Satellite Channel Markov Model of Ka-band based on Principal Component

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1 JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY Satellite Chael Markov Model of Ka-bad based o Pricial Comoet Yecai Guo College of Electroic ad Iformatio Egieerig, Najig Uiversity of Iformatio Sciece ad Techology, Najig, Chia Najig Uiversity of Iformatio Sciece ad Techology Jiagsu Key Laboratory of Meteorol Observatio ad Iformatio Processig, Najig, Chia guo-yecai@163.com Tao Yua College of Electroic ad Iformatio Egieerig, Najig Uiversity of Iformatio Sciece ad Techology, Najig, Chia Najig Uiversity of Iformatio Sciece ad Techology Jiagsu Techology ad Egieerig Ceter of Meteorology Sesor Network, Najig, Chia yuatao_1988@yeah.et Zhag Xiuzai College of Electroic ad Iformatio Egieerig, Najig Uiversity of Iformatio Sciece ad Techology, Najig, Chia Najig Uiversity of Iformatio Sciece ad Techology Jiagsu Key Laboratory of Meteorol Observatio ad Iformatio Processig, Najig, Chia iuzaizhag@16.com Abstract With the cosideratio of the eistig Ka-bad satellite chael model i data rocessig method deficiecy, the Ka-bad satellite chael roagatio characteristic is aalyzed ad the ifluece of meteorological factors o the satellite chael is discussed. The chael of meteorological factor ricial comoet is obtaied by usig the ricial comoet aalysis ad fuzzy clusterig aalysis method is itroduced ito chael classificatio. The Ka-bad satellite chael multi-sates Markov model is established ad simulated fially. By comarig the level crossig rate ad average fade duratio with the former. The results show that this roosed chael model is more accurate ad effective ad it is sigificat to the Ka-bad satellite commuicatio research. Ide Terms Ka-Bad; Pricial Comoet Aalysis; Fuzzy Clusterig; Rai Attetio; Markov Model I. INTRODUCTION With the develomet demad of satellite commuicatio chael caacity ad the more ad more crowd of the C, Ku bad, it is ecessary for the satellite commuicatio system to work i higher frequecy bad, larger badwidth, ad high sectrum efficiecy. The Ka-bad satellite commuicatio system with widely badwidth, large commuicatio caacity, arrow beam, small size of termial ad strog ability of review the iterferece will become the ievitable tred of the future satellite commuicatio. For the roagatio characteristics of mobile satellite chael, may domestic ad foreig orgaizatios have roosed the chael statistical model i the sigle eviromet, Its market has become the key oit of the iteratioal comaies. Cosequetly, more ad more researchers have begu to egage i the satellite commuicatio research, more ad more coutries ad istitutios have have take art i the develomet ad use of the Ka-bad satellite commuicatio system [1, ]. With the foudatio of the former chael model, first of all, we aalyze roagatio characteristic of Ka-bad satellite chael, such as the multiath, raifall, atmosheric absortio ad atmosheric scitillatio. Secodly, i view of the chael characteristics of the Ka-bad satellite commuicatio, the Ka-bad satellite chael multi-state Markov model is established ad the erformaces are simulated based o ricial comoet aalysis ad fuzzy cluster aalysis method. Satellite chael roagatio characteristic Aalysis Pricial Comoet Aalysis Method Fuzzy clusterig aalysis Establish the Markov model Model erformace aalysis Figure 1. The modelig idea of the multi-states Markov chai model 14 ACADEMY PUBLISHER doi:1.434/jw

2 17 JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY 14 The Fig. 1 is the modelig idea of the multi-states Markov chai model of the Satellite Chael i Ka-bad. The results show that this roosed chael model is more accurate ad effective tha the revious roosed models ad it is sigificat to the satellite commuicatio research. II. KA-BAND SATELLITE CHANNEL PROPAGATION CHARACTERISTIC ANALYSIS AND ITS MODEL I the rocess of sigal trasmitted from the satellite to earth receivig termial, the cloud roduce the shadow effect, due to reflectio ad scatterig of the buildigs, moutais ad so o, the multiath effect is serious. The evirometal characteristics of chaels is show i Fig.. Esecially for ka-bad satellite sigal, due to raifall ad atmosheric absortio, that ca roduce rai atteuatio ad gas absortio. Figure. The evirometal characteristics of chaels A. Multi-Path Effect Reflectig, scatterig ad diffractio caused by multiath effect eists widely i each frequecy of satellite commuicatio ad that may roduce very serious effect o sigal [1]. The study have roved that Rice distributio ca be used to describe multi-ath effect, the amlitude robability desity fuctio ca be eressed as r r + A Ar Rice ( r e( I (, r (1 where I is the first kid of modified zero order Bessel fuctio. is the ower of scatterig comoet, A is the value of lie of sight (LOS, K A / is the Rice factor. B. Shadow Effect Satellite commuicatio eeriece ls is from satellite to earth, the stregth of the sigal will weake whe it ass away the trees, buildigs, ad cloud, etc.. The study have roved that the Logormal distributio ca be used to describe shadow effect[1], the amlitude ad hase of the robability desity fuctio ca be writte as Log 1 (l r- ( r e[- ] ( dr d Log ( 1, (3 where the d ad are the stadard deviatio ad mea, resectively. C. Raifall Characteristics Rai atteuatio effect refers to the ifluece o sigal trasmissio, it could cause the sigal atteuatio ad absortio. The degree of the rai atteuatio is relate to frequecy, raifall rate ad other factors. I lower L-bad ad S-bad chael model, it is scarcely cosider raifall atteuatio [], but with the icrease of the sigal frequecy, esecially le Ka-bad high frequecy bad commuicatio, rai atteuatio may be the mai factors caused commuicatio error, therefore we must cosider the effect of rai atteuatio [3, 4, 5, 6]. The mai effects of rai atteuatio are absortio, scatterig ad radiatio, the secific descritio as follows: Rai Atteuatio. The satellite l caused by raifall ca be eressed as AR (, RLR R (db (4 where LR ( R, (km is the the rai layer legth of the waves which deeds o raifall rate ad elevatio. The atteuatio R (db/km ca be calculated from the ower time law relatioshi R (mm/h. kr (5 R where k is the value of k H or k V, is the value of H ad V. As the frequecy rage from 1 to 1 GHz. Raifall Noise. Electromagetic wave absortio atteuatio caused by raifall could have ifluece o earth statio, this kid of raifall oise reduced to receivig atea iut is equivalet to the atea thermal oise, it has great ifluece o the received sigal to oise ratio. Usually, the higher is the atea elevatio, the smaller is the raifall effect of oise. Raifall oise ca calculated the followig formula. - A/1 Tr (1-1 Tr (6 where the A deote raifall atteuatio(db, Tr is the raifall temerature(7k. Raifall to Polarizatio Effect. Geeral the olarizatio iterferece is measured by XPD (cross olarizatio idetificatio rate which is that the sigals ass through the rai belt, ca be calculated by the followig formulas. XPD U- V( f log A R (7 U C C C C (8 f f 8GHz f GHz V( f.6 GHz f 35GHz (9 14 ACADEMY PUBLISHER

3 JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY where U is the sum of gai i db. V( f is the fuctio of f, C f is the frequece factor, C is lie olarizatio imrovemet factor, C is geograhic gai factor ad C is raidro agle factor. D. Atmosheric Scitillatio Characteristics The so-called scitillatio is refers to the raid sigal amlitude ad hase fluctuate caused by the wave roagatio ath o the small irregularities. Troosheric scitillatio haeed i Ka-bad usually occurs at low elevatio (5 o ~15 o, hot ad humid climate coditios of satellite commuicatio system. That will cause the sigal atteuatio ad ca be described as X ( t l W( t (1 where Wt ( is sigal istataeous value. ITU-R has divided the above factors ito three categories: slowly varyig factors A, fast varyig factors A, ad the o middle factor A (gas absortio, A c (cloud atteuatio, X (the attetio caused by the atmosheric scitillatio, the total value of atteuatio III. A A ( A A X A (11 total o c r KA-BAND SATELLITE CHANNEL ANALYSIS METHOD BASED ON THE PRINCIPAL COMPONENT I this aer, we use ricial comoet aalysis to get mai ifluece factors o the Ka-bad satellite chael [8], the secific stes are show as below. A. The Costructio of Origial Data Matri After collectig Ka-bad satellite chael origial data, we assume that it has samles, each samle has idees, the observed origial data value of show as ca be X (, i 1,,..., ; j 1,,..., (1 B. Origial Data Stadardizatio The key of ricial comoet aalysis is to get ricial comoet, its tool is covariace matri. Because covariace matri is suscetible to ide of the dimesio ad the order of magitude, we must make the origial data tur ito stadardizatio data via some stadardizatio rocessig. where variable ad j 1 i 1 -j (13 s j is the samle mea of the j th s 1 j ( - j i 1 is the variace. The correlatio coefficiet matri of the samle for ca be writte as R ( r (14 where 1 r. i, j 1,,..., ki kj k 1 The calculatio of the related hysical quatity. I the sectio, we must calculatio related hysical quatities, such as eigevalues, eige vector, variace cotributio rate, cumulative variace cotributio rate ad the etractio of ricial comoet. Assume that 1,,..., deote the eigevalues ad 1, the corresodig eige vector is a1, a,, a. If the cotributio rate of the former r eigevalues has reach to 85%, we ca obtai the former ricial comoet. Pricial comoet scores are the ew data of the origial data i the ew coordiate system defied by ricial comoet where j 1,,, r. IV. Y a (15 j kj k k 1 FUZZY CLUSTERING METHOD OF KA-BAND SATELLITE CHANNEL It is the most imortat to determie the state of Ka-bad multi-state satellite chael. I some revious researches, the chael was divided ito good-state, bad-state or good-state, medium-state, ad bad-state, accordig to their ersoal eeriece. These methods were simle ad rough ad had a lot of roblem, such as, whether this state divisio is reasoable, how to defie the above three states ad what the stadard of the state divisio is suitable, etc.. This sectio will give fuzzy clusterig aalysis method, which cotais the state divisio method of the multi-sates satellite chael i theory [9]. A. Data Stadardizatio We determie data samles ad feature variables (calibratio at first. The elevatio agle, doler effect, multiath effect, ad shadowig atteuatio effect are the feature variables ad eressed them as elevatio degree ( e, doler frequecy shift ( f d, the mea value (, variace ( of LOS ad Rice/Rayleigh atteuatio factor ( K. The origial data are show as (16 I order to rule out the differeces of differet data, we eed to stadardize the four hysical quatities i the above. The stadardizatio rocedure is show as follows Traslatio-stadard. The deviatio trasform ( reresets the characteristic variables ( i 1,,..., ; k 1,,3,4,5 (17 14 ACADEMY PUBLISHER

4 174 JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY 14 where 1 1 k, k ( k i1. i1 s Traslatio-rage trasformatio. After the mea value of each variable is, the stadard deviatio is 1, ad the ifluece of dimesio has bee elimiated, but the may ot be i the iterval [,1]. Traslatio-rage trasformatio mi( 1 i ma( mi( 1 i 1 i We ca make 1 ow. ( k 1,,3, 4,5 (18 B. Establish Fuzzy Similar Matri The et is the rocess of establishig fuzzy similar matri. Accordig to agle cosie method, the elemets of similar matri is writte as r m k1 jk m m jk k1 k1 (19 We ca obtai fuzzy similar matri R of the LMSC ad R ( r. C. Dyamic Fuzzy Clusterig I the fuzzy clusterig aalysis, it is require that the equivalece matri should have refleivity, symmetry ad trasitivity, but there are oly two former roerties i the geeral fuzzy similar matri. Therefore, we eed to reform the fuzzy similar matri as follow R R R R R 4 ( k1 k ( m (, ma(mi(, (1 R R R r mm r r rji k 1 k t( R R ( t mm ( After obtaiig the fuzzy equivalece matri tr (, we ca array the differet elemets from big to small accordig to the value order of ad obtai the dyamic clusterig figure of Ka-bad. TABLE I. V. MULTI-STATES MARKOV SATELLITE CHANNEL MODEL OF KA-BAND We ca obtai the reresetative Ka-bad satellite chael states from the above aalysis. Whe the mobile termial moves alog with a certai ath, the several chael states will covert mutually. The rocess ca be eressed by the multi-state Markov model. The detail rocedure of the Markov model is give by the followig stes. A. Determiatio of Every Sigle State Statistical Model Accordig to the fuzzy clusterig method, we ca get the best clusterig umber of the Ka-bad is. The first state of the LMSC follows the Rayleigh model, the secod obeys the Suzuki model, ad the third oe obeys the Rice model,..., the th state obeys the Suzuki distributio. Their resective arameters ca be gaied from the origial data. B. Establishmet of Ka-Bad Satellite Chael Markov Model Ka-bad satellite chael Markov model ca be described as the trasitio matri P ad state matri S. The states trasitio matri of Markov model is writte as P ( i, j (3 deotes the trasitio robabilities from the state i to the state j, ad j1 1,( i 1,,,, the state vector S [ s1, s, s ]. This Markov chai is a eriodic, irreducible ad ormal, so its steady state distributio eists ad is equal to the limit distributio, the VI. S S (4 SIMULATION AND COMPARISON I order to validate the validity of Ka-bad satellite chael model, the relevat data of Najig area was used to simulate the model. Assume that the satellite's height is km, trasmissio frequecy is 3 GHZ, vehicle termial movemet seed for 36 km/h. Accordig to ITU-R related material, we ca get the origial data of satellite chael. MEASURED DATA K A R (db A (db A c (db Tr (K XPD (db X (db L( bf db(db ACADEMY PUBLISHER

5 Level crossig rate( db Average fade duratios( db Received sigal level (db JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY Accordig to fuzzy clusterig method, we ca kow that the best clusterig umber of the Ka-bad is 3, so the Markov model has three states S [ s1, s, s3 ]. We divide the measured data (sigal eveloe ito 3 states. The evelo from -5dB to -15dB are s 1, from -16dB to -6dB are s, from -6dB to -36dB are s 3. The state series S={,,,1,3,3,1,1,,,3,1,3,1,1,,,3,,,1,,,1,1,, 3,1,,,3,1,,3,1,,,,3,1,,3,,3,1,,3,1,,3,,3,3,1,1,3,,3,3,,1,,.1,1,3,,}. The trasitio matri P ad state vector S ca be got from the state divisio series state 1 state state Traveled distace (m MD GMM PAMM Figure 3. State divisio Sigal level (db/rms Figure 4. Average fadig duratio MD GMM PAMM most imortat idicators of chael roerties i satellite chael models. Esecially, whe the sigal level is less tha db []. We ca erceive that the simulated average fade duratio, level crossig rate based o ricial comoet aalysis are more agreeable with the measured data tha that oe s based o geeral model. The simulatio of ricial comoet aalysis Markov model i low level shows better coicide tha geeral Method [1]. The simulatios demostrate that the simulatio model is effective. So the ricial comoet aalysis Markov model has some realistic meaig. VII. SUMMARY The Ka-bad satellite chael multi state model based o ricial comoet aalysis is roosed based o the aalysis of Ka-bad satellite chael trasmissio characteristic. The roosed model is better tha some revious oe. Firstly, the ricial comoet aalysis method ad fuzzy weighted aalysis method are alied to satellite chael modelig. Mathematical modelig method is used to solve some key roblems i the chael modelig [7]. Secodly, The ifluecig factors of satellite chael etire l are cosidered, such as free sace loss, cloud atteuatio, rai atteuatio, atteuatio of troosheric scitillatio. The isufficiet of the former models which just cosider oe or several factors i a model are overcome. Further, the roosed model has strog ortability because of the mai chael characteristic aalysis data are from the ready-made model of ITU-R i this aer, the related data ca be calculated accordig to the local meteorological statistics. Fially, the most imortat two order statistics(afd ad LCR of the measure of chael roerties are obtaied by usig the comuter simulatio, the correctio of roosed chael model ca be verified by the comariso of simulatio results ad measured data, ad the model's ractical sigificace ca be illustrated. ACKNOWLEDGMENT This work is Project suorted by the Peak of Si Major Talet Cultivate Projects of Jiagsu Provice (No.86, 1 Jiagsu Provice Uiversities Sciece, Techology Achievemet Idustrializatio Project (No.JHB1-9, the major roject of Uiversity Natural Sciece of Jiagsu Provice (No. 13KJA511, A Project Fuded by Priority Academic Program Develomet of Jiagsu Higher Educatio Istitutios(PAPD, Uiversity Postgraduate Research ad Iovatio Projects of Jiagsu rovice (CX1B_33Z Sigal level (db/rms Figure 5. Level crossig rate Accordig to the Matlab simulatio of the above arameters, we ca get the secod order statistics (average fadig duratio ad level crossig rate ad they are show i Fig. 4 ad Fig. 5. The average fadig duratio (AFD ad level crossig rate (LCR are the REFERENCES [1] Gao Diabo, Che Xihe, "Lad Mobile Satellite Commuicatios Chael Simulatio ad Certaity Model Aalysis", Joural of Chagchu ost ad commuicatios college, vol. 53, No. 1, , Jue 1. [] C. Alasseur, S. Scalise, L. Husso, ad H. ErstA, "Novel Aroach to Model the Lad Mobile Satellite Chael through Reversible Jum Markov Chai Mote Carlo 14 ACADEMY PUBLISHER

176 JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY 14 Techique", IEEE Tras. Wireless Commuicatios, vol. 1, No. 1,. 189-194, Jue 8.

[4] Michael Cheffea, "Chael Simulator for Lad Mobile Satellite Chael alog Roadside Trees", IEEE trasactios o ateas ad roagatio, vol. 13, No. 11,. 84-844, October 11. [5] M. Milojević, M. Haardt, E.

[6] She Dogya, Rog Jia, "The Si-State Markov Model for Lad Mobile Satellite Chaels", Microwave Proagatio Ad Emc Techologies For Wireless Commuicatios, IEEE Iteratioal Symosium,. 9-94, March 5.

6 176 JOURNAL OF NETWORKS, VOL. 9, NO. 7, JULY 14 Techique", IEEE Tras. Wireless Commuicatios, vol. 1, No. 1, , Jue 8. [3] Sayata Hazra, Abhit Mitra, "A ew lad mobile satellite chael model with akagami-q distributio", 1 Natioal Coferece o Commuicatios, , Christchurch, New Zealad, October 1. [4] Michael Cheffea, "Chael Simulator for Lad Mobile Satellite Chael alog Roadside Trees", IEEE trasactios o ateas ad roagatio, vol. 13, No. 11, , October 11. [5] M. Milojević, M. Haardt, E. Eberlei, A. Heuberger, "Chael Modelig for Multile Satellite Broadcastig Systems", IEEE Tras. Broadcast, vol. 4, No. 5, , July 9. [6] She Dogya, Rog Jia, "The Si-State Markov Model for Lad Mobile Satellite Chaels", Microwave Proagatio Ad Emc Techologies For Wireless Commuicatios, IEEE Iteratioal Symosium,. 9-94, March 5. [7] Yag Migchua, "Markov Chai Based Two-State Satellite Mobile Chael Model ", Vehicular Techology Coferece 11 IEEE,. 1-14, Jauary 11. [8] Che Xiutig, "The Alicatio of Three State Chael Model i the Mobile Satellite Commuicatio System", Joural of Harbi Istitute of Techology, vol. 33, No. 1, , May [9] She Dogya, "Mobile Satellite Commuicatio Chael Model ad Simulatio Based o the Ideedece of the Shadowig", Joural of Yua Uiversity, vol., No. 4, , November 8. [1] Wag Guowei, "A Weighted Sace Fuzzy Dyamic Clusterig Algorithm", Comuter Egieerig ad Alicatios, vol. 3, No. 1, , May 1. [11] Ferado Pérez Fotá, "Statistical Modelig of the LMS Chael", IEEE Tras. Vehic. Techol, vol. 3, No. 1,. 4-44, Jauary 1. he has bee egaged i teachig ad research work i Najig Uiversity of Iformatio Sciece ad Techology ad obtaied the PhD. from Northwester Polytechical Uiversity i 3. At reset, his iterest is i meteorological telecommuicatio techology, uderwater commuicatio theory ad alicatio, etc. Yua Tao, male, bor i 1988, Master, he graduated from Aqig Teachers College i 11, her research iterest is i meteorological satellite commuicatio research. At reset, his iterest is i meteorological commuicatio techology, uderwater commuicatio theory ad alicatio, etc.. Zhag Xiuzai, male, bor i 1979, lecturer egaged i teachig ad research work at Najig Uiversity of Iformatio Sciece ad Techology, obtaied a master's degree of atmosheric remote sesig sciece ad techology i NUIST i Jue 9, ad erolled i doctoral meteorological iformatio techology ad security rofessioals i Setember 9 i NUIST, curretly egaged i meteorological satellite commuicatios techology research work. Guo Yecai, male, bor i 196, Ph.D., Professor, doctoral tutor of meteorological iformatio security ad techology rofessioal. I 6, he was the atioal wiers of atioal outstadig doctoral dissertatios. He was the traiig object of "si talets eak" i Jiagsu rovice i 8 ad oe of the leaders of the advatage discilie "sesor etwork ad moder meteorological equimet" of colleges ad uiversities of Jiagsu rovice i 9. After graduatig from Aqig Teachers College i 1986, 14 ACADEMY PUBLISHER

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