The Application of GIS and Diversity Combining in Designing of Wireless Communication Systems in the Presence of Fading

Transcription

1 Recent Advances n Geodesy and Geomatcs Engneerng The Applcaton of GIS and Dversty Combnng n Desgnng of Wreless Communcaton Systems n the Presence of Fadng DRAGANA KRSTIC, MARKO KOVACEVIC, GORAN STAMENOVIC, ALEKSANDAR STEVANOVIC, DEJAN RANCIC Department of Telecommuncaton, Department of Computer Techncs Faculty of Electronc engneerng, Unversty of Ns Aleksandra Medvedeva 4, Ns SERBIA dragana.krstc@elfak.n.ac.rs Abstract: - In ths paper, the applcaton of Geographc Informaton System GIS n desgnng of wreless communcaton systems wth dversty combnng n the presence of Rce fadng wll be presented. The applcaton of these solutons n desgnng of wreless telecommuncatons systems smplfes t, makes the tme requred for ts confguraton shorter and gves better economc effects. The obtaned gan whch has been made usng dversty technques s shown n some fgures. Key-Words: - Dversty Technque, Equal Gan Combnng EGC, Geographc Informaton System GIS, Rce fadng Introducton One of the most etensve applcaton of Geographc Informaton System GIS s n telecommuncatons, partcularly n the plannng, nstallaton and mantenance of telecommuncaton systems. The development of a broad and publcly avalable GIS has long been one of the strategc nterests of the developed countres due to the mpact that such a system can have on the development of socety as a whole. Therefore, there are many nvestments, contnually nvestgaton and workng on mprovng the estng system. There are numerous software tools whch deal wth calculaton of range of wreless communcaton systems. Some of them are less and some are more specalzed. These systems can be used n desgnng of wreless and moble telecommuncaton systems, radar networks, and rado-relay lnks wth mportant savngs n tme, human and materal resources because the most of network desgn works s the computer's work, and there are not gong outsde. Fundamental obstructon n wreless telecommuncaton systems s fadng. The fadng s changng of sgnal envelope at the recever. It may be fast or slow fadng. Fast fadng s caused by multple sgnal propagaton paths. Fast fadng can be modelled by Rce, Raylegh, Nakagam-m, Nakagam-q, Webull, Hoyt or other probablty densty functons []. The slow fadng s caused by the effect of shadows. Ths fadng s modelled usually by lognormal or gamma dstrbuton. The most often way to mtgate fadng nfluence on system performance s dversty technque []-[5]. The applcaton of GIS n desgnng of wreless communcaton systems wth Selecton Combnng SC combnng n the presence of Rce fadng s presented n [6]. In ths paper, the applcaton of GIS and Equal Gan Combnng EGC wll be consdered. Mathematcal Problem Formulaton In ths paper, a transformaton of the two random varables wth Rce dstrbuton and ts applcatons n wreless dgtal communcaton systems wll be consdered. The two random varables wth Rce dstrbuton are transformed nto a random varable. A new random varable s equal to the sum of two random varables wth Rce dstrbuton. The probablty densty and jont probablty densty of ths random varable and ts frst dervatve are determned. Ths random varable s obtaned as the sgnal at the output of the EGC combner wth two nputs that are used to reduce the mpact of fadng on system performance [7, 8]. The Rce fadng appears at the entrances of the combner. The system error probablty and the outage duraton can be determned by usng these probablty densty functons [9]-[]. ISBN:

2 Recent Advances n Geodesy and Geomatcs Engneerng The sgnal envelope n wreless communcaton systems has often Rce probablty densty. When there s a drect component of the waves wth more scattered components that are resultng n the refusal, refracton, scatterng and bendng of electromagnetc waves they can be descrbed wth Rce dstrbuton []. It can be shown, by the applcaton of the central lmt theorem, that the probablty densty of equvalent sgnal envelope at the recever s Rce. Ths knd of fadng occurs n a varety of satellte telecommuncaton systems, rado relay for telecommuncaton systems wth mcroand macro-dversty system and so on. Let and be two Rce non-dentcal and noncorrelated random varables. Ther probablty densty functons are: + A A p e I,,. By seres epanson of the Bessel functon t s obtaned: + A A e! p + A e f A,, e,, a f A The cumulatve probablty denstes are: t e,, F p t dt a t f A t dt + t a f A,, t e dt,, γ, a f A 3 Frst, the sum of two Rce dstrbuted random varables wll be consdered. The probablty densty of the sum of two Rce random varable s equal to the convoluton's ntegral of the probablty densty of ndvdual summands. The cumulatve probablty densty of the sum of two ndependent random varables, Rce dstrbuted, s obtaned by the ntegraton of the probablty densty of the sum of two ndependent random varables, Rce dstrbuted. The characterstc functon of the sum of two ndependent Rce dstrbuted random varables s equal to the product of two characterstc functons of Rce dstrbuted adders. The moments of Rce's sum of two random varables can be epressed dependng on the ndvdual moments of Rce dstrbuted adders. The central moments of random varables can be epressed accordng to the ordnary moments of the same random varable. Let: + 4 Then, Probablty densty functon of s: p p p d + A A p e I, e f A,, p a a e f A,, d p k k a f A,, k! k a e f A,, d p d a k! k k f A,, + k+ a e f A,, p da k! + k+ k k k f A,, k k k k + k+ A, e f, a 9 The statstcal characterstcs of the sgnal envelope at the output of dual EGC combner can be calculated by usng ths probablty densty obtaned by the sum of two Rce dstrbuted random ISBN:

3 Recent Advances n Geodesy and Geomatcs Engneerng varables. Hence, the ndependent and nondentcal Rce fadng s appeared at the nput of EGC combner. Now, the cumulatve probablty densty of the combner output sgnal, the characterstc functon of the combner output sgnal, the moments of the EGC combner output sgnal, the error probablty for coherent and noncoherent system, that uses a dversty technque to reduce the mpact of Rce fadng on system performance and the system outage probablty, can be determned. The characterstc functon of the sum + s: M s M s M s k a s M s f A,, k! k k Γ + a s k + k k k! k f A,, Γ + 3 k + In ths way, we can determne the characterstc functon of the sum of two Rce dstrbuted random varables. Ths s very mportant for dversty systems usng EGC combner. For ths combner the sgnal at the output s equal to the sum of the sgnal from ts nput. In ths way one can determne the characterstc functon of the sgnal at the output of dual EGC combner n the presence of Rce fadng. It can be calculated the system error probablty and the system outage probablty by usng ths characterstc functon. The moments are sgnfcant: the mean value of the random varable. Because of ths, let calculate the moments of Rce dstrbuted random varables. The moment of the n-th order of s: n n n n m p d m a e d n n 4 5 n+ +,, m a f A e d 6 a n,, Γ + mn f A n + 7 The mean value of s: a f A,, Γ + + The root mean square value of s: a f A,, Γ + + The varance s: The moment of the n-th order of s: a n f A,, Γ + n n + The mean value of s: a f A,, Γ + + The root mean square value of s: a f A,, Γ + + The varance of s: The moment of the n-th order of the sum + s: n n n n n n n n + 5 n n a n f n + A,, Γ + n a f + A,, Γ + 6 The moments of the sum of two random Rce dstrbuted varables can be determned by usng these formulas, where the moments of summands are known. Ths formula s obtaned usng a bnomal form. In a smlar way, we can determne the central moments. Moments are mportant parameters of a random process because the ISBN:

4 Recent Advances n Geodesy and Geomatcs Engneerng probablty densty of a random varable can be determned by usng them. Then, the error probablty of wreless telecommuncatons systems can be determned by usng ths probablty densty functon. In ths way, we can determne the power of EGC dversty system that s used to reduce the mpact of Rce fadng on system performance. The jont probablty densty functon of and ɺ s: + A ɺ A β p ɺ ɺ e I e π β 7 ɺ β ɺ ɺ,, π β p e f A e 8 Ths s an epresson for the jont probablty densty of the sgnal and ts frst dervatve. Random process whch s obtaned as the frst dervatve of Rce random process s Gaussan random process. The mean value of obtaned Gaussan random process s zero. The varance of ths process s equal to: π f m Ω where f m s mamal frequency and Ω s bquadratc mean value of the sgnal. Rce random process and dervatve of Rce random processe are ndependent and these processes are n quadrature. The level crossng rate can be determned by usng the jont probablty densty of the sgnal and ts dervatve. The level crossng rate s equal to the mean value of the frst dervatve of sgnal. The jont probablty densty functon of and ɺ s: + A ɺ A ɺ ɺ π β p e I e β 9 ɺ a β ɺ ɺ,, π β p e f A Let t be: + ɺ ɺ + ɺ 3 3 ɺ ɺ ɺ The condtonal jont probablty densty of and ɺ s: p ɺ ɺ J p, ɺ ɺ ɺ where: ɺ 3 ɺ J ɺ ɺ ɺ 33 By substtutng and averagng t s obtaned: ɺ p ɺ ɺ d dɺ p, ɺ ɺ p ɺ p d d πβ ɺ ɺ ɺ e e ɺ ɺ β f π A,, ɺ β e e f, β A, 33 Ths s an epresson of the jont probablty densty of the sum of two ndependent Rce random varables and ts frst dervatve. Usng ths epresson t can be determned the jont probablty densty of the sgnal and ts dervatve at the et of EGC combner wth two nputs when there s a Rce fadng. Ths combner s used to reduce the effect of fast Rce fadng on the system performance. The average level crossng rate of the output sgnal, for the value whch s equal to the threshold, can be calculated by ths jont probablty densty. One can determne the average outage duraton,whchs an mportant parameter of the telecommuncaton system, can be determned from the quotent of the outage probablty and level crossng rate. 3 Performances of Software Component for Calculaton of Wreless Telecommuncaton Systems 3. System model Below we wll descrbe mplemented software component ncludng system archtecture wth key Use-Case Dagrams and other mportant UML dagrams. Snce the system was developed usng Ratonal Unfed Process RUP methodology for software development [3], the system wll be ISBN:

5 Recent Advances n Geodesy and Geomatcs Engneerng descrbed, accordng to the RUP templates for system modelng, and 4+ model system [4]. Logcal vew Process vew Scenaros Fg. 4+ vew model Development vew Physcal vew Ths model presents, n fact, fve dfferent vews of the system, wth dfferent aspects, whch are ntertwned:. User vew of the system - a descrpton of archtecture, presented wth seres of use cases or scenaros, whch descrbe the sequence of nteractons between objects and processes. In essence, a user vew of the system s a descrpton of the functonalty of the system and s used to dentfy the system archtecture as well as ts valdaton;. The logcal archtecture of the system - descrbes the most mportant classes n the system and ther organzaton level; 3. Processng system archtecture - descrbes the most mportant processes n the system and ther organzaton; 4. Implementng the system model - descrbes the mplementaton of the software components; 5. The physcal model of the system - descrbes the hardware used n the system. 3. User s vew User's vew s presented wth a seres of use cases of the system organzed nto charts accdental use. User's vew of the system s gven by the dagram n Fg.. As one can see, there s one use case - the calculaton of range of a wreless telecommuncaton channel. The actors: Benefcary - A person who mports the necessary nformaton on the recever, transmtter, and telecommuncatons channel and start calculatng the range and error probablty of a wreless telecommuncaton channel and vsualzaton of range of a wreless telecommuncaton channel. The cases of use: -The calculaton of range of telecommuncaton channels Short descrpton of basc course:. The user, by clck on the tem Sgnal range ; from the Tools menu opens dalog bo for the calculaton of-wreless telecommuncatons channel range.. The user ntates, by double-clck on the map, marks drawng at the poston of clcked pont and dsplay the dalog nformaton about the coordnates and alttude of clcked pont when we use the Choose of the transmtter poston. 3. The user enters transmtter on dalogue for the calculaton of wreless telecommuncaton channels range the relatve heght and emtted power use of the case Set transmtter parameters. 4. The user nputs parameter sets on the dalog for the calculaton of wreless telecommuncaton channels range: the requred SNR at the recepton, presence/absence and speces of dversty recepton, nose factor and bandwdth when we use the Set of the recever parameters. 5. The user enters the telecommuncatons channel parameters on dalogue for the calculaton of wreless telecommuncaton channels range: modulaton format for transmsson and carrer frequency use of the case Settng telecommuncaton channel parameters. 6. The user, by clck on the Calculate on dalogue for the calculaton of wreless telecommuncatons channel range, ntates the calculaton of the output data the wreless telecommuncatons channel range and the error probablty for nput parameters. As a result, output calculated data are dsplayed on the dalog bo, and vsual representaton of the calculated data on the map use of the case Calculaton of the range and the error probablty. 4 Evaluaton of Developed Software Component Based on the above model a software component for the calculaton of a wreless telecommuncaton system range s created. The advantages of usng dversty technques n the presence of Rce fadng wll be presented. ISBN:

6 Recent Advances n Geodesy and Geomatcs Engneerng Fg.. The user's vew of the system Fg.3. Intal screen The practcal part of ths paper was realzed through the mplementaton of the descrbed software components and ntegraton nto the actual dedcated GIS. It s used then for the desgn of wreless telecommuncatons system n the presence of Rce fadng. The product was developed for a known user, n order to acheve the necessary functonalty, wth the request that the system s optmal and requres the least engagement of resources. Intal data entry screen s shown n Fg. 3. The transmtter parameters, such as the relatve heght, emtted power, carrer frequency [5], [6], are entered after determnng the poston of the transmtter by clckng on the GIS map the system determnes the transmtter coordnates. Also, the recever parameters are entered nto the frst step: SNR sgnal-to-nose rato at the recepton, nose factor and bandwdth. As an mportant parameter, the nformaton f dversty recepton at the recever s present s entered, the type of combnng and the number of branches. Transmtter coordnates are: Y and X5585., absolute heght [m]: 54.8 and relatve heght [m]: ; emtted power [dbm]: ; SNR at the recever [db]: 5.6, dversty recepton: no, nose factor [db]:, bandwdth [khz]:, modulaton format: BDPSK, carrer frequency [MHz]: 9; after calculatng: range [km]:., the error probablty:.. Bass on mathematcal models that have been performed n prevous Secton, transmsson wthout usng dversty technques and the usng of EGC combnng wth two branches are shown here. ISBN:

7 Recent Advances n Geodesy and Geomatcs Engneerng Based on defned parameters and the requred error probablty, the system calculates the mamum range and the transmsson wth as lttle as possble error probablty for the gven dstance between transmtter and recever. Also, based on a specfed range and the desred error probablty, t s possble to calculate the mnmum of power needed at the transmtter. The results obtaned by modellng the sgnal transmsson wthout the use of dversty technques, as well as dual EGC combnng are presented n Fgs 4. and 5. The applcaton of GIS n desgnng of wreless telecommuncaton systems n the presence of Rcan fadng wthout the use of dversty technques s presented n Fg. 4. When the error probablty s -3 and SNR at the recever s 5.6 db, the range s. km. The applcaton of GIS n desgnng of wreless communcaton systems n the presence of Rce fadng wth EGC dversty combnng wth two branches, wth the same error probablty: -3 and when SNR at the recepton s.7 db, s shown n Fg. 5. It can be seen from ths fgure that the range was ncreased to.58 km wth usng of dversty technque. Based on these results, t was shown that the ntegraton of software components descrbed n the estng specal-purpose GIS, usng dversty technques and proper technques of recevng, dependng on the user s needs, can optmze the essental parameters of the transmtter and recever. Developed software component that allows you to defne and set the transmtter to the selected locaton, settng ts parameters, calculate the lne of sght, coverage and range of wreless sgnals n the presence of Rce fadng wth or wthout the use of dversty technques. Ths s acheved by optmzaton of resources n the desgn and mantenance of wreless communcaton systems. Fg. 4. The applcaton of GIS n the desgn of wreless telecommuncaton systems n the presence of Rce fadng wthout the use of dversty technques The error probablty: -3, SNR at the recepton 5.6 db, range:. km 5 Concluson The results obtaned n ths paper can be used n wreless and moble communcaton systems. The dversty technque wth EGC combnng s used to reduce the mpact of fadng. Ths type of combnng and applcaton of Geographc Informaton System are presented n ths paper. The dstance between the transmtter and recever can be ncreased wthout ncreasng the power of the transmtter n ths way. Also, the transmsson power for the same dstance between the transmtter and recever for the same power of nose, nterference and fadng can be reduced. Based on these software components and the obtaned results, the optmal telecommuncaton system can be desgned. It s possble to acheve a greater dstance between the recever and transmtter for the same sgnal strength and the same sgnal qualty by usng ths software. Also, t s possble to reduce the sgnal strength for the same range and same qualty of connecton, or the same power and same range to mprove sgnal qualty by reducng the error probablty. Fg. 5. The applcaton of GIS n the desgn of wreless telecommuncaton systems n the presence of Rce fadng and dual EGC dversty combnng The error probablty: -3, SNR at the recever.7 db, range:.58 km ISBN:

8 Recent Advances n Geodesy and Geomatcs Engneerng Applcaton of the proposed solutons n practce smplfes the desgn of wreless telecommuncatons systems, makes the tme requred for ts confguraton shorter and leads to consderable economc savngs. Ths paper can be useful for nsttutons that deal wth wreless transmsson, moble telecommuncatons, radar networks or rado-relay lnks. Acknowledgment Ths paper has been supported by the Serban Mnstry for Scence under the projects TR3335 and III 446. References: [] M. K. Smon, M. S. Aloun, Dgtal Communcaton over Fadng Channels, Second Edton, Wley Interscence, New Jersey, 5. [] H. C. Yang, M. S. Aloun, Performace analyss of multbranch swtched dversty systems, IEEE Trans. Commun., vol. 5, May 3, pp [3] Y. C. Ko, et al., Analyss and optmzaton of swtched dversty systems, IEEE Trans. Commun., vol. 49, Nov., pp [4] Y. C. Ko, M. S. Aloun, M. K. Smon, Outage probablty of dversty systems over generalzed fadng cjannels, IEEE Trans. Commun., vol. 48, Nov., pp [5] V. Emaman, M. Kaveh, Combatng shadowng effects for systems wth transmtter dversty by usng collaboraton among moble users, Proc. Int. Symp. on communcatons ISC`, Tawan, Nov., pp [6] D. Krstć, G. Stamenovć, S. Panć, Z. Popovć, D. Rančć, M. Stefanovć, The Applcaton of GIS n Desgnng of Wreless Communcaton Systems wth SC Combnng n the Presence of Rcean Fadng, 9 th Internatonal Conference on Software, Telecommuncatons and Computer Networks SoftCOM, ISBN , IEEE Catalog Number: CFP87A-CDR, September 5-7,, Splt Hvar Dubrovnk, Croata [7] A. Annamala, C. Tellambura, and V. K. Bhargava, Equal-gan dversty recever performance n wreless channels, IEEE Trans. Commun., /; DOI:.9/ [8] A. Annamal, V. Ramanathan, and C. Tellambura, Analyss of equal-gan dversty recever n correlated fadng channels, n Proc. IEEE Vehcular technology conf., Brmngham, AL, May, pp [9] A. A. Dayya, N. C. Beauleu, Swtched dversty on mcrocellular Rcan channels, IEEE Trans. Veh. Technol, vol. 43, no. 6, Nov. 994, pp [] G. M. Vetta, U. Mengal, D. P. Taylor, An error probablty formula for noncoherent orthogonal bnary FSK wth dual dversty on correlated Rcan channels, IEEE Commun. Lett., vol. 3, Feb. 999, pp [] F. Lazaraks, G. S. Tombras, K. Dangaks, Average channel capacty n a moble rado envronment wth Rcan statstcs, IEICE Trans. Commun., vol. E77-B, July 994, pp [] S.O. Rce, Statstcal propertes of a sne wave plus random nose, Bell Syst. Tech. J, vol.7, Jan. 948, pp [3] C. V. Geambasu, I. Janu, I. Janu and A. Gavrla, Influence factors for the choce of a software development methodology, Accountng and Management Informaton Systems, Vol., No. 4,, pp [4] P. Kruchten, Archtectural Blueprnts -The 4+ Vew Model of Software Archtecture, IEEE Software 6, Nov. 995, pp [5] N. S. Adaw, et al., Coverage predcton for moble rado systems operatng n the 8/9 MHz frequency range, IEEE Trans. Veh. Technol., 988, 37,, pp [6] N. H. Sheperd, Rado wave loss devaton and shadow loss at 9 MHz, IEEE Trans. Veh. Technol, vol. VT-6, June 977, pp ISBN: