Generator of Time Series of Rain Attenuation: Results of Parameter Extraction

Transcription

1 32 M. GRÁBNER U.-. FIEBIG V. KVIERA GENERATOR OF TIME SERIES OF RAIN ATTENUATION: RESULTS... Generator of Tme Seres of Ran Attenuaton: Results of Parameter Extracton Martn GRÁBNER 1 Uwe-arsten FIEBIG 2 Václav KVIČERA 1 1 Dept. of Mcrowave ommuncatons TESTOM Hvožďanská Praha 4 zech Republc 2 Insttute for ommuncaton and Navgaton DLR Germany D-822 Wesslng PO Box 1116 Germany grabner@testcom.cz uwe.febg@dlr.de kvcera@testcom.cz Abstract. Ran attenuaton has a sgnfcant mpact on the avalablty of mllmeter wave communcaton systems. In order to dynamcally smulate such rado systems several generators of artfcal tme seres of ran attenuaton have been developed. Ths paper brefly descrbes the DLR channel model and presents the results of model parameter extracton from tme seres ured on terrestral mcrowave paths n the zech Republc. The generated tme-dscrete tme seres of attenuaton s denoted by y = y(t s ) where = 12 and 1/T s s the samplng rate. T s s typcally n the order of 1 mnute. The next value of attenuaton y +1 s obtaned as the outcome of a sngle experment of a Gaussan random varable n wth dstrbuton N( σ 2 ) see Fg. 1. Power level Keywords Mcrowave communcaton propagaton mllmeter wave ran attenuaton channel model. Last generated sample y Lkelhood of next sample y Introducton Ran fadng events may cause severe outages n mllmeter wave communcaton systems. Dfferent fade mtgaton technques are beng developed n order to overcome such propagaton mparments. Recently several tme seres generators have been developed [1] [2]. They produce artfcal tme seres of ran attenuaton for the purpose to smulate fade mtgaton technques under realstc channel condtons. Apparently the generated tme seres should be smlar to the ured ones n terms of ther statstcal and dynamcal characterstcs. In ths paper the DLR channel model [3] [4] s brefly descrbed. So far the DLR channel model has been appled successfully to satellte mcrowave paths whch are subect to ran fadng. In ths paper the DLR channel model s appled to three terrestral mcrowave paths n the zech Republc. 2. DLR hannel Model The DLR channel model s based on a mx of a 2 nd order Markov chan and Gaussan random varables. These defne transton probabltes of the Markov chan. tme Fg. 1. Prncple of generatng subsequent samples of an artfcal ran attenuaton tme seres wth the DLR channel model. The parameters σ depend on the prevous value of the chan y as well as on the attenuaton trend descrbed by a segment type s : y s + 1 = n n = N = Λ 2 ( σ ) = ( y s ) σ = σ ( ( y y ) Λ( x) K y s D for x > 1dB = for x 1dB U for x < 1dB where D and U denote down constant and up segment type respectvely. K s a postve constant determnng the duraton of a segment relatve to 1/T s where typcally K=1 s chosen. In the contnuous-valued model descrbed above the model parameters are the functons (y s) σ(y s). The dscrete-valued verson of the DLR channel model apples an nternal quantzaton procedure and assgns dfferent dscrete attenuaton levels to the states of a Markov chan see Fg. 2. ) (1)

2 RADIOENGINEERING VOL. 14 NO. 1 APRIL (SMPs) of the quantzed verson of the DLR channel model: 4 db 5 db 6 db onstant Down D D U U σ σ σ = 1 KM. (2) These parameters can be extracted from the ured tme seres of ran attenuaton by means of a straghtforward model parameter extracton process. 7 db 8 db 9 db Up 3. Model Parameter Extracton Ths chapter descrbes the procedure of the DLR model parameters extracton. Fg. 2. DLR channel model as a dscrete-valued 2 nd order Markov chan. Groupng of transtons allows for a reducton of the number of transton probabltes. A dscrete-valued 2 nd order Markov chan over M states s completely defned by ts M 3 transton probabltes. Wth a quantzaton step sze of 1 db and M= a total of 6 transton probabltes has to be derved. Ths s very cumbersome to handle. However groupng the 2 nd order transtons nto three groups reduces the number of transton probabltes to 3M 2. Furthermore all M transton probabltes emergng from a partcular state can be very accurately descrbed by a Gaussan dstrbuton whch results n only 3M dstrbutons to descrbe the channel model see Fg. 3. The use of Gaussan dstrbutons was observed emprcally to be vald for large datasets. 4 db 5 db 6 db 7 db 8 db 9 db -1 onstant Down Up +1 Fg. 3. DLR channel model: Descrpton of the transton probabltes by Gaussan dstrbutons. A Gaussan dstrbuton s fully descrbed by ts mean value and ts standard devaton. Thus to fully descrbe the DLR channel model a total of 3M mean values and 3M standard devatons have to be determned. The set of these 3M mean values and 3M standard devatons represents the specfc channel model parameters 3.1 Measured Tme Seres and Preprocessng TESTOM has been carred out long-term urements of the receved sgnal level on terrestral mcrowave paths n several frequency bands. A model parameter extracton procedure was appled on ured data summarzed n Tab. 1. Path Frequency (MHz) Length (km) Data amount (years) TESO hloumek Strahov TESTOM Úvaly TESTOM Tab. 1. Overvew of avalable ured tme seres of attenuaton. The samplng tme of the ured data s.1 second. One-second block averagng s performed pror to parameter extracton n order to obtan a tme seres wth a samplng tme T r = 1 s. A zero attenuaton level s determned so that t corresponds to a monthly medan value of the ured receved sgnal level. Then a movng averagng wth a wndow sze of 6 seconds s appled to remove fast fluctuatons caused by a scntllaton effect. The resultng sequence s denoted x n = x(nt r ) n = 12 and has a samplng tme of 1s. Flterng s employed because the DLR model s ntended to generate only slow varatons of a sgnal caused by ran fadng events. 3.2 Extracton Process An extracton process s appled on the fltered tme seres x n = x(nt r ) n = 12 n order to derve the SMPs. Note that the ured tme-seres has a samplng rate 6 tmes larger than the samplng rate of the channel model. Frst the tme seres x n n = 12 s mapped onto a dscrete-valued tme-seres d n where the elements of d n can take on ntegers rangng from 1 to M representng attenuaton levels. Then three matrces H D H and H U of sze M M assgned to the correspondng 3 types of segments are determned. An element h kl of H b b {DU} gves the number of transtons from attenuaton level k to attenuaton level l

3 34 M. GRÁBNER U.-. FIEBIG V. KVIERA GENERATOR OF TIME SERIES OF RAIN ATTENUATION: RESULTS... between samples d n and d n+k for K = 6 and for all n;.e. only samples separated by 6 seconds are consdered; matrx H b contans those transtons whch are obtaned for the case that b = Λ(d n d n K ) wth K = 6. A convenent determnaton of these matrces s to go sample-wse through the whole tme seres d n and to ncrement the elements h kl of H b accordng to above rules. The rows of matrces H D H H U provde dstrbutons for every state. These dstrbutons descrbe the probablty of the transton from one state to another under the condton of the trend Λ whch s ether down constant or up. Fnally the parameters descrbed by eqn. (2) are extracted from the dstrbutons. The receved sgnal fluctuates around the free space level whch represents zero attenuaton. That s why negatve attenuaton values may occur. In order to process these values properly we consdered n our nvestgaton attenuaton values rangng from -5 to +45 db. 4. Results Ths chapter presents the results of both the model parameter extracton and the smulaton wth the DLR channel model. The examples of extracted parameters and of generated tme seres of attenuaton are shown. The frst and the second order statstcs of ured and smulated tme seres are compared. 4.1 Extracted Parameters Fg. 4 shows the DLR model parameters extracted from the attenuaton tme seres obtaned on the path TESO - hloumek n 3. Snce the parameters descrbe transton probabltes mean values are almost lnearly dependent on an attenuaton level. It means the next attenuaton level wll have a smlar value as the prevous one for most of the tme. However sgnfcant relatve dfferences are obvous between the curves for down constant and up segments. Standard devaton slghtly ncreases wth an attenuaton level and s mnmal around the zero level (5 db because of the shft reasoned n the last paragraph of the secton 3.2). Polynomal fttng of the model parameters from Fg. 4 was performed n order to provde one quanttatve example of the contnuous DLR channel model. The resulted polynomals are as follows: D U ( y) = [ ] y(3) ( y) = [ ] y(3) ( y) = [ ] y(3) ( y) = [ y D σ ] (4) σ σ ( y) = [ ] y(4) ( y) = [ ] y where : ( n) n 1 n 2 T [ y y K y 1]. y = (3) Note that the dscrete-valued model was actually used for calculatons presented n the next sectons. mean and sgma (db) mean down mean const mean up sgma down sgma const sgma up attenuaton (db) Fg. 4. Extracted parameters and σ as functons of the attenuaton level and of segment type path TESO - hloumek year Generated Tme Seres The DLR channel model has been set up wth above extracted parameters. It generates a tme seres wth a samplng tme of 1 mnute. The generaton followed eqn. (1) wth parameters T s = 6 s and K = 1. The duraton of all generated tme seres of attenuaton has been days. Fg. 5 shows an example of an artfcal tme seres of attenuaton generated by the DLR channel model wth a parameter set extracted from the TESO - hloumek ured data. The receved sgnal level relatve to the free space level s depcted. The smulated tme-seres looks very smlar to those whch have been ured. 4.3 Statstcs omparsons of statstcs are presented n ths secton. Frst order statstcs are represented by cumulatve dstrbutons of attenuaton (DA). The second order statstcs are represented by fade duraton dstrbutons umulatve Dstrbutons Fgs. 6 through 8 show the comparson of the cumulatve dstrbutons of attenuaton (DA) calculated from ured tme seres ( ) and from generated ones ( smul ). Note that model parameters were always extracted from the same ured data that was used for comparson. (4)

4 RADIOENGINEERING VOL. 14 NO. 1 APRIL smul receved sgnal level (db) attenuaton (db) - attenuaton (db) tme (mnute) Fg. 5. Artfcal tme seres of receved sgnal level generated by DLR model wth parameter set extracted from path TESO - hloumek year 3. smul probablty (-) 1e probablty (-) Fg. 8. DA for path Úvaly - TESTOM year sm db db sm db db sm db db sm db db attenuaton (db) 1e probablty (-) Fg. 6. DA for path TESO - hloumek year e probablty (-) smul Fg. 7. DA for path Strahov - TESTOM year Fade Duraton Statstcs Fgs. 9 through 11 show the fade duraton statstcs of ured and generated tme seres. These statstcs represent the probablty that an attenuaton sample at an arbtrary tme nstant s part of a fade whch exceeds a gven attenuaton level for a tme duraton whch s longer than the value on the abscssa. 1e-5 1 fade duraton (sec) Fg. 9. Fade duraton statstcs obtaned from ured and smulated tme seres for path TESO - hloumek year Dscusson on the Results The fgures reveal a very good ft of ured and smulated tme-seres n terms of the frst order statstcs (cumulatve dstrbutons of attenuaton). The best ft was obtaned for data from the TESO - hloumek path see Fg. 6. Dfferences at hgher attenuaton values are generally larger than at lower attenuaton values. The ft of the second order statstc s not as good as of the frst order statstcs. Fgs. 9 through 11 ndcate that the generated fade events can be shorter than the ured ones. These dfferences are smallest for the Strahov TESTOM path. These dfferences are generally not so large when the DLR channel model s appled to a satellte lnk. One of the reasons for these dfferences mght be that spurous multpath fadng whch often occurs burst-lke (many short and deep fades wthn a short amount of tme) nfluence the SMPs such that long fades are less lkely to occur. These effects cannot be smulated by the DLR channel model snce t does not follow fast fluctuatons.

5 36 M. GRÁBNER U.-. FIEBIG V. KVIERA GENERATOR OF TIME SERIES OF RAIN ATTENUATION: RESULTS... probablty (-) sm db db sm db db sm db db sm db db ) Tme Varablty Dynamc and Space Features of haracterstcs of Electromagnetc Waves for Advanced Telecommuncaton Systems. References [1] FIEBIG U.-. ASTANET L. LEMORTON J. MATRIIANI E. PÉREZ-FONTÁN F. RIVA. WATSON R. Revew of propagaton channel modellng. In Proceedngs of 2 nd Internatonal workshop of OST28 Acton. May 3 p probablty (-) 1e-5 1 fade duraton (sec) Fg.. Fade duraton statstcs obtaned from ured and smulated tme seres for path Strahov - TESTOM year e-5 1 fade duraton (sec) sm db db sm db db sm db db sm db db Fg. 11. Fade duraton statstcs obtaned from ured and smulated tme seres for path Strahov - TESTOM year onclusons Ran fadng generators are ntended to support the smulaton of mcrowave or mllmeter wave rado systems that are mpared by the ran attenuaton. The results of the DLR channel model parameter extracton were presented n ths paper. Tme seres of receved sgnal level ured on the three terrestral mcrowave paths were processed to obtan the parameters for the model. In contrast to satellte paths at whch the DLR model has proven excellent performance terrestral paths are more lkely to be subect to multpath propagaton. It seems that ths effect may nfluence the extracton process and cause poorer results wth respect to fade duraton statstcs. Acknowledgements The Mnstry of Educaton supported ths research under the grant No. O 28.1 (TESTOM task No. 9- [2] ASTANET L. LEMORTON J. LAOSTE F. RIVA. MATRIIANI E. FIEBIG U.-. VAN DE KAMP M. MARTELLUI A. Development and valdaton of tme seres syntheszers for Ka-band satellte communcaton systems. In Proceedngs of th Ka-Band Utlzaton onference. Vcenza (Italy) October 4. [3] FIEBIG U.-. Modellng ran fadng wth a tme-seres generator consderng seasonal and durnal varatons. In Proceedngs of the 8th Ka-Band Utlzaton onference. Baveno/Strese (Italy) 2. [4] FIEBIG U.-. Satellte channel modellng for ran fadng. In Proceedngs of AAIA Internatonal ommuncatons Satellte System onference. Yokohama (Japan) 3. About Authors... Martn GRÁBNER receved the B.S. and M.S. degrees n Electrcal Engneerng from the zech Techncal Unversty n Prague n 1998 and respectvely. He has been wth the Department of Mcrowave ommuncatons TESTOM. Hs work s focused on the propagaton of rado waves and on the qualty of terrestral mcrowave systems. Uwe-arsten FIEBIG receved hs Dploma degree n Electrcal Engneerng from the Techncal Unversty of Munch. In 1988 he oned the Insttute for ommuncatons and Navgaton of DLR (German Aerospace Research) as a member of the research staff. In 1993 he receved hs PhD from the Unversty of Kaserslautern. In 1994 he became head of the Department ommuncatons Systems. From 1996 tll 1998 he spent several months at the ommuncatons Research enter (R) Ottawa anada at the Yokohama Natonal Unversty Japan and at the Unversty of Pretora South Afrca. Hs nterests are n the feld of satellte navgaton and communcatons and moble rado. He lectures satellte communcatons at the Unversty of Ulm Germany and the Unversty of Lnz Austra. Václav KVIČERA receved the M.S. and Ph.D. degrees n Electrcal Engneerng from the zech Techncal Unversty n Prague n 1971 and 1986 respectvely. He s a senor researcher at the Department of Mcrowave ommuncatons TESTOM. Hs work s amed at electromagnetc wave propagaton n frequency bands of fxed lnks especally at the nfluence of hydrometeors n frequency bands above GHz.