IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 Opimal configuraion algorihm of a saellie ransponder M S Sukhodoev, I I Savenko, Y A Marynov, N I Savina and V V Asmolovskiy Tomsk Polyechnic Universiy, 30, Lenina ave., Tomsk, 634050, Russia Tomsk Sae Universiy, 36, Lenina ave., Tomsk, 634050, Russia E-mail: smike@pu.ru Absrac. This paper describes he algorihm of deermining he opimal ransponder configuraion of he communicaion saellie while in service. This mehod uses a mahemaical model of he payload scheme based on he finie-sae machine. The repeaer scheme is shown as a weighed oriened graph ha is represened as plexus in he program view. This paper considers an algorihm example for applicaion wih a ypical ransparen repeaer scheme. In addiion, he complexiy of he curren algorihm has been calculaed. The main peculiariy of his algorihm is ha i akes ino accoun he funcionaliy and sae of devices, reserved equipmen and inpu-oupu pors ranged in accordance wih heir prioriy. All described limiaions allow a significan decrease in possible payload commuaion varians and enable a saellie operaor o make reconfiguraion soluions operaively.. Inroducion The complexiy and funcionaliy of he modern saellie payload are consanly increasing. I allows increasing he payload hroughpu and using saellie posiions effecively on he geosaionary orbi. Thus, asronauics has an increasing problem concerning he scheme size of he onboard communicaion equipmen (OCE). I is possible o specify he following facors ha lead o payload srucure complicaion: he number of OCE ransponders; funcional backup; he use of scheme wih muliple frequency ransformaions; he provision of a sraigh and reverse communicaion link. Modern saellie payload may include up o 00 ransponders and each ransponder can include up o 0 devices (along wih swiches). Therefore, payload communicaion marix can increase significanly forcing he payload scheme increase up o a huge size. Hence, he manual saellie payload reconfiguraion becomes a difficul ask for he operaor. The curren paper suggess deermining he algorihm of OCE opimal configuraion [5]. The auhors offer o consider OCE as an oriened weighed graph. Also his paper describes a mahemaical model based on auomaa heory ha allows defining crieria ha should be considered during deerminaion of he ransponder opimal configuraion.. Relaed work Scieniss [] define 3 asks arising when deermining he opimal saellie payload configuraion: Conen from his work may be used under he erms of he Creaive Commons Aribuion 3.0 licence. Any furher disribuion of his work mus mainain aribuion o he auhor(s) and he ile of he work, journal ciaion and DOI. Published under licence by Ld
IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 Iniial saellie payload configuraion. This ask occurs a he repeaer designing sage and consiss in defining of iniial posiions of swiches for he opimal iniial saellie payload configuraion before saellie sars. Mainenance configuraion. This ask requires minimizaion of he number of swiches as well as he number of heir revoluions. Mainenance configuraion wih acive ransponders. This ask arises in case of acive equipmen failure. When solving his ask i is necessary o decrease inacive ime of acive channels and minimize he number of roaing swiches. The auhors sugges mahemaical models for each of he asks described above. Also he paper consiss of he descripions of successful algorihms, developed by he auhors. Their models allow finding all possible OCE configuraions, which are no always necessary for he operaor. In aricle [] oher scieniss sugges using he breadh-firs search recurren algorihm o search all possible ways of channels commuaion. The conduced experimens showed he effecive resuls of a small commuaion nework (seven swiches and en amplifiers) bu i is expeced ha he algorihm will be limied due o a significan ime increase for daa processing on huge commuaion nework. We should noe ha i is of grea imporance for he operaor o find a single opimal soluion for a specific OCE configuraion sae insead of all possible configuraions. 3. The use of auomaa heory for creaing a repeaer mahemaical model The applicaion of auomaa heory allows considering OCE as a mahemaical sysem wih inpu and oupu channels. This mahemaical sysem can be only in one finie condiion and a one discree insan in ime ha allows describing he ways of is sae ransiions. In auomaa heory he noion of an absrac auomaon (AA) is described by a six-componen se: A = (S,X,Y, δλ,,s ), where S = { s,,s z,,sz} se of saes, or AA alphabe; X = { x,,,, xz xz} se of inpu signals, or inpu AA alphabe; Y = { y,,y z,,yz} se of oupu signals, or oupu AA alphabe; δ ransiion funcion of AA, which brings a sae inpu signal pair ( s k,x f ) ino accord wih AA sae, (s i ), ha is, si = δ( s,x ) k f, si S. λ ransiion funcion of AA, which brings a sae-inpu signal pair ( sk,x f ) ino accord wih AA sae ( y i ), ha is, yi = λ( sk,x f), yi Y. s iniial sae of a finie auomaon. The absrac auomaon can be represened graphically as a black box ha convers inpu signals o oupu ones []. X Y АА Figure. Graphic represenaion of an absrac auomaon 3.. OCE as a finie Moore machine In OCE here are wo main processes: ransformaion of he inpu frequency ino he oupu one (receiving device); signal power amplificaion.
IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 Figure. Graphic represenaion of OCE as a finie auomaon A Mealy auomaon has been chosen for descripion of he mahemaical model of he repeaer as he repeaer sae depends on inpu signal ses. Swiches posiions and acive devices saes define OCE sae a any momen of ime. P= { p,,p z,,pz} finie se of swiches posiions; D= { d,,,, dz dz} finie se of device saes (on/off); T = {,,,, z Z } finie se of ransponders, which are deermined by OCE configuraion, = P, D, where P posiions of swiches belonging o swiches posiions and devices saes i { } OCE, P P. D saes of devices belonging o OCE, D D. S {,, i = Z} Therefore, i may be concluded ha he main ask of ransiion funcion δ is a ransponder commuaion by calculaing he required posiion of swiches P and devices saes D relaively curren iniial sae s k and inpu frequency x f. Auomaa heory implies ha only one symbol from he inpu se can be fed o he device inpu a a ime. Thus, he main purpose of he ransiion funcion is o find he opimal commuaion of one ransponder. The opimal ransponder commuaion is a minimal number of swiches in he ransponder, ha is, he power of se P ends o minimum P min where P he number of ransponder swiches. The quaniy of possible OCE saes is finie and differs due o he number of swiches of differen ypes, which can ake several posiions depending on he ype and possible saes of devices. I is defined as follows: n m n = i= j= i ( j ) where m ransponders number, n ransponder devices number, p i j - ransponder swiches, s funcion deermining he oal quaniy of saes of he swich according o is ype. The saes ransien ime is defined by he urn-on ime of one ransponder, which is dermined by he characerisics of he devices conained in he ransponder. Inpu and oupu ses are he ses of inpu and oupu signal frequencies defined by he repeaer configuraion. The oupu frequency, which is defined by he frequency ransform funcion, will correspond o inpu frequency. This funcion depends on OCE configuraion/sae s i. The formula considering a muliple frequency ransformaion is as follows: d s p (, ) (, ), x f p + f p = y i k i m i i k= 0 m= 0 where d he number of reducing converers belonging o he ransponder, u - he number of increasing converers belonging o he ransponder, p d frequency decreasing converer pd P, pu frequency increasing converer P, f funcion of calculaing he converer frequency. pu u 3
IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 Modelling ask is solved using an OCE design framework []. This mahemaic model () allows he framework o realize he required funcions, namely: calculaions of he oupu frequency of he ransponder, specifying he crieria of selecion of he repeaer opimal configuraion, which are considered by he shores-pah algorihm described below [7]. 4. Descripion of he shores-pah algorihm There are many algorihms used for finding as shor pah as i is possible, such as he algorihms of Dijksra, Floyd Warshall, А*, An colony [4]. The mos suiable algorihm is Dijksra's algorihm. The algorihm proposed in his paper is a paricular case of he repeaer reconfiguraion ask. The essence of his algorihm is finding he opimal configuraion of a ransponder aking ino accoun he following limiaions: use of a minimal number of ransponder devices; working capaciy and he sae of onboard equipmen (on, off or malfuncion); back-up equipmen compliance of inpu pors wih oupu pors ranged according o heir prioriy. A program descripion of he repeaer schema is represened as a graph and is sored in he mulilinked lis. I is conneced wih he represenaion of graph nodes by he full-fledged sofware models of he devices wih heir prese behaviour and properies. I allows defining he device saus, is ype or he swich posiion. The lis is formed during he algorihm iniializaion and has algorihm complexiy O (n ). This lis sores he objec poiners, as well as he poiners o inpu and oupu devices wih differen degrees of conneciviy. These srucures are called plexuses. Figure 3. Graph descripion using plexus This proposed algorihm uses a prioriy marix o opimize he search of he ransponder opimal configuraion. This marix consiss of inpu and oupu pors sored by prioriy. Le us consider a repeaer acive scheme wih an acive ransponder and malfuncion devices (Figure 4). This scheme consiss of a receiving device, filers, power amplifiers, an oupu muliplexer and swiches allowing he repeaer reconfiguraion. The acive ransponder is marked up by a bold line, he reserved devices - by haching, and ou of service devices are marked up by double haching. 4
IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 Figure 4. Example of an acive scheme of he repeaer The curren repeaer configuraion should be aken ino consideraion when he repeaer scheme ransforms ino o a weighed direced graph. For his purpose i is necessary o follow he rules given below: all devices are marked as graph nodes; all possible device links are presened as arcs ha connec corresponding graph nodes. A ha one considers he direcions, a which he signal passes in he ransponder; he weighs (lenghs) of he arcs ha are included ino he reserved devices are se o be equal o a maximal number of swiches in one marix of swiches. The res weighs are se o be equal o. This weigh disribuion provides he use of he reserved devices only in case when all possible varians of pass hrough he basic devices are impossible; he links of malfuncion devices are no represened in he graph (for example, C 5 and H devices in Figure 5); he swiches, hrough which acive ransponders pass, are represened as wo nodes in he graph. Their arcs are conneced using he curren OCE scheme configuraion and sae (for example, B swich is represened as B. and B. nodes conneced respecively). The weighed oriened graph corresponding o he example of he acive scheme of he repeaer is represened in Figure 5. 5
IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 Figure 5. Weighed oriened graph corresponding o he curren repeaer scheme Furher, i is necessary o idenify he shores roue from one node ha represens an inpu por o all possible graph nodes. To solve his ask Dijksra's algorihm is proposed. This algorihm allows finding he shores roues from one node o all possible graph nodes in he weighed oriened graph for arcs wih posiive value weigh. Thus, we can idenify all possible repeaer configuraions for he chosen inpu por. Figure 5 shows he example of his soluion for A inpu node. The value of he shores roue o each node is marked up in he cener of each node and is graphically represened using bold graph arcs. Furher, he operaor is offered o choose one of he possible ransponder configuraions according o he marix of he prioriy oupu pors. This considers he curren repeaer configuraion and devices saes. In case oupu por K3 has a higher prioriy for inpu por A he possible shores roues for he specified ransponder are he following: A - B - B4 - C6 - D4 - E4 - F4 - G4 - G5 - H5 - J9 - J - J - J3 - K3 A - B - С3 - В - D4 - E4 - F4 - G4 - G5 - H5 - J9 - J - J - J3 - K3 A - B - C3 - D - E - F - G - G. - G5 - H5 - J9 - J - J - J3 - K3 A - B - B4 - C6 - D4 - E4 - F4 - G4 - H4 - J7 - J6 - J5 - J4 - J3 - K3 A - B - С3 - В - D4 - E4 - F4 - G4 - H4 - J7 - J6 - J5 - J4 - J3 - K3 Thus, he proposed algorihm complexiy will be equal o O(n ) a wors, and a bes i will be Ω ( n). I has been experimenally proven ha finding he shores roue for OCE, conaining abou 300 devices and abou 00 swiches on PC wih Inel Core i3 processor, is less han second. This allows he operaor o make promp decisions abou OCE reconfiguraions or o execue i in an auomaic mode. References [] Gulgonul S E, Koklukaya, Erurk I and Tesneli A Y 0 Proceedings of he Firs IEEE Aerospace and Elecronic Sysems Sociey (AESS) European Conference on Saellie Telecommunicaions 6400090 [] Sahakis A, Danoy G, Bouvry P, Talbi E and Morelli G 05 Engineering Opimizaion 47() 709-734 6
IOP Conf. Series: Maerials Science and Engineering 4 (06) 0098 doi:0.088/757-899x/4//0098 [3] Savenko I I, Sukhodoev M S, Tsapko S G and Simonov P K 05 Inernaional Siberian Conference on Conrol and Communicaions, SIBCON 05 7478 [4] Savenko I I, Sukhodoyev M S, Kosmynina N A, Ryzhkov D N and Tsapko S G 04 Componens of Scienific and Technological Progress 9() 3-33 [5] Marynova Y A, Marynov Y A, Musafina D B and Asmolovskiy V V 04 Proceedings of 04 Inernaional Conference on Mechanical Engineering, Auomaion and Conrol Sysems, MEACS 04 6986883 [6] Teresa M Braun 0 John Wiley & Sons, New York, A.B.D. [7] Ozhiganov A A 03 Tuorial 7