Deployment of High Altitude Platforms Network: A Game Theoretic Approach

Transcription

1 Worsop on Computng, Networng and Communcatons Deployment of Hg Alttude Platforms Networ: A Game Teoretc Approac Ru Zong, Xnbo Gao, Xuyu Wang, Lv Zongtng Scool of Electronc Engneerng, Xdan Unversty, X an 7171, Cna Emal: zongru@xdan.edu.cn, {xbgao.xdan, wangxuyu316, lvzongtng}@gmal.com, Abstract Te Hg Alttude Platforms (HAPs) ave been consdered as a promsng tecnque for provdng wreless communcaton and oter servces. Tey operate at an alttude from 17m to m, wc explot bot advantages of satelltes and terrestral wreless communcaton networs. It s possble to deploy HAPs networ rapdly and adjust tem dynamcally to cover specfc regons requrng communcaton servces. In ts paper, te problem of deployng HAPs networ to provde wreless communcaton for terrestral users s nvestgated. Te am of deployment s to provdng communcaton servces to ground users as many as possble wt qualty of servce (QoS) guaranteed. To fnd an optmal soluton, we model te problem as a potental game. And a restrcted spatal adaptve play (RSAP) learnng algortm s ntroduced for te game. Usng ts algortm, te HAPs can be deployed to cover te user areas n a self-organzed manner wt g QoS aceved. Fnally, te smulaton results also demonstrate tat te HAPs networ can aceve te optmal deployment. Index Terms Wreless communcaton, Hg alttude platform, Qualty of servce, Potental game, Learnng algortm I. INTRODUCTION Te g alttude platform system s consdered as a promsng wreless communcaton system wc s expected to co-wor wt terran and satellte communcaton systems n a complementary and ntegrated fason [1]. Hg Alttude Platforms are usually based on quas-statonary aeral platforms (or arsp, balloon, UAV, and etc.) operatng n te stratospere, at an alttude of 17m to m []. Tey ave te potental to provde varous nds of communcatons servces and oter applcatons cost effectvely (e.g., broadband, moble communcaton, or envronment montorng). Many countres proposed ter own researc projects on HAPs system,.e. CAPANINA, HALO, SyNet, etc.[3]. Te Internatonal Telecommuncaton Unon (ITU) as recognzed te HAP from 1997 as a separate category of rado statons: Te Hg Alttude Platform Staton (HAPS) and attrbuted te, 31/8 and 47/48 GHz frequency ranges for ts operaton. Comparng wt terrestral communcaton nfrastructure and satellte communcaton system, HAPs ave te advantage of easy and rapd deployment, g cost-effectve, wde range coverng, low transmsson delay and flexble operaton [4]. Snce te HAPs can be easy to launc and fast to deploy, tey are sutable for consttutng networs over certan ground area to provde communcatons or survellance servces. A sngle HAP staton can supply a muc larger coverage area tan a terrestral base staton wt comparatve g communcaton capacty. And te cannel attenuaton s muc less tan te terrestral cannel. HAPs networ are desgned to provde wreless communcaton servce. Snce te HAPs are operatng at te g alttude space, tey can be deployed flexbly wtout te restrctons by te Geograpcal condtons. Prevous wor focuses more attentons on studyng te capablty of te HAP staton on provdng wreless communcaton servce. A settng of multple HAPs communcaton networs s proposed n [5] and te capacty of networs s presented. In [6] te performance of multple HAPs scenaro s analyzed n te terms of CINR and capacty. However, tere s lttle lterature nvolvng ow to deploy te HAPs networs effectvely accordng certan msson requrement. It s generally expected tat te deployment of te HAPs sould cover te ground user as many as possble wt requred qualty of servce. A metod based on K-mean clusterng for placement of multple HAPs s presented n [7]. Gven te number of ground nodes and area coverage, te ground users are clustered to determne te HAPs locaton. In [8], a deployment optmzaton model of arsps s developed for HAPs based genetc algortm, wose soluton as g tme complexty. Bot above metods are centralzed controllng sceme, wc need central controller calculate te optmal confguraton and coordnate te movement of HAPs. In addton te QoS for users and nterferences between HAPs are not taen nto consderaton. Tese factors are mportant for practcal applcaton. In ts paper, we nvestgate te deployment problem of HAPs networ provdng wreless communcaton for terrestral users. Te HAPs coverage and nterference model are taen nto consderaton. In our system, QoS for ground users are determned by te transmttng data rate between HAPs and users. Te objectve of te HAP networ deployment s formulated to maxmze te total transmttng rate of HAPs networ, meanwle, and to guarantee te user mnmum servce requrement. It s expected tat te deployment could be mplemented n a self-organzed way. Te HAPs cooperate to accompls te am of provdng optmal wreless servces. Consequently, a game-teoretc analyss s called for te deployment problem. Te HAPs are modeled as ratonal and self-organzed players wc see optmal confguraton to maxmum ter utltes of te HAPs. We ntroduced restrcted spatal adaptve play (RSAP) learnng algortm to solve te /1/$6. 1 IEEE 34

2 Fg.. HAPs coverage model Fg. 3. Interference model Fg. 1. HAPs networ communcaton system deployment game. Te learnng algortm guarantees tat te HAPs explore te dstrbuton of user and converge to te optmal postons wt g probablty. Te smulaton results sow te effectveness of our sceme. Te rest of te paper s organzed as follows. Secton II ntroduces te HAPs networ deployment problem, and te problem s modeled as a potental game. Ten n secton III, te learnng algortm s proposed to aceve optmal confguraton for te deployment game. Te smulaton results sow te effectveness of te algortms n secton IV. At te last secton, we provde te concludng remars. II. DEPLOYMENT PROBLEM FORMATION Consder a communcaton system n wc Hg Alttude Platform delver wreless communcaton (or oter wreless servces) to ground users (sow n fg.1). Hg Alttude Platforms act as wreless base statons. And tey ln wt eac oter to construct bacbone networs. Te ground users could access to te networ for moble communcaton and oter wreless servces. A. Problem formaton Let {1,,,, K} be a set of HAPs, te servce provders. Eac HAP operated at te alttude. Tere are a number of ground users requrng communcaton servces. Let {1,,,, N} be te set of users and u { s u 1,, s u,, u u s N} be te users dstrbuton on te ground, were s denotes te poston of user. Te HAPs deployment problem s am to see a tuple of optmal locatons { s1,, s,, sk} ( s denotes te poston of HAP at g alttude space) for HAPs. Te optmal deployment sould fulfll users servce requests as many as possble wt certan qualty level guaranteed. Te HAP could delver communcaton servces wtn ts coverage regon from te g alttude space. Te QoS tat HAP provdes for users depends on te HAP s transmttng power sadowed on te footprnt area (as fg. ). For a HAP-to-ground communcaton ln, te recevng sgnal power on te ground s related to te pat loss of te cannel, wc can be consdered as free space propagaton model [9]. Let p t be te transmttng power of te HAP, and p r be te recevng power of te user on te ground. Tere s u pr( s, s) pt, {1,..., N}, (1) u s s u were s s s te dstance between user and HAP, and s te sgnal fadng factor. For te common HAPs communcaton lns, s ~4 [3]. denotes te loss factor specfed by te gven transmttng rado wave and envronment. Te recevng power of user s also affected by te antenna. If te effect of beam sapes for drected antenna s taen nto consderaton, p t wll cange wt transmttng angle. In ts paper, we do not consder te beam sape and gan of antenna for te rado sgnal transmttng, and assume tat p t s constant for any angle of te antenna(suc as omn antenna). Wen users receve communcaton servces, te transmttng data rates sould be mantaned at certan level to guarantee te QoS. For a partcular traffc type along wt te requred bt error rate are not dscussed ere. Te maxmum teoretcal transmttng data rate from HAP to a ground user s gven as follow[5], 1 r Blog (1 CINR ), () were r s te maxmum transmttng data rate from HAP to user, te CINR s te carrer-to-nterference-plus-nose rato (CINR) of te cannel between HAP and te user. B denotes te communcaton bandwdt. It s very common tat a user may fall n mult-haps servce coverage areas as sown n fg.3. However, user wll only set up a ln wt te HAP wc can provde best QoS and oter HAPs sgnal power wll nterfere wt te ln. We ave te CINR expresson [5] as g pr, CINR, (3) NT glpr, l l \ were te N T denotes te termal nose power observed by te user, wc s constant for certan bandwdt. p r, s te user s recevng power from te HAP tat offers communcaton servces, and p rl, denotes te nterference sgnal power from oter HAPs tat ave not offered te communcaton servces to user. g and g l are te gan factor for te users recever. Tey are constant for a gven scenaro. If tere s no nference from oter HAPs, From (3), we can see tat te data rate only depends on te recevng sgnal power. Te recevng CINR s determned by HAP s transmttng power and te dstance between t and user. Gven a maxmum transmttng power, te HAP could only delvered servce 1 Te Sannon equaton s only perfectly accurate for a Gaussan nose source. Interference wll only be approxmately Gaussan. 35

3 wtn a lmted range (denoted as S r ) accordng to mnmum data rate demand. Te goal of a HAP s to maxmze te total data rate to fulfll ground users demands. Gven M users wtn HAP s servce range, te total data rates from HAP s M M R r Blog (1 CINR ) 1 1 M g Pr, B 1 NT glpr, l l \ log (1 ) For te HAPs networ, te sum data rate of all HAPs, namely te trougput of te networ, s gven as follow R. (5) Gven a number of Users and ter postons, te goal of HAPs networ s to solve te followng optmzaton problem, max R( s1,, s,, sk), mn (4) subject to s, (6) r r. In te constrans, denotes te HAP s avalable postons space. Here s s assumed dscrete and fnte. r mn s te mnmum data rates between HAP and user. Te data rate for a user sould exceed te mnmum data rate to ensure te qualty of certan communcaton servce. Te sum data rate provde by HAPs networ s determned by te locatons of HAPs and users and te HAP s transmttng power. In ts paper we assume tat te HAP s transmttng power s uncangeable. Te total data rate of HAPs networ s only te functon of HAPs postons { s1,, s,, sk} u u u u and users dstrbuton { s1,, s,, sn}. As te HAPs ave lmted communcaton scopes S r, tey can detect te presents of te users wtn ter coverage regon. In fact, te sensng range s muc larger tan te servce range, snce te recevng power level cannot fulfll te mnmum data rate for te wreless communcaton. We assume te HAPs could only sense te users postons wtn ter maxmum communcaton scopes S r. under ts stuaton, te deployment s muc complcated. B. Game teoretc model Te proposed HAPs deployment problem s to fnd te optmal poston of te mult-haps. We wll sow tat te optmzaton problem can be model as a game and tere exst Nas Equlbrum tat s te optmal or suboptmal soluton for te optmzaton problem. Snce ndvdual HAPs do not collaborate among temselves, evenly tey may mpar te beneft of eac oter. Ts communcaton scenaro can be modeled as a non-cooperatve game [1]. Te HAPs are non-cooperatve players and ter avalable postons are ter acton sets. Gven certan users dstrbuton on te ground, te areas tat te HAPs could cover represent te set of admssble strateges of ts HAP. In non-cooperatve game, te selfs players are tryng to maxmze ter own utltes. In te deployment game, te HAP wll beneft temselves from provde more servces to ground users. Let u denotes te utlty of player HAP. Ten, A Nas * equlbrum of ts game [1] s a tuple of actons{ s } K, suc 1 tat for any * * * * * u ( s,, s,, s ) u ( s,, s,, s ), s. (7) 1 K 1 K In oter words, a Nas Equlbrum of ts game s a locally optmal strategy for eac player tat no player as an ncentve to unlaterally move. Intutvely we can assgn te data rate R as HAP s utlty functon, snce te rewards tat servce subscrbers pay to provders can be evaluated by te accessng data rate. Here we defne te utlty of eac HAPs U wc satsfes U( s, s) ( s, s) ( s, s), (8) were s denote te HAP provde no servces to any user. Te player s utlty functon U( s, s ) denotes te contrbuton of te global payoff, te total data rates, under strategy{ s, s }. Ts utlty functon mples te sngle HAP s contrbuton to te global proft. By allocatng HAP ts utlty functon, te global object functon wll possess te monotoncty relatve to sngle HAP s payoff. Wereas tang data rate of HAP as utlty functon does not sow ts property. Based on above defnton we ave followng proposton. Proposton: Te HAPs deployment game s a potental game [11] and as a pure strategy (determnstc) Nas equlbrum. Ts proposton comes from te fact tat we can defne te potental functon ( s1,, s,, sk) ( s1,, s,, sk), (9) wc satsfes U( s, s) U( s, s) ( s, s) ( s, s). (1) were s te actons of HAPs except. Hence, we can start from an arbtrary determnstc acton vector, and at eac step once one player ncreases t s utlty s ncreased dentcally. Snce can accept a fnte amount of values, t wll eventually reac a local maxmum. At ts pont, no player can aceve any mprovement, and we reac a Nas Equlbrum (NE). Fndng te optmal deployment of te HAPs s to maxmzng te ground objectve functon, wc leads to a pure NE maxmzng te potental functon. Te NE can be reaced n a dstrbuted metod. In te sequence, we propose a learnng algortm to aceve te NE, wc gve us a satsfed soluton for te HAPs deployment problem. III. SOLUTION TO DEPLOYMENT GAME In te above secton, we ave developed te matematc bass for te settng n te deployment of HAP networ. Te deployng optmzaton problem as been modeled as a potental game. Ts secton focuses on solutons to te deployment game. Wen te users postons are nown, t s muc easer to determne te best locaton for HAPs by searcng or genetc 36

4 algortm. However, te centralzed algortms are nvald n practces, because te users dstrbuton s often unnown and even cangng n te deployment process. Generally, a eurstc algortm could be appled for ts game, suc as greedy algortm. Wle ts nd of metod often converge to local optmal. We ntroduced te RSAP learnng algortms for te deployment game. Te learnng algortms allow te HAPs worng n a self-organzed manner. Te HAPs determne ter deployng polcy by ter own utlty wtout central controller. Te algortms wll lead to game convergng to NE, were HAPs aceve optmal deployment for gven users. A. RSAP Learnng Algortm Some games may result n Nas Equlbra tat are suboptmal from te pont of vew of all players. So te learnng dynamcs as been ntroduced to game teory. Te learnng algortm wors n te form of repeated game. It could fnd te optmal solutons of te maxmzng te group s objectve functon. In a general game, te players are permtted to tae any actons n ters strateges sets. In te process of deployment game, a HAP can only move to a poston wtn a fxed radus around ts current poston at eac tme slot. Tat means te player can only adopt restrcted actons wc s depended on ts current acton state n te game. For ts restrcted-acton potental game, te restrcted spatal adaptve play (RSAP) [1] learnng algortm are ntroduced. It allows eac player coose an actons from a lmted acton set determned by ts prevous acton. Te algortm guarantees te teraton process probablstc convergng to a pure Nas Equlbrum tat maxmzes te potental functon. Let s ( t 1) be te acton at tme t1. Te set of actons R avalable for player at tme t wll be denoted as ( s ( t1)). It s a functon of player s acton at tme t1. Te learnng algortm are descrbed as follow. Algortm II: RSAP Learnng Algortm Step 1: cosen one player HAP randomly, (wt equal probablty for eac player) and permtted to select a new acton. All oter players mantan ter states,.e. s() t s( t 1). Step : te actve player HAP randomly selects a tral poston s ˆ from ts state-dependent acton set R ( s ( t1)) wt te followng probabltes: Pr[ sˆ s] (1 z), R for any s ( s( t1)) \ s( t1); (1) R Pr[ ˆ s s( t1)] 1 (( ( s( t1) 1) / z), were z denotes te maxmum number of actons n any R restrcted acton set for player,.e., z max ( s ). R s Step 3: After player cooses a tral acton s ˆ, updated ts acton state at tme t wt te followng probabltes: exp U ( ˆ s, s ( 1)) t Pr[ s ( ) ˆ t s] D, (13) exp{ U( s( t1))} Pr[ s( t) s( t1)] D were D exp{ U ( ˆ s, s( t1))} exp{ U( s( t 1))}, (14) and s an exploraton parameter. Step 4: Repeat te process from step 1. Ts algortm nduces a marov process wc as a unque statonary dstrbuton [1]. Te statonary dstrbuton s n te jont actons set tat maxmze te potental functon [13]. Tat means te statonary dstrbuton s te NE of game. Tere are exp{ ( s )} ( s ) for any s * [1], (15) * exp{ ( s )} s A were s denotes te acton profle, and s te acton profle space. As and suffcently large tmes t >, te game converges to te optmal dstrbuton were te acton profles maxmze te potental functon. In ts deployment game, all te players can evaluate s utlty usng only local nformaton wtout te global users dstrbuton. All te learnng process can be carred out by te players temselves wtout any supervson. For suffcently large t and, te optmal soluton to te deployment of te HAPs over specfc msson space could be obtaned troug te learnng algortm. IV. SIMULATION RESULTS In te followng smulaton, te scenaro s set wtn 5m5m area. Wtn te area, 5 users are located n four parttons. Users dstrbuton meets Gaussan dstrbuton wtn two parttons, wc smulate te urban populaton dstrbuton. Te oter two parttons are unform dstrbuton, wc correspond wt te rural populaton dstrbuton. Te HAP s s assumed at an alttude of m. For te communcaton cannel, tere are = and =.1. Te HAP s transmttng power P t s 1W. We assume te communcaton bandwdt B=1MHz, and te termal nose N T =51-13 W. For eac user, te mnmum transtng rate r mn to mantan communcaton servce s set as Hz. All HAPs ntally start at locaton (,, ). As menton before, we assume te HAPs locaton s dscrete and fnte. In te smulaton, te HAPs moves 1m at eac tme step n four drectons along te axes. For te learnng algortm, te s.. Fg. 4 sows te deployment results from te vew of overloong. Tere are 5 and 8 HAPs beng deployed over te area. Cause te constrant of mnmum servce data rate, te coverage regon radus s about 5m. From te fgure we can see tat te HAPs tend to cover more users n ter footprnt areas. Despte startng from orgn (,,m), te HAPs ave scattered to converge to user-dense-regon. Besde tey avod fallng nto te local extreme wc near te startng ponts. 37

5 Fg. 5 sows te global maxmum data rate cangng wt te teraton steps. Te global maxmum data rate also denotes te potental functon of te deployment game. As te teraton number goes up, te HAPs could aceve good performance. Snce te learnng algortm usng probablty decson metod, 5 4 optmzatons problem of total trougput of HAPs networ. We model te deployment problem as potental game to develop dstrbuted deployng metods. Te RSAP learnng algortm s ntroduced to lead te game to Nas equlbrum, wc offers te optmal soluton to te HAPs deployment problem. Te learnng algortm allows HAPs beng deployed n a self-organzed manner wtout any pror nformaton, wle te cost s slow convergence to global optmal solutons. Fnally te smulatons sow te effectveness of our metods. Y (m) 3 ACKNOWLEDGMENT Ts wor was supported by te Natonal Natural Scence Foundaton of Cna (No. 6835). Global Capactty (KHz) Y (m) X (m) (a) 5 HAPs X (m) (b) 8 HAPs Fg. 4. Te deployment of dfferent numbers of HAPs 4 x HAPs 5 HAPs 5 1 Iteraton Number Fg. 5. Global maxmum data rate of HAPs networ we can see tat tere s stll fluctuaton around te optmal confguraton. Generally te smulaton results sow tat te HAPs could aceve a global optmal deployment. Te HAPs could catc te dstrbuton of users and perform a good dstrbuton. REFERENCES [1] G. M. Djunc, J. Fredenfelds, and Y. Ounev, Establsng wreless communcaton servces va g alttude aeronautcal platforms: a concept wose tme as come? IEEE Commun. Mag., vol.35, no.9, pp , Sep. 1997, [] T. C. Tozer and D. Grace, Hg-alttude platforms for wreless communcatons, IEE Electron. Commun. Eng. J., vol.13, pp , 1. [3] S. Karapantazs and F. Pavldou, Broadband communcatons va galttude platforms: a survey, IEEE Communcatons Surveys & Tutorals, vol.7, no.1, pp.-31, Frst Qtr. 5 [4] A. Z. Alejandro, L. C. Jose, and A. D. Joss, Hg-Alttude Platforms for Wreless Communcatons, Unted Kngdom: Wley Press, 8. [5] D. Grace, J. Tornton, G. Cen; G.P. Wte,and T.C. Tozer. Improvng te system capacty of broadband servces usng multple g-alttude platforms, IEEE Trans. Wreless Commun., vol.4, no., pp. 7-79, Marc 5 [6] G. Cen, D. Grace, and T. C. Tozer, Performance of multple g alttude platforms usng drectve HAP and user antennas, Wreless Personal Communcatons, vol. 3, no. 3-4,pp , 5. [7] Ha Yoon Song, A metod of moble base staton placement for g alttude platform based networ wt geograpcal clusterng of moble ground nodes, 8 Internatonal Multconference on Computer Scence and Informaton Tecnology, pp , Oct. 8 [8] Xuyu Wang; Xnbo Gao; Ru Zong; and Peng Ceng, "An optmal model and soluton of deployment of arsps for g alttude platforms," 1 Internatonal Conference on Wreless Communcatons and Sgnal Processng (WCSP), pp.1-6, 1-3 Oct. 1 [9] Aao Oladpo, Stratosperc propagaton and HAPs cannel modelng, master tess, Blenge Insttute of Tecnology, Sweden, 7. [1] A. B. MacKenze and L. A. DaSlva, Game Teory for Wreless Engneers. syntess lectures on communcatons. Morgan & Claypool Press, 6. [11] D. Monderer and L. Sapley, Potental games, Games Econom. Beav., vol.14, no.1, pp , May [1] J. R. Marden, G. Arslan, and J.S. Samma, Cooperatve control and potental games, IEEE Trans. Syst., Man, Cybern. B, Cybern., vol.39, no.6, pp , Dec. 9 [13] H. P. Young, Indvdual Strategy and Socal Structure. Prnceton. NJ: Prnceton Unv. Press, V. CONCLUSION In ts paper, te deployment problem of HAP networs s explored. Ensurng g QoS s set as te target of networng. Te HAPs networ deployment problem s formulated as 38