EE6604 Personal & Mobile Communications. Week 7. Path Loss Models. Shadowing

Transcription

1 EE6604 Personal & Mobile Communications Week 7 Path Loss Models Shadowing 1

2 Okumura-Hata Model L p = A+Blog 10 (d) A+Blog 10 (d) C A+Blog 10 (d) D for urban area for suburban area for open area where A = log 10 (f c ) 13.82log 10 (h b ) a(h m ) B = log 10 (h b ) C = 5.4+2[log 10 (f c /28)] 2 D = [log 10 (f c )] log 10 (f c ) Okumura and Hata s model is in terms of carrier frequency 150 f c 1000 (MHz) BS antenna height 30 h b 200 (m) MS antenna height 1 h m 10 (m) distance 1 d 20 (km) between the BS and MS. The model is known to be accurate to within 1 db for distances ranging from 1 to 20 km. 2

3 The parameter a(h m ) is a correction factor (1.1log 10 (f c ) 0.7)h m (1.56log 10 (f c ) 0.8) a(h m ) = for medium or small city 8.28(log 10 (1.54h m )) for f c 200 MHz 3.2(log 10 (11.75h m )) for f c 400 MHz for large city 3

4 Large City Suburban Open Area Path Loss (db) Log(distance in km) Path loss predicted by the Okumura-Hata model. Large city, f c = 900 MHz, h b = 70 m, h m = 1.5 m. 4

5 CCIR Model To account for varying degrees of urbanization, the CCIR (Comité International des Radio- Communication, now ITU-R) developed an empirical model for the path loss as: L p (db) = A+Blog 10 (d) E where A and B are defined in the Okumura-Hata model with a(h m ) being the medium or small city value. The parameter E accounts for the degree of urbanization and is given by E = 30 25log 10 (% of area covered by buildings) where E = 0 when the area is covered by approximately 16% buildings. 5

6 Lee s Area-to-area Model Lee s area-to-area model is used to predict a path loss over flat terrain. If the actual terrain is not flat, e.g., hilly, there will be large prediction errors. Two parameters are required for Lee s area-to-area model; the power at a 1 mile (1.6 km) point of interception, µ Ωp (d o ), and the path-loss exponent, β. The received signal power at distance d can be expressed as or in decibel units µ Ωp (d) = µ Ωp (d o ) d β f d o f o n α 0 µ Ωp (dbm)(d) = µ Ωp (dbm)(d o ) 10βlog 10 d d o 10nlog 10 f f o +10log 10 α 0, where d is in units of kilometers and d o = 1.6 km. The parameter α 0 is a correction factor used to account for different BS and MS antenna heights, transmit powers, and antenna gains. 6

7 Lee s Area-to-area Model The following set of nominal conditions are assumed in Lee s area-to-area model: frequency f o = 900 MHz BS antenna height = m BS transmit power = 10 watts BS antenna gain = 6 db above dipole gain MS antenna height = 3 m MS antenna gain = 0 db above dipole gain If the actual conditions are different from those listed above, then we compute the following parameters: α 1 = α 2 = α 3 = BS antenna height (m) m MS antenna height (m) 3 m transmitter power 10 watts α 4 = BS antenna gain with respect to λ c/2 dipole 4 α 5 = different antenna-gain correction factor at the MS 2 κ 7

8 Lee s Area-to-area Model The parameters β and µ Ωp (d o ) have been found from empirical measurements, and are listed in the Table below. Terrain µ Ωp (d o ) (dbm) β Free Space Open Area North American Suburban North American Urban (Philadelphia) North American Urban (Newark) Japanese Urban (Tokyo) For f c < 450 MHz in a suburban or open area, n = 2 is recommended. In an urban area with f c > 450MHz, n = 3 is recommended. The value of κ in is also determined from empirical data as κ = 2 for a MS antenna height > 10 m 3 for a MS antenna height < 3 m. 8

9 Lee s Area-to-area Model The path loss L p (db) is the difference between the transmitted and received field strengths, L p (db) = µ Ωp (dbm) (d) µ Ωt (dbm). To compare with the Okumura-Hata model, we assume a half wave dipole BS antenna, so that α 4 = 6 db. Then by using the same parameters as before, h b = 70 m, h m = 1.5m, f c = 900 MHz, a nominal BS transmitter power of 40 dbm (10 watts), and the parameters in the Table for µ Ωp (dbm) (d o ) and β, the following path losses are obtained: L p (db) = log 10 d Free Space log 10 d Open Area log 10 d Suburban log 10 d Philadelphia log 10 d Newark log 10 d Tokyo 9

10 Tokyo Newark Philadephia Suburban Open Area Free Space Path Loss (db) Log(distance in km) Path loss obtained by using Lee s method; h b = 70 m, h m = 1.5 m, f c = 900 Mhz, and an isotropic BS antenna. 10

11 COST231-Hata Model COST231 models are for propagation in the PCS band. Path losses experienced at 1845 MHz are about 10 db larger than those experienced at 955 MHz. The COST-231 Hata model for NLOS propagation is where L p = A+Blog 10 (d)+c A = log 10 (f c ) 13.82log 10 (h b ) a(h m ) B = log 10 (h b ) 0 medium city and suburban areas C = with moderate tree density 3 for metropolitan centers 11

12 COST231-Walfish-Ikegami LOS Model For LOS propagation in a street canyon, the path loss is L p = log 10 (d)+20log 10 (f c ), d 20 m where the first constant is chosen so that L p is equal to the free-space path loss at a distance of 20 m. The model parameters are the distance d (km) and carrier frequency f c (MHz). 12

13 COST231-Walfish-Ikegami NLOS Model h b h b h Roof BS d MS h h Roof m w b φ MS incident wave direction of travel Definition of parameters used in the COST231-Walfish-Ikegami model. 13

14 For NLOS propagation, the path loss is composed of three terms, viz., L p = The free-space loss is L o +L rts +L msd for L rts +L msd 0 L o for L rts +L msd < 0 L o = log 10 (d)+20log 10 (f c ) The roof-top-to-street diffraction and scatter loss is L rts = log 10 (w)+10log 10 (f c )+20log 10 h m +L ori where (φ), 0 φ 35 o L ori = (φ 35), 35 φ 55 o (φ 55), 55 φ 90 o h m = h Roof h m 14

15 The multi-screen diffraction loss is L msd = L bsh +k a +k d log 10 (d)+k f log 10 (f c ) 9log 10 (b) where and L bsh = k a = k d = k f = 4+ 18log 10 (1+ h b ) h b > h Roof 0 h b h Roof 54, h b > h Roof h b, d 0.5km and h b h Roof h b d/0.5, d < 0.5km and h b h Roof 18, h b > h Roof h b /h Roof, h b h Roof 0.7(f c /925 1), medium city and suburban 1.5(f c /925 1), metropolitan area h b = h b h Roof. 15

16 k a is the increase in path loss for BS antennas below the roof tops of adjacent buildings. k d and k f control the dependency of the multi-screen diffraction loss on the distance and frequency, respectively. The model isvalidforthe followingranges ofparameters, 800 f c 2000(MHz), 4 h b 50 (m), 1 h m 3 (m), and 0.02 d 5 (km). The following default values are recommended, b = (m), w = b/2, φ = 90 o, and h Roof = 3 number of floors+roof (m), where roof = 3 (m) pitched and 0 (m) flat. 16

17 3GPP 3-D Path Loss Models The 3GPP path loss models are valid from 2 to 6 GHz for different BS and MS antenna heights. The 3GPP path loss models are categorized into urban macrocell (UMa) and urban microcell (UMi) cases, corresponding to BS antenna heights of 25 m or less and 25 m or more, respectively. The UMa and UMi cases are further categorized into LoS, NLoS, and outdoor-to-indoor scenarios. The distance definitions are defined below for outdoor scenarios and for outdoor-indoor scenarios. 17

18 3GPP 3-D Path Loss Model Distance Definitions # &%! " # $% Definition of d 2D and d 3D for outdoor mobile stations. # $%&'( # $%*+! " # )%&'( # )%*+ Definition of d 2Dout, d 2Din, d 3Dout and d 3Din for indoor mobile stations. 18

19 LoS Probability The various 3GPP path loss models make use of the probability of LoS condition. For microcells and outdoor MSs, the probability of LoS is P LoS = min(18/d 2D,1)(1 e d 2D/36 )+e d 2D/36 For microcells and indoor MSs, the above formula is used with d 2D replaced by d 2Dout. For macrocells and outdoor MSs, the probability of LoS is where and P LoS = ( min(18/d 2D,1)(1 e d 2D/63 )+e d 2D/63 ) (1+C(d 2D,h m )) C(d 2D,h m ) = g(d 2D ) = 0, h m < 13 m ) 1.5 g(d2d ), 13 m h m 23 m ( hm (1.25e 6 )d 2 2D ed 2D/150, d 2D > 18 m 0, otherwise For macrocells and indoor MSs, the above formulas are used with d 2D replaced by d 2Dout. 19

20 3GPP 3D-UMa LoS For macrocells with LoS conditions L UMaLoS (db) = 22.0log 10 (d 3D ) log 10 (f c ), 10 m < d 2D < d BP L UMaLoS (db) = 40log 10 (d 3D ) log 10 (f c ) 9log 10 ( d 2 BP +(h b h m ) 2), d BP < d 2D < 50 h b = 25 m; 1.5 m h m 22.5 m Thebreakpointdistanceisgivenbyd BP = 4h b h m f c /ccorrespondingtothelastlocalmaxima in the flat earth model. In the 3D-UMa scenario the effective antenna heights h b and h m are computed as follows: h b = ĥb h E, h m = ĥm h E, where ĥb and ĥm are the actual antenna heights, and the effective environment height h E depends on the link between a BS and a MS. For LoS links, h E = 1 m with probability 1/(1+C(d 2D,h m )), where the function C(d 2D,h m ) is defined earlier. Otherwise, h E is chosen from a discrete uniform distribution on the set {12,15,...,(h m 1.5)}. The shadow standard deviation is σ Ω = 4 db. 20

21 3GPP 3D-UMa NLoS For macrocells with NLoS conditions L UMaNLoS (db) = max { } L UMaNLoS (db), L UMaLoS (db), where L UMaNLoS (db) = log 10 (W)+7.5log 10 (h build ) ( (h build /h b ) 2) log 10 (h b ) +( log 10 (h b ))(log 10 (d 3D ) 3) +20log 10 (f c ) ( 3.2(log 10 (17.625)) ) 0.6(h m 1.5) and 10 m < d 2D < 5,000 m h build = average building height W = street width h b = 25 m, 1.5 m h m 22.5 m, W = 20 m, h build = 20 m Applicable ranges: 5 m < h build < 50 m 5 m < W < 50 m 10 m < h b < 150 m 1.5 m h m 22.5 m The shadow standard deviation is σ Ω = 6 db. 21

22 3GPP 3D-UMa O-to-I For macrocells with outdoor-to-indoor conditions For a hexagonal cell layout: where L UMaO to I (db) = L b (db) +L tw (db) +L in (db) L b (db) = L UMa (db) (d 3D out +d 3D in ) L tw (db) = 20 (loss through wall) L in (db) = 0.5d 2D in (inside loss) 10 m < d 2D out +d 2D in < 1000 m 0 m < d 2D in < 25 m h b = 25 m,h m = 3(n fl 1)+1.5, n fl = 1,2,3,4,5,6,7,8 d 2D in is assumed uniformly distributed between 0 and 25. The shadow standard deviation is σ Ω = 7 db. The building penetration loss (BPL) or loss through wall in the 3GPP 3D-UMa O-to-I model is 20 db. However, this will vary greatly depending on the building. Moreover, the building penetration loss increases with frequency. An empirical BPL model is BPL (db) = 10log 10 ( A+Bf 2 c ), where f c is the frequency in GHz, A = 5 and B = 0.03 for low loss buildings and A = 10 and B = 5 for high loss buildings. 22

23 3GPP 3D-UMi LoS, NLoS and 3D-UMi O-to-I The microcell LoS path loss is the same as the macrocell LoS path loss L UMaLOS (db), except that h E = 1 m with probability one and the shadow standard deviation is σ Ω = 3 db. For NLoS and a hexagonal cell layout where L UMiNLoS (db) = max { L UMiNLoS (db), L UMiLoS (db) }, L UMiNLoS (db) = 36.7log 10 (d 3D ) log 10 (fc) 0.3(h m 1.5) 10 m < d 2D < 2000 m h b = 10 m 1.5 m h m 22.5m The shadow standard deviation is σ Ω = 4 db. The microcell outdoor-to-indoor path loss is the same as the macrocell outdoor-to-indoor path loss L UMaO to I (db), except that h b = 10 m instead of h b = 25 m. The shadow standard deviation remains at σ Ω = 7 db. 23

24 Shadowing Shadows are very often modeled as being log-normally distributed. Let Then distributions of Ω v and Ω p are where and ξ = ln10/10. p Ωv (x) = p Ωp (x) = Ω v = E[α(t)], µ Ωv = E[Ω v ] Ω p = E[α 2 (t)], µ Ωp = E[Ω p ] 2ξ xσ Ω 2π exp ξ xσ Ω 2π exp ( 10log10 x 2 µ Ωv (dbm) 2σ 2 Ω ( 10log10 x µ Ωp (dbm) 2σ 2 Ω µ Ωv (dbm) = 10E[log 10 Ω 2 v] µ Ωp (dbm) = 10E[log 10 Ω p ] ) 2 ) 2 24

25 Shadowing By using a transformation of random variables, Ω v (dbm) = 10log 10 Ω 2 v and Ω p (dbm) = 10log 10 Ω p have the Gaussian densities p Ωv (dbm) (x) = p Ωp (dbm) (x) = 1 exp 2πσΩ 1 exp 2πσΩ (x µ Ω v (dbm) ) 2 2σ 2 Ω (x µ Ω p (dbm) ) 2 Note that the standard deviation σ Ω of Ω v (dbm) and Ω p (dbm) are the same. However, for Rician fading channels the means differ by where 2σ 2 Ω µ Ωp (dbm) = µ Ωv (dbm) +10 log 10 C(K) C(K) = 4e2K (K +1) π 1 F 2 1(3/2,1;K) 1F 1 (, ; ) is the confluent hypergeometric function (see Chap. 2, Appendix 3). Note that C(0) = 4/π, C( ) = 1, and 1 C(K) 4/π for 0 K.. 25

26 Shadow Simulation Shadows can be modelled by low-pass filtering white noise. Here we suggest a first-order low pass digital filter. In a discrete-time simulation, the local mean Ω k+1 (dbm) at step k+1 is generated recursively as follows: Ω k+1 (dbm) = ξω k (dbm) +(1 ξ)v k k is the step index. {v k } is a sequence of independent zero-mean Gaussian random variables with variance σ 2. ξ controls the shadow correlation The autocorrelation function of Ω k (dbm) can be derived as: φ Ω(dBm) Ω (dbm) (n) = 1 ξ 1+ξ σ2 ξ n 26

27 The variance of log-normal shadowing is σ 2 Ω = φ Ω (dbm) Ω (dbm) (0) = 1 ξ 1+ξ σ2 Consequently, we can express the autocorrelation of Ω k as φ Ω(dBm) Ω (dbm) (n) = σ 2 Ω ξ n Notice that the shadows decorrelated exponentially with the time lag in the autocorrelation function. Suppose we use discrete-time simulation, where each simulation step corresponds to T seconds. For a mobile station traveling at velocity v, the distance traveled in T seconds is vt meters. Let ξ D be the shadow correlation between two points separated by a spatial distance of D meters. Then the time autocorrelation of the shadowing is φ Ω(dBm) Ω (dbm) (n) φ Ω(dBm) Ω (dbm) (nt) = σ 2 Ωξ (vt/d) n D MeasurementsinStockholmhaveshownξ D = 0.1forD = 30meters(roughly). However, this can vary greatly depending on local topography. 27