A Novel Channel Model for Land Moble Satellte Navgaton Andreas Lehner, Alexander Stengass, Insttute of Communcatons and Navgaton German Aerospace Center (LR) 1 ABSTRACT In 2002 the German Aerospace Centre (LR) performed a measurement campagn of the land moble multpath channel. From ths data we derved a channel model that s synthessng the measured channel mpulse response. It allows the realstc smulaton of the multpath channel by approxmatng every sngle reflecton. Ths model ncludes tme varant reflectors approachng and recedng n dependency of the azmuth and elevaton of the satellte. All the sgnal processng had been realsed ndependently of the transmtted sgnal. Therefore the usablty for both, navgaton systems (GPS as well as GALILEO) and wdeband communcaton systems s gven. 2 INTROUCTION Besdes the onosphere one of the most sgnfcant problems to acheve an accurate navgaton soluton n ctes wth GPS or GALILEO s the multpath recepton. Varous channel models do exst for ground to ground communcatons (e.g. COST 207 for the GSM system). But there s stll a lack of knowledge for broadband satellte to earth channels [1]. Therefore the German Aerospace Centre (LR) performed a measurement campagn n 2002. In ths campagn we used a Zeppeln to smulate a satellte transmttng a 100 MHz broadband sgnal towards earth. To ensure a realstc scenaro the sgnal was transmtted between 1460 and 1560 MHz just nearby the GPS L1 band. Ths sgnal was receved by a measurement van and was recorded usng a regular tme grd. The so gathered data was then passed through a super resoluton algorthm to detect the sngle reflectons. In a further step we tracked the detected reflectons n tme and ganed a knowledge about the characterstcs of any solated reflecton. Ths ncludes both oppler shft and delay of the reflecton. On top of ths we ganed knowledge about the drect path behavour. 3 IRECT PATH In an open envronment the drect path would be best represented by the lne of sght (LOS) transmsson of the sgnal. In an urban envronment ths LOS sgnal s often blocked so that the frst receved path s attenuated and possbly delayed wth respect to the LOS. In ctes we had been able to dentfy three major types of obstacles that nfluence the sgnal recepton. 1. House fronts 2. Trees 3. Lampposts 3.1 The nfluence of House fronts When the LOS ray s gong to be blocked by a house front the sgnal s obvously affected. Fgure 1 shows the vehcle on a track durng the measurement drvng nto the shadow of a buldng. The x-axs ndcates the drven dstance from start. At about 3886 m the vehcle s enterng the shadowed area. Fgure 1: ffracton by a house front measurement n comparson to the model used 2132
From ths nstance on the sgnal s strongly attenuated. Ths behavour s well known from the so called Knfe Edge Model [2]. In ths model t s assumed that a planar wave s httng a half sded nfntvely large plate. The calculated attenuaton from ths model s also dsplayed n Fgure 1. From ths comparson the smlarty of measurement and model s obvous. Therefore the knfe edge model s selected to model ths effect. Ths process s moton dependent only. 3.2 The nfluence of trees As t s shown n Fgure 2 the LOS sgnal can be attenuated by trees. The measured process on the one hand sde s dependent on the length of the LOS sgnal beng wthn the tree, on the other hand sde an addtonal process s vsble caused by branches and leafs. In contrast to approaches where branches and leafs are modelled as very complex scatterers [3] we use a combnaton of an attenuatng only cylnder modellng the transmsson through the tree and a statstcal fadng process modellng the branches and leafs. Ths process s moton dependent only. 3.3 The nfluence of lampposts Surprsngly a lamppost has a strong effect on the LOS sgnal. Fgure 3 shows an example of a lamppost wth a dameter of 20 cm. When passng by such a post the strength of the sgnal begns to oscllate, goes down quckly n the drect shadow of the post and comes up agan oscllatng behnd. We model a lamppost wth a double knfe edge model where we assume two overlappng knfe edge plates beng present. One s reachng from /2<x< and the other s reachng from <x</2. Both edges are smulated separately and then added coherently. Fgure 3 shows the near perfect match of model and measurement. Ths process s also moton dependent only. 4 REFLECTE SIGNAL In the measurement data many reflectons appear n the urban envronment [4, 5]. In contrast to ray tracng algorthms [6] we do not model a specfc scenery. We assume reflectons to be statstcally dstrbuted n the x,y,z space and generate them statstcally. In order to match the measured statstc we must take a closer look at the echo dstrbuton. 4.1 Influence of the relatve angle Fgure 2: Sgnal attenuaton by seres of trees - comparson of measurement and cylnder model Let us assume a recever to be at poston RX, a satellte at poston S and a reflector at poston R. Then the relatve azmuth recevng angle α s the angle at the recever (see Fgure 4). Fgure 3: LOS sgnal beng affected by a lamppost - comparson of measurement and model 2133 Fgure 4: efnton of the angle α. We can see a clear dependency on the relatve azmuth angle n the measurement data (Fgure 5) wth a maxmum of the lkelhood dstrbuton at α = 180. For ths fgure we averaged over all occurrng absolute azmuth angles θ by
( α θ ) ( θ ) θ p p( α ) = (1) p α θ p ( α θ ) p ( θ ) Ths on the frst look astonshng result can be easly understand f one has n mnd the very rectangular structure of urban ctes. ue to ths structure a corner reflector (see Fgure 6) occurs very often n ctes. The man characterstc of ths reflector s that a ray comng from a satellte s beng reflected back nto the satellte drecton n the x-y plane. Its elevaton s unchanged. Then t s obvous that t s most lkely to receve reflectons from the opposte sde of the satellte. the hghest lkelhood of recevng a reflector s when the reflector s on the rght or on the left sde. The lkelhood of recevng a reflector from the front s close to zero. Ths as well on the frst look astonshng result becomes more plausble when one has an urban canyon n mnd. It must be unlkely that a reflectng obstacle s n near front poston of the car, otherwse one would overrun t n the next second. To calculate the condtonal lkelhood of a reflector beng present at a certan poston for a specfc satellte azmuth one has to multply the statstcs shown n Fgure 5 and Fgure 7. The result of ths operaton s shown n Fgure 8, here the satellte poston had been chosen at 25 azmuth. Fgure 5: Lkelhood dstrbuton of the relatve azmuth angle α (at 50 elevaton). Fgure 7: Lkelhood of reflectors beng at a certan 2- poston. Movng drecton of the recever s n x- drecton only. Fgure 6: Corner reflector as t can be often found n ctes. 4.2 Geometrc occurrence of reflectors Fgure 7 shows the lkelhood dstrbuton of reflectors n a top vew. In ths fgure the recever s movng n x-drecton only. It can clearly be seen that 2134 Fgure 8: Condtonal lkelhood of reflectors beng at a certan 2- poston. Satellte at 25 azmuth. 4.3 Lfespan of reflectors In the measurement data the channel appears rapdly changng. Many echoes dsappear and others appear at new postons. Ths process s hghly correlated to the recever speed. When the car stops the reflectons
4.5 Fadng process of reflectons Fgure 9: Lve dstance of echoes reman n the scenery. Therefore we defned a lfe dstance of each reflector. Ths lfe dstance s the dstance the recever s travellng untl the echo dsappears. Fgure 9 shows a hstogram of the echo lfe dstances. It can be seen that the lfe dstance of the reflectors s usually well below 1 m. Most reflectors exst along a moton path below 5 m. Therefore the channel s changng rapdly. When a car drves through an urban envronment, the recever moves through a quas statonary feld radated by the reflectors. Therefore the recever recognses a varaton of the actual power of the reflector (see also Fgure 12). Interestng enough ths fadng process does not even come to a stop when the car does not move. We assume that the channel s changng for example due to trees n the wnd and other cars. Furthermore there was no correlaton between ths fadng process and the recever speed. Therefore we assume ths process to be tme dependent only. The typcal bandwdth of such a process s n the range of some Hertz. The deepness of the fades s expressed by the Rce factor K Rce. P const K Rce = (2) Pfad It defnes the rato between the constant power P const and the power of the fadng process P fad. Fgure 11 shows the dstrbuton of the Rce factor 4.4 Mean power of reflectors Fgure 10 shows the power dstrbuton n dependency of the relatve poston. Snce reflectors n the real world have a gven geometrcal sze of course ther dstance plays a major role for the mean receved power. Havng agan n mnd the urban canyon, t s qute understandable that the most powerful reflectons are on the sdes of the streets. Wth ncreasng dstance the mean power of the reflectons s decreasng. Besde the mean power map we have derved a power varance map (not shown) to allow a certan varaton n ths process, lke we observed t n the measurements. Fgure 11: Rce factor hstogram of the fadng process. 4.6 Tme seres characterstc of reflectors Classcal channel models lke the GSM channel model [7] use tme nvarant path delays and model the change of the reflector over the tme by the assumpton that many echoes are receved at almost the same path delay and ther absolute azmuth s equally dstrbuted. The resultng oppler spectrum, the so called Jakes spectrum [8], s gven by: Fgure 10: Mean power of the reflectors n dependency of ther relatve poston. 2135
S( f ) = const f 1 f max 0 2 f else < f max (3) sngle reflector s modelled. In terms of the reflector the artfcal scenery generates a contnues seres of recever postons accordng to the actual speed. The recever s movng only n x-drecton. To smulate turns the relatve azmuth of the satellte s changed. 4.7 Number of echoes Ths approach s feasble for narrow band systems lke GSM but n a wde band system such as GPS/GALILEO we regard the modellng accuracy as nsuffcent. Fgure 12 shows the sldng wndow Fourer transform of an solated reflecton. There t urng a drve through a cty the number of echoes beng receved changes. For a navgaton recever that tres to estmate the channel mpulse response (super resoluton for multpath mtgaton) a hgh number of reflectons s a hgh stress scenaro. Other phases wth a lower number of echoes are less crtcal. Besdes the mean number of echoes t s therefore very mportant to exactly model ths ncreasng and decreasng process. A sample of t s shown n Fgure 14. Please note the relatvely hgh number of echoes Fgure 12: Sldng wndow Fourer transform of an solated reflecton. Fgure 14: Number of echoes at the same tme durng a 15 mn drve trough a cty. Fgure 13: Model of an solated reflector can be seen that the echo s best charactersed by a trace n oppler frequency. Wthn 1.6 s the oppler frequency of the reflector changes from +30 Hz to -5 Hz. In the same perod the path delay of the reflector changes. The varablty of the reflector s clearly dependent on the vehcle speed. Therefore we mplemented the channel model usng a geometrcal reflector representaton. Ths means we ntalse a reflector at a randomly chosen poston (accordng to the measured statstcs) and pass by wth a recever wth the actual speed. Then both, path delay and phase of the reflecton can be calculated geometrcally. Ths causes the man process to be moton dependent only. Fgure 13 shows how a (up to 50) at the same tme. We had been able to detect two processes: An extremely narrow band process wth hgh power and a lower powered wde band process. Ther combnaton results n a very good approxmaton of the process. 5 MOEL The block dagram n Fgure 15 gves an overvew of the mplemented model. The x-coordnate and the relatve satellte azmuth are derved from the user speed, user headng and satellte azmuth as explaned n secton 4.6. Ths drves the artfcal scenery (Fgure 16) where house fronts, trees and lampposts affect the drect path. Controlled by a number of echo generator the actual amount of reflectons s created n the scenery at postons accordng to the lkelhood dstrbuton. The reflectors power, bandwdth, rce factor and lfespan are taken from the statstcs. Ther delay and phase s therefore changng accordng to ths statstcal parameters and accordng to the 2136
Fgure 15: Block dagram of the channel model. Fgure 17: Example of generated echoes. Plotted s the path delay of the reflectons over tme. Fgure 16: A pcture of the artfcal scenery. Brown are house fronts, green cylnders are trees, red are poles. Fgure 18: Example of generated echoes. Plotted s the oppler of the reflectons over tme. recever movement relatve to the reflector poston. In Fgure 17 - Fgure 20 an example output of the channel model s gven. In ths scenaro the car drove wth a varable speed (usng a sn(t) lke stop and go functon) through the cty. At 4.7 s the speed of the vehcle was nearly 0 km/h. In Fgure 18 the oppler shft of every echo s shown. The red dotted lne s the theoretcal lmt for the oppler shft gven by f oppler = ( ) v RX S fc c0 change much - clearly vsble by the low oppler bandwdth and the long lastng echoes (long lnes) n Fgure 17. In ths stuaton only the tme drven fadng process s changng the channel. But nether an echo s termnated nor a new one s generated n ths stuaton. Furthermore one can see regons where (4) where v s the speed vector of the vehcle, RX s the recever poston, fc s the carrer frequency, S s the satellte Poston and c0 s the speed of lght. In ths fgure and n the detal (Fgure 20) one can determne solated echoes changng ther oppler shft durng ther lfe dstance (for example the mnt green colored echo lastng from 0.81-1.35 s). The rapd changes n the channel are vsble wthn the dsplayed perod of around one second many echoes de and others are generated. Around the standstll the channel does not Fgure 19: etal of Fgure 17. 2137
REFERENCES Fgure 20: etal of Fgure 18. more echoes are present than n others. ue to ths precse modellng of reflectons new recever algorthms for e.g. multpath mtgaton can be tested n very realstc smulatons now. An mportant mprovement compared to regular statstcal models s the geometrcal reflector representaton whch guarantees the realstc delay and phase correlaton among the occurrng echoes. 6 SUMMARY In ths paper we have presented our new channel model for the land moble multpath channel. Ths channel model s based on a new approach: The combnaton of statstcal data from a measurement and a determnstc scenaro. The determnstc scenaro s used for the drect path modellng. Ths ncludes effects such as shadowng by house fronts, tree dampng or refractng lampposts. The reflectons of ths channel model are generated statstcally n the geometrc scenaro. Ther generaton s drven by data obtaned from the measurement only. The model ncludes: Elevaton changes, azmuth changes, speed changes and a varable number of reflectors. 1. Schwekert R., Wörz T.: "Sgnal desgn and transmsson performance study for GNSS-2", Tech. note on dgtal channel model for data transmsson, ESA, 1998. 2. Orfands J. S. : "Electromagnetc Waves and Antennas", Internet www.ece.rutgers.edu/ orfand/ewa, Rutgers Unversty, June 2004. 3. Yvo L. C. de Jong and Matt H. A. J. Herben: "A tree-scatterng model for mproved propagaton predcton n urban mcrocells", IEEE Transactons on Vehcular Technology, pages 503 513, March 2004. 4. Stengass A., Lehner A.: "Measurng the navgaton multpath channel a statstcal analyss", ION GPS 2004 Conference Long Beach, Calforna USA, September 2004. 5. Stengass A., Lehner A.: "Measurng Galleo s multpath channel", Global Navgaton Satellte Systems Conference (GNSS2003), Graz, Austra, 2003. 6. Esbr-Rodrguez O., Konovaltsev A. and Hornbostel A.: "Modelng of the GNSS drectonal rado channel n urban areas based on synthetc envronments", Proceedngs of ION NTM, Jan. 2004. 7. COST 207 WG1: "Proposal on channel transfer functons to be used n GSM tests 1986", Techncal report, CEPT Pars, 1986. 8. Jakes W. C.: "Mcrowave Moble Communcatons", John Wley & Sons, Inc., New York, 1974. 9. Parknson B. W., Splker J. J.: "Global Postonng System Theory and Applcatons I", volume 163 of Progress n Astronautcs and Aeronautcs. Amercan Insttute of Aeronautcs and Astronautcs, Inc, Washngton, 1996. 10. Parknson B.W., Splker J.J.: "Global Postonng System Theory and Applcatons II", volume 164 of Progress n Astronautcs and Aeronautcs. Amercan Insttute of Aeronautcs and Astronautcs, Inc., Washngton, 1996. The model wll be avalable for download soon: http://www.kn-s.dlr.de/satnav/ 2138