ensors & Transducers 013 by IFA http://www.sensorsportal.com Dstrbuted Relay electon and Power Allocaton Usng tackelberg and Aucton Games n Mult-user Mult-relay Networks Erqng ZHANG xng YIN Lang YIN hufang LI chool of Informaton and Communcaton Engneerng Beng Unversty of Posts and Telecommuncatons Beng 100876 Chna Tel.: 86+18801110165 E-mal: sxhd004@16.com Receved: 3 eptember 013 /Accepted: 5 October 013 /Publshed: 30 November 013 Abstract: Ths paper focuses on the problem of dstrbuted relay selecton and power allocaton problem n a mult-user mult-relay network ams to maxmze users achevable rate whle consume less power of relays whch are selected for helpng users transmt nformaton. At frst we use the aucton game theory to choose the relays for each user prelmnarly then for each user and the selected relays we model the nteracton between them as a two-level tackelberg game the relays modeled as the servce provder and the users modeled as customers who wll buy power from the provders. Based on ths game model we get the relays at relatvely better locatons for each user and the optmal power need to buy from them. Otherwse as the users wll not exchange nformaton between themselves we recalculate the power allocated to each user for relays the power users buy from t exceeds the maxmzng transmt power. mulaton results show the effectveness of our proposed scheme. Copyrght 013 IFA. Keywords: Dstrbuted relay selecton Power allocaton mult-user mult-relay network tackelberg game Aucton game. 1. Introducton In recent years cooperatve communcaton [1-] has been proposed as an emergng transmt strategy to spread the whole coverage and ncrease system relablty whch has been wdely used n wreless networks. Generally n such a network all nodes can act as the relay nodes to help each other s transmsson to ther destnatons. In ths way cooperatve communcaton can effcently takes advantages the broadcastng nature of wreless communcaton networks as well as the nherent multuser and spatal dverstes. However n a practcal applcaton especally n commercal networks the nodes usually represent dfferent nterest groups e.g. servce provders and clents. Thus the practcal problems appear such as when and whether to cooperatve whch manly depends on ther own avalable rado resources and traffc loads. Extremely the selfsh user would occupy the avalable resources as much as possble to maxmze ts own beneft rather than to share them wth others. Accordng to the descrpton mentoned above how to analyze the behavors of raton users n Artcle number P_1471 17
wreless networks has become an urgent need to be addressed. Recently t has been proved that game theory can be a promsng tool n solvng the resource allocaton problem of cooperatve communcaton network due to ts natural and flexble represents of how the autonomous nodes nteract and cooperate wth each other and has been used n modelng the nteractons n dfferent network layers among users wth varous benefts [3]. There have been volumes of exstng lteratures based on game theory on the decson-makng problems on when whether and how to cooperate n wreless networks. In [4] the problem of cooperaton among energy constraned nodes n wreless ad hoc networks was addressed and Generous TIT-FOR-TAT (GTFT) scheme was proposed to solve ths problem based on the hstorcal statstcs. The author of [5] proposed a prcng algorthm that encourages forwardng among autonomous nodes through a rembursng forwardng scheme for mult-hop wreless networks. Based on the results n [5] a prcng game that stmulates cooperatve dversty among selfsh nodes n commercal wreless ad hoc networks was studed n [6]. The research results abovementoned were based on an asymmetrc structure model between the source and relay nodes. The source node has the opportunty to get the relay s help whle the relay node cannot get beneft from the source that s the roles of the two nodes are unequal makng t hard to fully reveal the ratonal behavors between all nodes partcularly n cases when both nodes only have lmted rado resources. In addton the works n [4-6] are based on non-cooperatve game whch s manly focused on each node s ndvdual utlty rather than the utlty of the whole system. In contrast the schemes based on cooperatve game [7-10] can acheve general pareto-optmal performance and maxmze the whole system payoff whle satsfyng the farness requrements. There are also some works studyng the relay selecton bandwdth and power allocaton based on game theory n cooperatve communcaton networks. In [11] the behavors of selfsh nodes n the case of random access and power control are examned. In [1] and [13] a two user network where each user can also work as a relay for the other s studed. By employng a two-user barganng game far bandwdth allocaton [1] and power allocaton [13] are found from Nash barganng soluton. In [14] and [15] the relay power allocaton and prcng problem n the downlnk of mult-user sngle-relay and sngleuser mult-relay wreless network s studed respectvely. The nteracton between the users and the relay s modeled as a two-level tackelberg game the optmal relay power prce that maxmzes the relay revenue s derved analytcally. Motved by [15] we use tackelberg and aucton games model to solve the relay selecton and power allocaton problem n a mult-user mult-relay network whch all the users can do the game process smultaneously. mulaton results show the advantage of our scheme compared wth other exstng algorthms. The rest of ths paper s organzed as follows. In ecton II the system model s gven and n ecton III the nteracton between each user and the selected relays whch can be obtaned by utlzng the aucton game theory can be modeled as a two-level tackelberg game where the relays and users are modeled as the servce provder and customers respectvely. In secton IV smulaton results are demonstrated and the concluson of the whole paper s gven n ecton V.. ystem Model Consder a wreless network where there are N users communcatng wth ther destnatons wth the help of M relays as shown n Fg. 1. Denote that the channel power gan from user to ts destnaton (drect lnk) as h the channel power gan from user to relay as f and the channel power gan from relay to ts destnaton as g respectvely. Amplfy-and-forward (AF) cooperaton protocol s employed n ths system. The cooperatve transmsson process conssts of two phases: n phase 1 user broadcasts ts nformaton to both the relays and ts correspondng destnaton and n phase relays whch receve the nformaton of user wll amplfy ths nformaton and forward t to the correspondng destnaton. All the users wll adopt the two phase cooperatve transmsson way the dfference s that the relays whch help to transmt nformaton are dfferent due to dfferent users. In phase 1 the receved sgnals at destnaton a nd relay can be denoted by y and y respectvel y whch can be expressed as and y Ph x (1) y Pf x () where x denotes the broadcast nformaton symbol wth unt energy from user to ts correspondng destnaton and relay and are the addtve whte Gaussan noses (AWGNs The rate of the drect transmsson from user to ts correspondng destnaton wthout relay nodes help s R Wlog 1 (3) 18
By (4) and (8) the recepton rate of destnaton from user by maxmal-rato combnng (MRC) detector wth relay s R W log 1 (9) For user the relay nodes help for transmttng consttute a set whch s denoted by L where L r1 rl then the rate of destnaton s Fg. 1. Mult-user mult-relay network. R Wlog 1 L L where L denotes a bandwdth factor. (10) where W s the bandwdth for transmsson and s a constant representng the capacty gap s the NR of the drect transmsson from user to destnaton and can be expressed by Ph (4) where P denotes the transmt power at user. In phase relay amplfes y and forwards t to correspondng destnaton wth transmtted power P and the receved sgnal at destnaton s where y Pg x (5) x y (6) y s the transmtted sgnal from user to correspondng destnaton that s normalzed to have unt energy and s the receved nose. ubsttutng () nto (6) Eq. (5) can be rewrtten as follows Y Pg Pf X Pf where P denotes the transmt power at relay. Utlzng (7) the relayed NR for user whch s helped by relay can be expressed as Pf Pg PP f g (7) (8) 3. Problem Formulaton and Energyeffcent Power Allocaton for U In ths secton n order for effcent utlzaton of the cooperatve dversty n multuser networks two fundamental problems on resource allocaton are studed. They are the relay selecton and power allocaton problems. Owng to the nodes n multuser cooperatve wreless networks belong to dfferent authortes and act selfshly the dstrbuted resource allocaton s adopted where the only local knowledge of channel nformaton s needed. Intally ncentves need to be provded by the users to relays n order to relay the nformaton of users. Consequently the users need to choose the optmal relay for maxmzng ther own benefts. Thus a dstrbuted resource allocaton scheme utlzng the tackelberggame-based scheme n our scenaro can be formulated as follows. 3.1. Problem Formulaton Consder there are many users transmt nformaton smultaneously the users wll not exchange any nformaton between each other and they can get every relay for help. The problem of nterest s to select approprate relays for each user to maxmze ts achevable rate and decrease the power of whole relays consumed as much as possble aucton game theory s used to fnd the relays for each user prelmnarly. uppose each relay s the obect for sale and N users are bdders. For each relay assume the power helpng each user s equal at frst.e. P P unt and for user f power P s gven the rate of the drect transmsson R and wth relay help R can be calculated R R wll be the prce of user to compete for relay as the value shows the ablty of relay for helpng 19
user transmt nformaton. Then the whole prces of N bdders competng for relay s denote as X R1 1 R11 R R RN N RN N and relay wll choose the bdders wth hghest N N N prces to provde help. Then for each relay we can fnd N users for help at frst n other words for each user there are M M M relays can provde help. Gven the M relays the tackelberg game model wll be used to help user to buy the optmal amount of power from relays and also helps the selected relays maxmze ther own utltes by askng the optmal prces. tackelberg game s dvded nto two levels: the users play the buyer-level game and the relays play the sell-level game. The users am to acheve the best performance wth relay nodes help wth the least rembursements to them whle the relays am to earn as much as benefts from spendng ther own transmsson power n helpng the users forward ts nformaton. Both of the two sub-game perfect Nash equlbrums can be found usng the backward nducton method. From the above we assume the number of relays M r M whch can provde help for user to be L denoted by r1 r rm r the power the relays spend to transmt nformaton s denoted as P P1 P P k P. The prce per unt of M power sellng from relay node L s denoted as p1 p p k pm P. Then the utlty functon of all the users denoted byu s N N M k k 1 1 k1 (11) U ar p P In (11) the frst part denotes all the users achevable rate wth the relay nodes help a denotes user s gan per unt of rate at the MRC output. The second part denotes the total payments pad by the whole users to relay nodes. The relay nodes utlty functon denoted by U s R N M R k k k 1 k1 U p c P (1) where c k denotes the cost of power for relayng data. Formula (11) s the sum of N sngle user s utlty essentally so we can fnd each user s maxmzng utlty and get the optmal soluton of (11). For user the utlty functon can be wrtten as: M k k k 1 U ar p P (13) and the utlty functon of relay nodes for helpng user s M k k k k 1 Q p c P (14) By dervaton ofu we can get U P k Pk k R a R If pk a then P p U P k k (15) 0 t means that user wll obtan a larger utlty by ncreasng P k. Now we wll determne the fnal relay nodes for user further accordng the relay reecton crtera n [15] all the relay nodes n r set ther ntal prces p R c f pk a P k k k then relay r k wll be reected by user. Wth the relay reecton crtera user excludes the least benefcal relay nodes at the very begnnng and t s proved that the relays are fxed and wll not change after the game s played. Then the fnal relay nodes for helpng user are denoted by r1 r rm r. After the relay selecton the optmal power that user need to buy from the selected relay nodes n r when acheves game equlbrum wll be calculated. uppose L n (10) equal to 1 and let (15) equal to 0 accordng (7) (8) and 10) we can get A B Y Y 4XW (16) * k k k Bk pk X P where k s the k th relay of r B k Pf r k X 1 A g r k r A Pf r k k Ph Y p A B r The optmal prce that each relay n r sells to user can be got by p P (17) * k k ck * Pk / pk. 3.. Problem olvng nce there are N users f they transmt nformaton at the same tme N game processes happens smultaneously. For users wll not exchange nformaton among themselves each user wll only know how much power he buys from the relay as one relay can help many relays t can t be guaranteed. 130
that the sum of optmal power each user buys lower than the maxmum transmt power of the relay so n connecton wth the relay node whch the users t helps buy the power larger than prescrbed power the power the relay node allocates to each user need to be re-calculated. uppose any relay the set of the users t helped s denoted as um u1 u um accordng to (16) we can get the optmal power allocated to each user denoted as Pm Pu P 1 u P u m. nce the utlty functon (13) s concave n P k [1 property 1] U wll decrease as P k s decreasng n order to reduce the power buyng from relay m but maxmze U as much as possble snce U s the sum of U1 N so we ust need to fnd the relay node m that U s not varyng obvously wth the decrease of P k. Accordng to (15) for users n u m we U U calculate u m then we sorted n P P U descendng order of the value of P U1 U Um assume we decrease the P1 P Pm * power of user umpm at frst f the sum of optmal power all users buy s stll larger than the maxmum transmt power of the relay m then we wll decrease * the power of user um 1Pm 1 untl the sum of the optmal power all users buy s lower than the maxmum transmt power of the relay m then we get the whole utlty of all the users U. The whole relay selecton and power allocaton process s summarzed as follows 1) Prelmnarly Relay electon: choose the frst N N N users to use th relay for helpng transmttng nformaton usng aucton game theory. ) Determne whch relays wll be help for each user accordng 1). R 3) Usng formula pk a to determne the P k fnal relays to help for each user. 4) Calculate the optmal power each user buys from the correspondng relays and the optmal prce that each relay sells to the user usng formula (16) and (17) respectvely. 5) Fnd the relays that the sum of the optmal power that users buy s larger than the maxmum transmt power of t and decrease the power of user U wth the smallest untl the whole power s P smaller than the maxmum transmt power of the relay. 6) Calculate the whole utlty of all the users U. 4. Performance Analyss In ths secton the smulaton results are gven whch demonstrates the relablty and effectveness of the proposed dstrbuted relay selecton and power allocaton based on tackelberg and aucton games n our scenaro. Fg. llustrates utlty of each user wth relay s dfferent prces. Consderng the nterference between users the system adopts TDMA for each user to transmt data the channels are assumed to be Raylegh fadng. uppose N =5 M =0 and the capacty gap s set to be 1. We suppose all the users undergo the same game process and take one of them for smulatng. We can see from the fgure that our proposed scheme the utlty of each user wll be ncreasng as the prce of each relay s growng but when the prce of the relay s hgher than a threshold the utlty of the user wll be decreasng t means that the proposed scheme converges to a better local optmum value and also there exsts a optmal prce for the relays. Moreover user s utlty wll ncrease as the value of M s growng t s because that as growng of the value of M there wll be more relays to help the user to transmt nformaton t wll mprove user s utlty. 4 3.5 3 User s Utlty.5 M=0 M=4 M=0 M=8 1.5 M=0 M=10 M=0 M=1 No Relay 1 0 5 10 15 0 5 30 35 40 Prce of relay Fg. Average utlty of each user wth relay s dfferent prces. 131
5. Conclusons In ths paper we propose a novel dstrbuted relay selecton and power allocaton scheme n a mult-user mult-relay network ams to maxmze users achevable rate whle consume less power of relays whch are selected for helpng users transmt nformaton. The aucton game s adopted to solve the relay selecton problem for each user then we model the nteracton between the users and relays as a twolevel tackelberg game and the relays modeled as the servce provder and the users modeled as customers who wll buy power from the provders. The smulaton results valdate the relablty and effectveness of our proposed scheme. Further study may focus on the EE optmzaton wth the mperfect channel sensng and energy harvestng for each U. Acknowledgements Ths work s supported by the grants from the Maor tate Basc Research Development Program of Chna (973 Program) (No.011CB30900) the Natonal cence and Technology Maor Proect (No.01ZX03003006) and the Natonal Natural cence Foundaton of Chna (No. 61139001). References [1]. J. N. Laneman G. W. Wornell and D. N. C. Tse An effcent protocol for realzng cooperatve dversty n wreless networks n Proceedngs of the IEEE IIT Washngton DC June 001 p. 94. [] T. E. Hunter and A. Nosratna Cooperaton dversty through codng n Proceedngs of the IEEE IIT Lausanne wtzerland June 00 p. 0. [3] V. rvastava J. Neel A. B. Mackenze et al. Usng game theory to analyze wreless ad hoc networks Commun. urveys Tuts. Vol. 7 No. 4 Forth Quarter 005 pp. 46 56. [4] V. rnvasan P. Nuggehall C.-F. Chassern and R. R. Rao An analytcal approach to the study of cooperaton n wreless ad hoc networks IEEE Trans. Wreless Commun. Vol. 4 No. March 005 pp. 7 733. [5] O. Iler.-C. Mau and N. B. Mandayam Prcng for enablng forwardng n self-confgurng ad hoc networks IEEE J. el. Areas Commun. Vol. 3 No. 1 Jan. 005 pp. 151 16. [6] N. hastry and R.. Adve tmulatng cooperatve dversty n wreless ad hoc networks through prcng n Proceedngs of the IEEE ICC Istanbul Turkey June 006 pp. 3747 375. [7] D. Grosu A. T. Chronopoulos and M.-Y. Leung Load balancng n dstrbuted systems: An approach usng cooperatve games n Proceedngs of the IPDP Aprl 00 pp. 5 61. [8] Z. Han Z. J and K. J. R. Lu Far multuser channel allocaton for OFDMA networks usng Nash barganng solutons and coaltons IEEE Trans. Commun. Vol. 53 No. 8 August 005 pp. 1366 1376. [9] Z. Han T. Hmsoon W. rwongparat and K. J. R. Lu Energy effcent cooperatve transmsson over multuser OFDM networks: Who helps whom and how to cooperate n Proceedngs of the IEEE Wreless Commun. Netw. Conf. New Orleans LA Vol. March 005 pp. 1030 1035. [10] R. Mazumdar L. G. Mason and C. Doulgers Farness n network optmal flow control: Optmalty of product forms IEEE Trans. Commun. Vol. 39 No. 5 May 1991 pp. 775 78. [11] A. B. MacKenze and. B. Wcker Game theory and the desgn of self-confgurng adaptve wreless networks IEEE Commun. Mag. Vol. 39 November 011 pp. 16 131. [1] Z. Zhang J. h H.-H. Chen M. Guzan and P. Qu A cooperaton strategy based on Nash Barganng oluton n cooperatve relay networks IEEE Trans. Veh. Technol. Vol. 57 No. 4 July 008 pp. 570 577. [13] G. Zhang H. Zhang L. Zhao W. Wang and L. Cong Far resource sharng for cooperatve relay networks usng Nash barganng solutons IEEE Commun. Lett. Vol. 13 No. 6 June 009 pp. 381 383. [14] Q. Cao H. V. Zhao and Y. D. Jng Power Allocaton and Prcng n Mult-User Relay Networks Usng tackelberg and Barganng Games IEEE Trans. Vehcular Technology Vol. 61 No. 7 eptember 01 pp. 3177-3190. [15] B. Wang Z. Han and K. J. Ray Lu Dstrbuted relay selecton and power control for multuser cooperatve communcaton networks usng tackelberg game IEEE Trans. Moble Comp. Vol. 8 July 009 pp. 975-990. 013 Copyrght Internatonal Frequency ensor Assocaton (IFA). All rghts reserved. (http://www.sensorsportal.com) 13
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