An Optimal Model and Solution of Deployment of Airships for High Altitude Platforms

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1 An Optmal Model and Soluton of Deployment of Arshps for Hgh Alttude Platforms Xuyu Wang, Xnbo Gao, Ru Zong, Peng Cheng. VIPS Lab, School of Electronc Engneerng, Xdan Unversty, X an 77, Chna. Department of Electronc Engneerng, Shangha Jao Tong Unversty, Shangha, Chna Emal: wangxuyu36@gmal.com, xbgao.xdan@gmal.com, zongru@xdan.edu.cn, chengpeng@sjtu.edu.cn Abstract In future communcaton system, the demand for hgh capacty s a challengng problem for wreless servces, especally for delvery of the last mle. A potental soluton s offered by the hgh alttude platforms (HAPs), whch can utlze the best character and tradeoff of both satellte and terrestral networks. Snce the performance of the HAPs depends on the structure of network, how to deploy the nodes of arshps for HAPs s ncreasngly mportant. In ths paper, an optmal model of deployment of arshps for HAPs s constructed and solved based on genetc algorthm. Frst, a heterogeneous system ncludng terrestral layer, HAP layer and GEO layer s gven. Then, an optmal model wth objectve functon of maxmum entropy and mnmum delay s establshed to optmze the deployment of arshps for HAPs. Fnally, a modfed genetc algorthm (GA) s employed to optmze the objectve functon and get the optmal soluton to the model. Smulaton results show that the establshed objectve functon and the soluton based on GA can reach the goal of on-demand deployment of arshp for HAPs. Index Terms Hgh alttude platform; etwork structure; ode deployment; Genetc algorthm. I. BITRODUCTIO Wth the development of modern communcaton system, the demand for hgh capacty has ganed much more attentons. Thus, the wreless solutons are becomng ncreasng mportant, whch can provde a varety of servces wthout relance on a fxed nfrastructure and solve the last mle problem,.e. delvery drectly to a customer s premses. Hgh alttude platforms (HAPs) operatng n the stratosphere at alttude between 7 and km offer a potental soluton, whch may be aeroplanes or arshps and may be manned or unmanned[][] [3]. Comparng wth terrestral nfrastructure, they cover large areas n lne-sght propagaton condton. In addton, they have advantages over satelltes, such as low cost, lower propagaton delays, ncremental deployment, and etc. Hence, HAPs can combne the advantages of both terrestral networks and satellte networks to offer hgh-capacty servces, whch has wde applcaton n the felds of broadcastng, multcast, rural sensng, polluton montorng, traffc montorng and control, dsaster recue and navgaton for mltary. Recently, t s well known that some projects of HAPs have been studed by many countres, for example, the Helet and CAPAIA projects of the European Unon [4], Sky Staton and SkyTower projects n the US[5], Skyet project n Japan[6], ETRI n Korea[7]. For these projects, on the one hand, a sngle HAP platform s studed, whch manly focuses on communcaton lnks establshment, array optmzaton, channel model, and system capacty[8][9][][][][3]. On the other hand, new scenaros that take advantage of ntegrated satellte-hap system are proposed, whch are utlzed to mprove system performance [4][5]. However, there are few works for the deployment of HAPs. Ha Yoog Song [6] only presents a method based on K-mean clusterng for placement of multple HAPs, but extng several problems regardng the clusterng results. In ths paper, a satellte-haps-terrestral system s gven, and an optmal model of deployment of arshps for HAPs s establshed, obtanng the on-demand deployment based on the objectves of maxmum entropy and mnmum delay. In addton, the genetc algorthm s utlzed to optmze the model. Fnally, the smulaton results show the effectveness of the proposed model and soluton. The rest of ths paper s organzed as follows. The satellte- HAPs-terrestral network system s presented n Secton II. The optmal model of deployment of arshps s proposed n Secton III. The genetc algorthm s ntroduced to optmze the objectve of deployment of arshps n Secton IV. Expermental results and analyss are gven n Secton V. The fnal secton s concluson and future work. II. BSATELLITE-HAP-TERRESTRIAL ETWORK SYSTEM A heterogeneous communcaton network system s shown n Fg., whch conssts of three layers,.e., terrestral layer, HAP layer and GEO layer. The three-layer network can provde users on the ground wth full connecton by arshps or a satellte. A. 7BTerrestral Layer In order to measure the sparse level of users on the ground, the grd structure s utlzed n terrestral layer. In Fg., the regon of a b area s dvded nto k l square grds, thus achevng two advantages: on the one hand, the ndex of the grd can substtute for ndexes of all users to descrbe the feature of the area; on the other hand, t s easy to determne the number and poston of users n the grd. Consderng the decreasng tendency of users from the urban to rural areas, we assume the dstrbuton of users obeyng Gaussan dstrbuton. Let ρ ( r k ) denote the dstrbuton of users for the hot spot k, that s r M k ρ( rk ) e σ () πσ where r k s the dstance between the center of the hot spot k and users, M s a constant, σ s the standard devaton //$6. IEEE

2 l k B. 8BHAP Layer Fg.. A satellte-haps-terrestral network system Although the heght range of stratospherc s typcally between and 5 km, the alttude of km s thought as the optmal poston for the deployment of arshps due to the show wnd speed and stable envronment. In addton, Ad hoc network structure s employed as the connecton of arshps n stratosphere. C. 9BGEO Layer Because of the large range that satellte covers, we assume that the satellte can connect to all users and arshps. And there s only one satellte whose space poston s defned as ( x, z ) n GEO layer. D. BSatellte-HAPs-Terrestral network In the satellte-haps-terrestral network, one-hop relay s assumed, that s to say, when one user s not covered by one arshp, the satellte or one of other arshps s utlzed as one relay to connect the user and the arshp. In addton, f there are other arshps used as the relay, selectng the mnmum relay dstance s consdered; otherwse selectng the satellte s assumed. Thus all the users are connected by HAPs n the heterogeneous network. The assumpton of one-hop relay s shown n Fg.. It s notced that the satellte, arshp or arshp 3 may be utlzed as one relay to connect arshp and the user. On the one hand, f there are arshp and arshp 3, arshp wll be selected due to the assumpton of the mnmum relay dstance. On the other hand, the satellte s selected when arshp and arshp 3 are not employed as the relay. III. BDEPLOYMET OPTIMIZATIO OF AIRSHIPS I HAP A. BProblem Formulaton In the satellte-hap-terrestral network, we focus on the problem of how to optmze the deployment of arshps so that the system can provde users wth far connectons. Gven the dstrbuton of users and satellte, space postons of arshps are optmzed based on crterons of maxmum entropy and mnmum delay, whch s a typcal mult-objectve optmzaton problem wth constrans. Fg.. The assumpton of one-hop relay B. BObjectve Functon Modelng In order to obtan the deployment of arshps based on entropy, the performance of power coverage of one arshp s frst consdered. We defne that the average dstance between arshp and the square area (, ) s r, whch s gven by n r n hur () q hu q where n s the number of users n the (, ) square area, r s the dstance between arshp and user ( x,), whch s defned as r ( m x ) + ( n y ) + (3) where ( m, n,) s the poston of arshp, ( x,) s the poston of the q user n the square area (, ), and hu s defned as the - ndcator varable of the connecton between arshp and user ( x,), that s hu r r R > R where R s the maxmum dstance that arshps can cover users. From Eq. (), we obtan P that s defned as the average coverage power of every user n the cell (, ),.e., P α r P (5) n where P s the power attenuaton of the unte length of the arshp, α s the attenuaton factor, s the number of arshps. The concept of entropy known from Shannon s nformaton theory s utlzed as an objectve of on-demand deployment of arshps. Let H denote the entropy of the average coverage power of every user n k l cells, that s (4)

3 3 where η s gven by k l log (6) k l H η η η P k l k l P Thus the objectve of on-demand deployment of arshps s formulated as max H (9) When H s theoretcal maxmum, we have η () k l Thus P s a constant, whch means that the average coverage power of every user n k l cells s equal. From Eq. (5), t s P notced that that the larger n, the larger, that s to say, r α the larger the number of users n the (, ) square area, the larger the coverage power of all the arshps n the (, ) square area. Therefore, on-demand deployment of arshps s attaned. For the purpose of measurng the total delay, we defne the avalable dstance between arshp and user ( x,) s d, whch s gven by (7) d hu r + ( hu ) w () where w s the relay dstance by other arshps or satellte, whch s expressed by w H + S () where H s the mnmal dstance between arshp and user ( x,), relayed by other arshps, that s H mn hh hu ( h + r ) (3) j j j j j {, + } where h j s the dstance between arshp and arshp j, whch s gven by hj ( m mj ) + ( n nj ) (4) and hh j s the - ndcator varable of the connecton between arshp and arshp j, that s hj h hhj (5) hj > h where h s the maxmum dstance that one arshp can communcate wth other arshps, and S s the dstance between arshp and user ( x,), relayed by satellte, that s S δ ( hhj huj ) ( sh + sukq ) (6) where sh s the dstance between arshp and the satellte, whch s expressed by sh ( m x ) + ( n y ) + ( z ) (7) and su kq s the dstance between the satellte and user ( x,), we have su ( x x ) + ( y y ) + z (8) kq and δ ( hhj hu j ) s the - ndcator varable whether the arshp can select the satellte to relay, gven by, when j j hh hu δ ( hhj hu j ) (9) when hhj hu j j For hhj hu j, δ ( hhj hu j ) means that arshp cannot connect user ( x,) by other arshps so that arshp connects the user ( x,) only by satellte; and for hhj hu j, δ ( hhj hu j ) means that the arshp can connect the user ( x,) by other arshps. Consequently, d s expressed as the avalable dstance between the arshp and user ( x,), relayed by other arshps, satellte. Wth the dstance between arshps, the satellte and the user long, the delay s utlzed as an mportant factor for the deployment of arshps. We only consder the propagaton delay and defne that the total propagaton delay between arshps and users s T, we have k l n d T () k l q c where c s the speed of lght. Thus, the objectve of the total delay s mn T () In addton, we have the followng space constrant for arshps. h, j hmn < j st. m a () n b where h mn s the mnmal safe dstance between two arshps. Hence the deployment of arshps based on the maxmum entropy and the total mnmal delay s descrbed as a mult-objectve optmzaton problem wth constran, whch s formulated as

4 4 max mn H T k l k l η log η k l n k l q P η k l P k l d hu r + ( hu ) w st. w H + S hj hmn, < j m a n b IV. 3BOPTIMIZATIO OF THE DEPLOYMET OF AIRSHIPS BASED O GEETIC ALGORITHM FOR The deployment of arshps n stratosphere s formulated as the mult-objectve optmzaton problem wth constrans. In classcal optmzaton theory, the optmzaton problem wth constran s transformed nto the one wthout constran by the Lagrange multpler method, thus solved by the gradent descent or other teratve algorthms. However, t s dffcult to obtan the global optmzaton soluton to the complcated nonlnear optmal problem wth constrans. For ths end, the genetc algorthm (GA), as a global-heurstc search and optmzaton technque, s employed to solve the problem. In genetc algorthms, frst of all, the soluton to the problem s encoded as the form of the chromosome, such as the strng of bnary numbers or real numbers. In addton, the generaton of the populaton of the chromosomes s teratvely generated by genetc operators, for example, crossover and mutaton. The populaton of the chromosomes wth larger ftness value s selected as the next generaton. Also, t s not stopped untl the termnaton condton s met. Hence the populaton n genetc algorthms s evolved toward the drecton of the global optmzaton soluton [7]. In the model, the populaton of the chromosomes s employed as the canddate soluton to the deployment of arshps that s the space poston of the arshps n stratosphere, and the ftness functon s used as the optmzaton objecton of the deployment of the arshps. The genetc operatons utlzed n the model are gven as follows. A. 3 BEncodng of the soluton In ths approach, the real-number encodng s employed as the encodng of the soluton, whch has the advantage of the computng cost wthout decodng, hgh encodng precson and large range of numbers. The space poston of the arshp s encoded as m a + ( b a) rand(, M ) (3) n a+ ( b a) rand(, M) (4) where M s the number of the populaton. B. 4 BFtness functon In genetc algorthms, the qualty of the soluton s evaluated d c by the ftness functon of the populaton. The hgher the ftness of the populaton s, the better the soluton to the ftness. Thus the probablty of the selecton of the populaton wth the hgher ftness s larger. Because the deployment of arshps s the mult-objectve optmzaton problem wth constrans, t should be frst transformed nto a sngle-objectve one. Then constrans of the objectve should be removed by certan penalty strateges. Thus the ftness can be computed. The process s expressed by F H λt L (5) L hj < hmn L (6) hj hmn where λ s the scalng factor, L s the penalty constant. C. 5 BSelecton The selecton operator utlzed here s based on spnnng the roulette wheel, whose basc prncpal s that the probablty of the selecton s determned by the proportonalty of the ftness of the populaton. The elte strategy by whch the largest ftness of populatons s drectly coped to next generaton s also employed n selecton process. The probablty of the selecton s expressed by F p (7) M F D. 6 BCrossover The lnear crossover operator s used, whch means that two new populatons are generated by the Hconvex combnatonh of the old two populatons. The crossover process s gven by new old old j m β m +( - β) m (8) m ( - β) m + β m (9) new old old j j old where m and populaton j respectvely, m and old m j are denoted as old populaton and new new m j are denoted as new populaton and populaton j respectvely, and β s the crossover factor. E. 7 BMutaton To obtan the hgh accuracy and tunng capablty, the no-unform mutaton s employed. The mutaton s expressed by old old t b m + ( b m ) r ( ) p >.5 new G m (3) old old t b m ( m a) r ( ) p.5 G where r and p are random values between and respectvely, and t s the current generaton number, G s the maxmum generaton number, b s the parameter of the no-unform degree. Fnally, the parameter soluton to ths problem s generated. The process of genetc algorthms s shown n Fg. 3.

5 5 (a). The deployment of three arshps. Fg. 3. The process of genetc algorthms. V. 4BEXPERIMETAL RESULTS AD AALYSIS In ths secton, we conduct smulaton experment to llustrate the effectveness of the proposed deployment of arshps scheme. In experment, we have consdered a feld of area of km * km, whch s unformly dvded nto * grds. The satellte located at a pont (5km, 5km, 36km). On the one hand, unformly dstrbuted users are generated n the feld; on the other hand, Gaussan dstrbuted users are generated wth ts mean of space poston at the pont (7km, 7km) and of varance 5km, whch s utlzed to measure the on-demand performance. We assume that the attenuaton factor α s, the maxmum dstance that arshps can cover users R s 7km, the maxmum dstance that arshps can communcate wth other arshps h s also 7km and the mnmal safe dstance between two arshps h mn s 3km. In GA, the optmal soluton depends upon these values. We have tred dfferent values of the populaton sze, mutaton probablty and crossover probablty to fnd the best soluton. The best result obtaned s gven as follow: the number of the populaton M s 6, the mutaton probablty s.8, crossover probablty s.8, and the maxmum generaton G s. The scalng factor λ s., and the penalty constant L s. Fg. 4 shows the deployment of dfferent numbers of arshps under gven dstrbuton of users and satellte. In Fg. 4(a), t s notced that the postons of two arshps are approxmately (7km, 7km, km), whch acheves the purpose for the demand of users followng by Gaussan dstrbuton; On the other hand, another arshp s approxmately at the pont (5km, 5km, km), whch may farly cover other areas. Smultaneously, Fg. 4(b-d) show smlar laws. Fg. 5 shows coverage power rates of four grd areas for the cases that λ and λ.. For λ, the deployment of arshps only consders the objectve of entropy that obtans far coverage power for every user, and thus any coverage power rate η s approxmately.5. On the other hand, for λ., a mult-objectve based on the entropy and mnmum delay can (b). The deployment of four arshps. (c). The deployment of fve arshps. (d). The deployment of sx arshps. Fg. 4. The deployment of dfferent numbers of arshps

6 6 6 obtan a trade-off soluton of deployment of arshps, whch may have small delay rather than dentcal coverage power rate. Fg. 6 shows the evoluton of best ftness for the cases that λ and λ.. For λ, the convergence rate s hgh. When the generaton s 45, the best ftness converges to.994, whch s approxmately a global optmal soluton. On the other hand, for λ., when the generaton s 45, the best ftness of the mult-objectve based on the entropy and mnmum delay can converge to.969, thus achevng a trade-off soluton of deployment of arshps. Fg. 5. The coverage power rate of grd areas. Fg. 6. The evoluton of best ftness. VI. 5BCOCLUSIO AD FUTURE WORKS In ths paper, we present a satellte-haps-terrestral system that s dfferent from tradtonal heterogeneous systems. In addton, an optmal model to acheve on-demand deployment of arshps for HAPs wth the objectve of maxmum entropy and mnmum delay s proposed. Then a modfed genetc algorthm s utlzed to optmze the model. Smulaton results ndcate that the method based on maxmum entropy and mnmum delay can acheve a good result for deployment of arshps n HAPs. In the future, the effect of the base statons over deployment of arshps can be consdered. Moreover, the number of arshps could be employed as an objectve to mnmze the cost of deployment of arshps. BACKOWLEDGMET Ths work was supported by the atonal atural Scence Foundaton of Chna (o. 6835). REFERECES [] G. M. Djuknc, J. Fredenfelds and Y. Okunev, Establshng wreless communcaton servces va hgh alttude aeronautcal platforms: a concept whose tme has come? IEEE Commun. Mag., pp.8-35, September 997. [] T. C. Tozer and D. Grace, Hgh-alttude platforms for wreless communcatons, IEE Electroncs and Communcatons Engneerng Journal, vol. 3, pp. 7-37,. [3] A. Mohammed, S. Arnon, D. Grace, M. Mondn, and R. Mura, Advance communcatons technques and applcatons for hgh-alttude platforms, Edtoral for a specal ssue n EURASIP Journal on Wreless Communcatons and etworkng, vol. 8, 8. [4] D. Grace, M. Mohorcc, M. Oodo, M. H. Capstck, M. B. Pallavcn, and M. Lalovc, CAPAIA communcatons from aeral platform networks delverng broadband nformaton for all, IST Moble Communcatons Summt. Dresden, Germany, 5. [5] A. K. Wdawan and R. Tafazoll, Hgh Alttude Platform Staton (HAPS): A Revew of ew Infrastructure Development for Future Wreless Communcatons, Wreless Personal Communcatons, Vol. 4, pp , 7. [6] T. C. Hong, B. J. Ku, J. M. Park, D.-S. Ahn, and Y.-S. Jang, Capacty of the WCDMA system usng hgh alttude platform statons, Internatonal Journal of Wreless Informaton etworks, vol. 3, pp.5-7, 5. [7] J.-M. Park, B.-J. Ku, Y.-S. Km, and D.-S. Ahn, Technology development for wreless communcatons system usng stratospherc platform n Korea, IEEE PIMRC, vol. 4, pp ,. [8] J. Thornton, D. Grace, M. H. Capstck, and T. C. Tozer, Optmzng an array of antennas for cellular cover coverage from a hgh alttude platform, IEEE Transacton on Wreless Communcatons, Vol., o. 3, pp , May 3. [9] F. Dovs, R. Fantn, M. Mondn, and P. Sav, Small-Scale Fadng for Hgh-Alttude Platform (HAP) Propagaton Channels, IEEE Journal on Selected Areas n Communcatons, Vol., o. 3, pp , Aprl. [] D. Grace, G. Chen, P. G. Whte, J. Thornton, and T. C. Tozer, Improvng System Capacty of Broadband Servces Usng Multple Hgh Alttude Platforms, IEEE Transacton on Wreless Communcaton, vol. 4, pp. 7-79, Mar. 5. [] C. Hu, X. Wang, Z. Yang, J. Zhang, Y. Xu, X. Gao, A Geometry Study on the Capacty of Wreless etworks Va Percolaton, IEEE Transactons on Communcatons,. [] G. Zhang, Y. Xu, X. Wang, M. Guzan, Capacty of Hybrd Wreless etworks wth Drectonal Antenna and Delay Constrant, IEEE Transacton on Communcatons,. [3] X. Wang, Y. Be, Q. Peng, L. Fu, Speed Improves Delay-Capacty Tradeoff n MotonCast, IEEE Transactons on Parallel and Dstrbuted Systems,. [4] P. Pace, G. Alo, F. De Rango, E. atalzo, A. Molnaro, and S. Marano, An ntegrated Satellte-HAP-terrestral system archtecture: resources allocaton and traffc management ssues, IEEE Vehcular Technology Conference (VTC4 Sprng), Mlan, Italy, pp87-875, May 4. [5] P. Pace, G. Alo, S. Marano, A multlayered archtecture supportng Qos for multmeda traffc connectons, Proceedngs of the IEEE Vehcular Technology Conference (VTC Sprng), Stockholm Sweden, pp.7-76, May, 5. [6] Ha Yoon Song, A method of moble base Staton placement for hgh alttude platform based network wth geographcal clusterng of moble ground nodes, Proceedngs of the Internatonal Multconference on Computer Scence and Informaton Technology, pp , 8. [7] Davs, L., edtor, Handbook of Genetc Algorthms, Van ostrand Renhold, ew York, 99.