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# Propagation Model

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### Propagation Model

1. 1. Microwaves UCL 1 Propagation models for wireless mobile communications D. Vanhoenacker-Janvier, Microwave Lab. UCL, Louvain-la-Neuve, Belgium AT1-Propagation in wired, wireless and optical communications
2. 2. Microwaves UCL 2 Content of the presentation - Free space losses - Plane earth losses - Models for wireless channel macrocells shadowing narrowband fast fading wideband fast fading megacells This presentation is based on the following reference: S.R. Saunders, Antennas and propagation for wireless communication systems, Wiley, 1999.
3. 3. Microwaves UCL 3 Free space losses emitter receiver GT GR LPT PR RT RTT R LLL GGP P = LT LR Where PR is the power at the receiver terminal PT is the power at the emitter terminal GT is the gain of the emitter antenna (dBi) GR is the gain of the receiver antenna (dBi) L is the path loss LT,E are the feeder losses (emitter, receiver)
4. 4. Microwaves UCL 4 Free space losses TI T TT P L GP EIRP == Effective isotropic radiated power: Effective isotropic received power: R RR RI G LP P = Path loss: ö ç è æ =÷ ö ç è æ = TRR RTT RI TI LLP GGP P P L log10log10
5. 5. Microwaves UCL 5 Free space losses Assuming 2 antennas, with their polarisation matched, the power density arriving to the receiving antenna is (feeder losses are neglected) 2 4 r GP S TT π = The power received by the antenna is 2 4 r AGP P eRTT R π = where AeR is the effective aperture of the receive antenna: eRR AG 2 4 λ π =
6. 6. Microwaves UCL 6 Free space losses And finally 2 4 ö ç è æ = r GG P P TR T R π λ Friis formula The free space loss becomes: 2 4 ö ç è æ== λ πr P GGP L R RTT
7. 7. Microwaves UCL 7 Plane earth loss Wireless environment is not governed by free space losses, due to the presence of the ground. Base station mobile This is not multipath!
8. 8. Microwaves UCL 8 Plane earth loss Assumption: flat reflecting ground ( ) ( ) 22 2 22 1 rhhr rhhr mb mb ++= +−= The lengths of the direct and reflected rays are: The amplitude of the fields is assumed to be the same, only the phase difference is taken into account: ù ê ê ë é +÷ ø ö ç è æ − −+÷ ø ö ç è æ + =− 11 22 12 r hh r hh rrr mbmb
9. 9. Microwaves UCL 9 Plane earth loss In most of the practical cases: rhh mb <<, And the amplitude of the electric field is ( )ψ∆+= jREEtot exp10 Then ( ) r hh rr bm2 12 ≈− E0 is the amplitude of the direct field r hh k bm2 =∆ψ
10. 10. Microwaves UCL 10 Plane earth loss ( )2 2 exp1 4 ψ π λ ∆+ ö ç è æ = jR rP P T R If the angle of incidence is small, the reflection coefficient is close to -1. 2 2 sincos1 4 ψψ π λ ∆−∆− ö ç è æ = j r PP TR The phase difference is small so that ψψ ψ ∆≅∆ ≅∆ sin 1cos
11. 11. Microwaves UCL 11 Plane earth loss 22 2 2 4 44 ö ç è æ ÷ ö ç è æ ≅∆÷ ö ç è æ ≅ d hh r P r PP bm TTR λ π π λ ψ π λ 2 2 ö ç è æ ≅ d hh PP bm TR The loss is increasing with the distance by 40 dB per decade and decreasing with the antenna heights. This is not an accurate model of propagation; it is sometimes used as a reference case.
12. 12. Microwaves UCL 12 Models for wireless channel Various types of models for the wireless channel: - empirical models, based on measurements linked to the environment and the parameters of the measurement campaign - deterministic models based on a fixed geometry (buildings, streets,…) used to analyse particular situations - physical-statistical models combination of deterministic models and statistics of various parameters (building heights, street width,…)
13. 13. Microwaves UCL 13 Models for wireless channel - Models for macrocells - Shadowing - Narrowband fast fading - Wideband fast fading - Megacells
14. 14. Microwaves UCL 14 Macrocells Macrocell geometry Definition: hb>h0
15. 15. Microwaves UCL 15 Macrocells Macrocell models are used by system designers to place the base stations. They are - simple - dependent on distance from the base station only - based on measurement (empirical models)
16. 16. Microwaves UCL 16 Macrocells-empirical models Example of measurements taken in a suburban area. Each measurement represents an average of a set of samples (local mean)
17. 17. Microwaves UCL 17 Macrocells-empirical models Simplest form for an empirical path loss model: kKKrndBL r k LP P n T R log10;log10)( 1 =+= == PR and PT are the effective isotropic transmitted and predicted isotropic received power, K and n are constants of the model.
18. 18. Microwaves UCL 18 Macrocells -empirical models Measurements taken in urban and suburban area usually find a path loss exponent close to 4, but with losses higher than predicted. ( ) ( ) refref LrrndBL KrndBL += += log10)( log10 Represented by the clutter factor
19. 19. Microwaves UCL 19 Macrocells -empirical models In urban and suburban areas J. Egli, “Radiowave propagation above 40 Mc over irregular terrain”, Proc. IRE, pp. 1383-1391, 1957. G. Delisle, J. Lefèvre, M. Lecours, J. Chouinard, ‘Propagation loss prediction : a comparative study with application to the mobile radio channel”, IEEE Trans. Veh. Techn., vol.26, n)4, pp. 295-308, 1985. 10log203,76 10log103,76 ≥−= <−= mmm mmm hforhL hforhL
20. 20. Microwaves UCL 20 Macrocells -empirical models Fully empirical model, based on an extensive series of measurements made around Tokyo city between 200 MHz and 2 GHz1 . Predictions are based on a series of graphs; the most important ones have been approximated in a set of formulae by Hata2. 1 Y. Okumura, E. Ohmori, T. Kawano, K. Fukuda, “Field strength and its variability in VHF and UHF land mobile radio service”, Rev. Electr. Communic. Lab., vol.16, pp. 825-873, 1968. 2 M. Hata, “Empirical formula for propagation loss in land mobile radio services”, IEEE Trans. Vehic. Techn., vol 29, pp. 317-325, 1980.
21. 21. Microwaves UCL 21 Macrocells -empirical models
22. 22. Microwaves UCL 22 Macrocells -empirical models The terrain categories proposed by Okumura are the following: - Open area: open space, no tall trees or buildings in the path, land cleared for 300-400m ahead, e.g. farmlands, rice fields, open fields - Suburban area: village or highway scattered with trees and houses, some obstacles near the mobile but not very congested - Urban area: built up city or large town with large buildings and houses with two or more storeys, or larger villages with close houses and tall, thickly grown trees.
23. 23. Microwaves UCL 23 Macrocells -empirical models Lee model is a power law model with parameters taken from measurements in a number of locations ( ) ö ç è æ++−+÷ ö ç è æ+÷ ö ç è æ= +÷ ö ç è æ−−−= +÷ ö ç è æ−−−= +÷ ö ç è æ−−−= 10 log106 10 log10 100 log20 900 loglog1.4364 900 loglog8.3670 900 loglog4.387.61 0 0 0 0 m mb Tb R R R h GG Ph Newark f nRP iePhiladelph f nRP suburban f nRP α α α α hb,hm in feet; PT in Watts, f in MHz, R in miles (R>1mile)
24. 24. Microwaves UCL 24 Macrocells -empirical models W.C.Lee, Mobile design fundamentals, John Wiley, New York, 1993.
25. 25. Microwaves UCL 25 Macrocells -empirical models Limitations of the empirical models: - they can only be used over parameter ranges included in the original measurement set. - environment must be classified subjectively according categories, which may be different in different countries. - they provide no physical insight into the mechanisms by which propagation occurs.
26. 26. Microwaves UCL 26 Macrocells-Physical models S. R. Saunders, F. Bonar, “Prediction of mobile radio wave propagation aver buildings of irregular heights and spacings, IEEE Trans. Ant. Prop., vol. 42, n°2, pp. 137-144.
27. 27. Microwaves UCL 27 Macrocells-Physical models S. Saunders, F; Bonar, “Explicit multiple building diffraction attenuation function for mobile radio wave propagation”, Electr. Let., vol. 27, n°14, pp. 1276-1277, 1991.
28. 28. Microwaves UCL 28 Macrocells-base station antennas
29. 29. Microwaves UCL 29 Shadowing
30. 30. Microwaves UCL 30 Shadowing Typical variation of shadowing with mobile position, at a fixed distance of the base station.
31. 31. Microwaves UCL 31 Shadowing
32. 32. Microwaves UCL 32 Shadowing
33. 33. Microwaves UCL 33 Narrowband fast fading After path loss and shadowing, there is still significant variation in the signal as mobile moves over distances which are small compared with the shadowing. This phenomenon is Fast fading and can be described by deterministic models statistical models
34. 34. Microwaves UCL 34 Narrowband fast fading Non-line-of-sight Line-of-sight
35. 35. Microwaves UCL 35 Narrowband fast fading Deterministic model: ray-tracing method The built-up area is composed of parallelepipedic blocs with plane faces representing buildings either vegetation. The field arriving at the receiver results from the combination of all components arriving at the terminal: - direct component (if it exists) - reflected components (various orders of reflection) - diffracted components (various orders of diffraction) - scattered components (d∼λ). It is necessary to know the√electrical characteristics of the blocs (ε and σ) at the frequency of interest.
36. 36. Microwaves UCL 36 Narrowband fast fading 3-D bloc model for “place du Levant” T
37. 37. Microwaves UCL 37 Narrowband fast fading 30 40 50 60 70 80 90 −60 −55 −50 −45 −40 −35 −30 12.5 GHz Distance from Maxwell building, [m] Receivedpower,[dB] 30 40 50 60 70 80 90 −65 −60 −55 −50 −45 −40 −35 −30 30 GHz Distance from Maxwell building, [m] Receivedpower,[dB] + Simulation winter Simulation summer Meas. winter Meas. summer Comparison between simulation and measurement
38. 38. Microwaves UCL 38 Narrowband fast fading LOS path (simulated, without trees)
39. 39. Microwaves UCL 39 Narrowband fast fading Path under the balcony
40. 40. Microwaves UCL 40 Narrowband fast fading T
41. 41. Microwaves UCL 41 Narrowband fast fading Statistical model for the multipath signal A sum of enough independent variables approaches very closely a normal distribution. In the NLOS case, the real and imaginary parts of the electric field components are composed of a sum of a large number of waves they have a normal distribution
42. 42. Microwaves UCL 42 Narrowband fast fading Complex baseband signal (Rice representation)
43. 43. Microwaves UCL 43 Narrowband fast fading Pdf of r is a Rayleigh function
44. 44. Microwaves UCL 44 Narrowband fast fading
45. 45. Microwaves UCL 45 Narrowband fast fading
46. 46. Microwaves UCL 46 Narrowband fast fading
47. 47. Microwaves UCL 47 Narrowband fast fading filtered
48. 48. Microwaves UCL 48 Narrowband fast fading Doppler effect on the direct wave v ϑ ( )( ) ö ç è æ ÷ ö ç è æ −= ÷ ö ç è æ ÷ ö ç è æ −= −= t v fjE vttfjE kxtjEEr ϑ λ π ϑ λ π ϑω cos2exp cos 1 2exp cosexp 00 00 00 xavv = xa df
49. 49. Microwaves UCL 49 Narrowband fast fading Effect of Doppler spread on signal spectrum: a different doppler shift affects all the multipaths λ v ffm 0±=
50. 50. Microwaves UCL 50 Narrowband fast fading Statistics of the angle of arrival of the multipaths Pdf of the arrival angle
51. 51. Microwaves UCL 51 Narrowband fast fading The mean power arriving from an element of angle dα ( ) ( ) αααα dpGP =)( has a given Doppler shift (G(α) is the antenna gain for α). The power spectrum of the received signal, S(f), is found by equating the power in an element of α to the power in an element of spectrum ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) α αααα αααααα d df pGpG fS dpGdpGdffSfP −−+ = −−+==
52. 52. Microwaves UCL 52 Narrowband fast fading Assuming a short dipole antenna: ( ) 5.1=αG and the spectral density becomes ( ) m m m fffor f ff fS < öç è æ− = 2 1 5.1 π
53. 53. Microwaves UCL 53 Narrowband fast fading Classical Doppler spectrum Very difficult to measure due to the small bandwith!
54. 54. Microwaves UCL 54 Narrowband fast fading Limited angle of arrival : −π/2 π/2 β β 1/2β p(α) β β ( ) ( )( )2 1 5.1 mm fff fS − = β 22 mm fff ≤≤−
55. 55. Microwaves UCL 55 Narrowband fast fading Other measurable parameters linked to the Doppler spectrum
56. 56. Microwaves UCL 56 Narrowband fast fading LCR Jakes
57. 57. Microwaves UCL 57 Narrowband fast fading AFD
58. 58. Microwaves UCL 58 Narrowband fast fading Exemple: Soit un système mobile à 900 MHz et un mobile se déplaçant à 100 km/h, combien de fois le signal sera-t-il de 20dB inférieur à sa valeur rms en 1 minute? Dans ce cas, Hz c vf f c m 33.83 103 36001010010900 8 36 = ⋅ == ( ) 1.020 25.099.01.05.2exp2 2 =−= ≅⋅⋅=−= dBrcar rr f N m R π Cela fait secondeparfois2125.0 == mR fN En doublant la fréquence et en divisant la vitesse par deux, on obtient le même lcr.
59. 59. Microwaves UCL 59 Narrowband fast fading Importance of interleaving
60. 60. Microwaves UCL 60 Narrowband fast fading Another way to see Doppler effect is to work in time domain. The inverse Fourier Transform of the power spectral density is the autocorrelation function. It expresses correlation between a signal at t and its value at t+τ. The autocorrelation function of the received signal writes down ( ) ( ) ( )[ ] [ ]2* αταατρ EttE += For the classical spectrum, one obtains ( ) ( )τπρ mfJt 20= The coherence time is defined as the time during which teh channel can be considered as constant. The signals, shorter then the coherence time are not affected by the Doppler shift nor the speed of the mobile.
61. 61. Microwaves UCL 61 Narrowband fast fading In the time domain:
62. 62. Microwaves UCL 62 Narrowband fast fading Exemple: Quel est le débit maximum pour éviter les effets de l’étalement Doppler dans un système mobile à 900 MHz pour une vitesse maximum du mobile de 100 km/h? La fréquence Doppler maximum est Hz c vf f c m 33.83 103 36001010010900 8 36 = ⋅ == Le temps de cohérence est ms f T m c 15.2 33.8316 9 16 9 === ππ C’est donc la durée maximum d’un symbole, cela fait un débit symbole minimum de 465 bits/sec.
63. 63. Microwaves UCL 63 Wideband fast fading
64. 64. Microwaves UCL 64 Wideband fast fading
65. 65. Microwaves UCL 65 Wideband fast fading
66. 66. Microwaves UCL 66 Wideband fast fading
67. 67. Microwaves UCL 67 Wideband fast fading
68. 68. Microwaves UCL 68 Wideband fast fading
69. 69. Microwaves UCL 69 Wideband fast fading
70. 70. Microwaves UCL 70 Wideband fast fading
71. 71. Microwaves UCL 71 Wideband fast fading
72. 72. Microwaves UCL 72 Wideband fast fading
73. 73. Microwaves UCL 73 Megacells
74. 74. Microwaves UCL 74 Megacells
75. 75. Microwaves UCL 75 Megacells
76. 76. Microwaves UCL 76 Megacells
77. 77. Microwaves UCL 77 Megacells Local multipath effects
78. 78. Microwaves UCL 78 Megacells Empirical narrowband models Empirical Roadside Shadowing model (ERS) Statistical models Loo model (shadowing due to roadside trees) Corazza model Lutz model (2 states: LOS and NLOS) Physical-statistical model for built up area
79. 79. Microwaves UCL 79 Megacells dm w hm hb hb h2 h1 L A' A Basic physical parameters:
80. 80. Microwaves UCL 80 Megacells Fade statistics: ( ) ( ) ( ) ( ) ( ) ( ) ϑφϑϕ ϑφ π π φθ dddwdddhTTwTdT hTTaT mbWmD w bHWDHAA m bmb ⋅⋅⋅ ⋅⋅= ∞ ∞2/ 0 2/ 0 0 0 0
81. 81. Microwaves UCL 81 Megacells 0 2 4 6 8 10 12 14 16 18 20 0 0.05 0.1 0.15 0.2 0.25 0.3 Building height, [m] Probabilitydensityfunction Guildford Building height distribution
82. 82. Microwaves UCL 82 Megacells 5 15 25 35 45 55 65 75 85 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Elevation angle, [deg.] Probabilitydensityfunction Maximum elevation angle for Iridium constellation at London
83. 83. Microwaves UCL 83 Megacells 0 10 20 30 40 50 60 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Street width, [m] Probabilitydensityfunction Street width distribution in Guildford
84. 84. Microwaves UCL 84 Megacells 0 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Satellite azimuth angle, [rad.] Probabilitydensity Distribution of the nearest satellite azimuth angle (relative to earth parallels) for Iridium at London
85. 85. Microwaves UCL 85 Megacells 0 1 2 3 4 5 6 0.15 0.152 0.154 0.156 0.158 0.16 0.162 0.164 0.166 0.168 0.17 Satellite azimuth angle, [rad.] Probabilitydensity Distribution of the global azimuth angle (relative to street axis) for Iridium constellation at London
86. 86. Microwaves UCL 86 Megacells