prcng for spectrum sharng n cogntve rado networks: Dynamc game, neffcency of ash equlbrum, and colluson. IEEE Journal on Selected Areas n Communcatons, 8, vol. 6, no., p. 9-. [6] IYATO, D., HOSSAI, E. Optmal prce competton for spectrum sharng n cogntve rado: A dynamc game-theoretc approach. In Proc. of the th IEEE Global Telecommuncatons Conference. Washngton (USA), 7, p [7] HOG, H., IU, K., HE, Z. A game theoretc analyss of prcng for spectrum sharng n cogntve rado networks. In Proceedngs of the st IEEE Internatonal Conference on Communcatons Technology and Applcatons. Bejng (Chna), 9, p [8] TA, X., LIU, Y., WEI, S. Game-based spectrum allocaton n cogntve rado networks. Journal of South Chna Unversty of Technology (atural Scence),, vol. 8, no., p. -6. (n Chnese) [9] LI, Y., YAG, R., YE, F. Prce game based spectrum sharng n cogntve rado networks. Advanced Materals Research,, vol. -6, p

7 88 Y. B. LI, R. YAG, Y. LI, F. YE, THE SPECTRUM SHARIG I COGITIVE RADIO ETWORKS BASED O COMPETITIVE [] CHUA, S., GOLDSMITH, A. Varable-rate varable-power MQAM for fadng channels. In Proc. of the 6 th IEEE Vehcular Technology Conference. Atlanta (USA), 996, p About Authors... Ybng LI was born n 967. He receved hs M.Sc. and Ph.D. from Harbn Engneerng Unversty n 997 and, respectvely. He s currently workng as a professor n the college of nformaton and communcaton at Harbn Engneerng Unversty. Hs man research nterests are cogntve rado technology, wreless communcaton technology, mage processng and nformaton fuson theory. Ru YAG was born n 98. She receved her M.Sc. from Harbn Engneerng Unversty n. She s currently workng towards her Ph.D. n college of nformaton and communcaton at Harbn Engneerng Unversty. Her research nterests nclude spectrum access n cogntve rado networks. Yun LI was born n 98. He receved hs Ph.D. degree n Communcaton and Informaton System from Harbn Engneerng Unversty. He s currently workng n Harbn Engneerng Unversty, Chna. Hs research nterests nclude mult-sensor data fuson, radar sgnal processng and radaton source dentfcaton. Fang YE was born n 98. She receved her Ph.D. degree n Communcaton and Informaton System from Harbn Engneerng Unversty n 6. She s currently workng as an assocate professor n Harbn Engneerng Unversty, Chna. Her research nterests nclude cogntve rado, ultra wdeband wreless communcaton.