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3.9 Predictable Link Budget Design using Path Loss Models
Most RF propagation models are derived from combined (i) analytical studies (ii) experimental methods Empirical Approach – measured data is fitted to a curve or an analytical expression uses field measurements implicitly accounts for all factors (known and unknown) model generally not valid for all frequencies or environments Classical Models have evolved to predict large scale path loss used to estimate receive signal strength as a function of distance used along with noise analysis techniques used to predict SNR for RF mobile systems
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Pr(d) = Median Path Loss Determination
estimate receive power at distance d from transmitter Ẽ = Ẽd Ẽ = total received electrical field (V/m) Ẽd = electric field of equivalent direct path N = number of paths between T and R Lk = relative loss of kth path k = relative phase shift of kth path if LOS exists L0 = 1 and 0 = 0 Pr(d) =
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3.9.1 Log Distance Path Loss Model
average received power decreases logarithmically with distance theory & measurements indicate validity for indoors & outdoors (1) Average Large Scale Path Loss Model distance dependent mean path loss - over significant distances (3.67) (3.68) d0 = close in reference distance, often determined emperically d = transmitter - receiver separation n = path loss exponent - indicates rate of path loss increase with d0
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Free Space Reference Distance, d0,
always in antenna’s far-field - eliminate near field effects for reference path must be specified for different environments Environment d0 large cellular 1km microcell 1m-10m Reference Path Loss, PL(d0) calculated using either (i) free space path loss (eqn 3.5) (ii) field measurements at d0 Path Loss Exponent, n Environment n free space 2 In building LOS Urban-cellular Obstructed in Building 4-6 Shadowed Urban Cellular 3-5 Obstructed in Factories 2-3
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Pr(d) (dB)= Pt(d) (dB) - PL(d) (dB)
3.9.2 Log Normal Shadowing surrounding clutter isn’t considered by log distance model averaged received power (eqn 3.68) is inconsistent with measured data measured PL(d) at any location is random, with log normal distribution about (normal distribution of log10(•) ) (3.69a) PL(d) = PL(d) (dB) = (3.69b) Pr(d) (dB)= Pt(d) (dB) - PL(d) (dB) antenna gains included in PL(d) = zero-mean Gaussian distributed random variable (in dB) = standard deviation of
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Log Normal Distribution - describes random shadowing effects
for specific Tx-Rx, measured signal levels have normal distribution about distance dependent mean (in dB) occurs over many measurements with same Tx-Rx & different clutter standard deviation, (also measured in dB) Lognormal Model For Local Shadowing typically, dB ranges from 5-12 let u = median path loss (dB) at distance d from transmitter distribution xdB of observed path loss has pdf given by: f(xdB) = Pr[xdB = x] = Pr(xdB > x) = it follows that =
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median 50% of samples expected to be > median &
Log Normal Graph: Pr(xdB > x) vs Gain/Loss Relative to Median Path Loss shown for dB = 4,6,8, 12 median 50% of samples expected to be > median & 50% expected to be < median all curves intersect at median Pr (Gain < Abscissa) Gain relative to Median Path Loss(dB) 1 0.5 10-1 10-2 10-3 10-4 dB = 12 dB 8 dB 6 dB 4dB dB loss relative to median path % time 6dB > 10dB 1% 12dB 10% 4dB > 7dB
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Path Loss Model Parameters for arbitrary location & specified Tx-Rx
d0 – close in reference distance - clutter standard deviation n – path loss exponent Used for system design & analysis simulations to provide estimated Pr(d) at random locations & n are derived from measurements using linear regression minimizes difference between measured & estimated path loss minimized in a mean-square sense over many measurements & d’s
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Q-function is used to determine probability that PR(d) threshold
where Q(-z) = 1- Q(z) Q(z) = (i) PL(d) is RV with a normal distribution in dB about as a result, Pr(d) inherits these characteristics (ii) Pr(d) > or Pr(d) < is determined from CDF 3.71 Pr [Pr(d) > ] = 3.72 Pr [Pr(d) < ] =
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3.9.3 Determination of % Coverage Area
in a given coverage area, let = desired receive signal level – could be determined by receiver sensitivity (or visa versa) random shadowing effects cause some locations at d to have received power, Pr(d) < Determine boundary coverage vs % area covered within a boundary, assuming a circular coverage area with radius R from base station likelihood of coverage at cell boundary is known (given) d = r represents radial distance from transmitter useful service area (coverage area): U() = % area with Pr(d) > U() = (3.73)
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Left Axis = % area with Pr(r) > (coverage area-use 3.73)
Right Axis = Pr[Pr(r) > ] (boundary coverage-use 3.68) /n = std deviation of path loss exponent 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 Pr[Pr(r) > ] 1 U() % /n Pr[Pr(r) > ] /n U() 0.95 2 0.99 0.70 0.9 0.60 0.82
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3.10 Outdoor Propagation Model
estimating PL(d) requires terrain profile for propagation over irregular terrain such as simple curved earth profile highly mountainous obstacles: trees, building, all models predict Pr(d) at given point or small area (sector) wide variations in approach, complexity, accuracy most based on systematic interpretation of empirical data - Longely Rice - Durkins Model - Okumura Model - Hata Model - Wideband PCS Microcell - PCS Extension to Hata Model - Walfisch – Bertoni Model
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3.10.1 Longely Rice Model (ITS irregular terrain model)
used for point-point systems under different types of terrain frequency ranges from 40MHz-100GHz (ii) Signal Strengths within radio horizon predicted using Geometric Optics Techniques (primarily 2-ray ground reflection) (iii) Diffraction Loss over isolated obstacles predicted using Fresnel- Kirchoff knife edge models (iv) Troposcatter over long distances predicted using Forward Scatter Theory (v) Far-Field Diffraction losses in double horizon paths predicted using Modified Van der Pol-Bremner Method (i) Median Transmission Loss predicted using path geometry of terrain profile & refractivity of troposphere
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Longely Rice Model: available as a computer program
calculates large scale median transmission loss over irregular terrain for frequencies between 20MHz-10GHz input parameters include: transmission frequency, path length & antenna heights, polarization, surface refractivity earth radius & climate ground conductivity & ground dielectric constant path specific parameters: antennas’ horizon distance, horizon elevation angle, trans-horizon distance, terrain irregularity Prediction Modes for Longely Rice 1. point-point mode: used when detailed terrain profile or path specific parameters are known 2. area mode prediction: uses estimated path specific parameters
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3.10.2 Durkins Model: similar to Longly-Rice
predicts field strength contours over irregular terrain adopted by UK joint radio committee consists of two parts (1) ground profile reconstructed from topographic data of proposed surface along radial joining transmitter and receiver models LOS & diffraction derived from obstacles & local scatters assume all signal received along radial (no multipath) (2) expected path loss calculated along the radial move receiver location to deduce signal strength contour pessimistic in narrow valleys identifies weak reception areas well
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3.10.3 Okumura Model – wholly based on measured data - no analytical explanation
among the simplest & best for in terms of path loss accuracy in cluttered mobile environment disadvantage: slow response to rapid terrain changes common std deviations between predicted & measured path loss 10dB - 14dB widely used for urban areas useful for - frequencies ranging from 150MHz-1920MHz - frequencies can be extrapolated to 3GHz - distances from 1km to 100km - base station antenna heights from 30m-1000m
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Okumura developed a set of curves in urban areas with quasi-smooth terrain
effective antenna height: - base station hte = 200m - mobile: hre = 3m gives median attenuation relative to free space (Amu) developed from extensive measurements using vertical omni- directional antennas at base and mobile measurements plotted against frequency
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Estimating path loss using Okumura Model
1. determine free space loss, Amu(f,d), between points of interest 2. add Amu(f,d) and correction factors to account for terrain L50(dB)= LF + Amu(f,d) – G(hte) – G(hre) – GAREA (3.80) L50 = 50% value of propagation path loss (median) LF = free space propagation loss Amu(f,d) = median attenuation relative to free space G(hte) = base station antenna height gain factor G(hre) = mobile antenna height gain factor GAREA = gain due to environment
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Amu(f,d) & GAREA have been plotted for wide range of frequencies
antenna gain varies at rate of 20dB per decade or 10dB per decade G(hte) = 10m < hte < 1000m (3.81a) G(hre) = hre 3m (3.81b) 3m < hre <10m (3.81b) model corrected for h = terrain undulation height isolated ridge height average terrain slope mixed land/sea parameter
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70 60 50 40 30 20 10 Amu(f,d) (dB) f (MHz) 100 80 5 2 1 d(km) Urban Area ht = 200m hr = 3m Median Attenuation Relative to Free Space = Amu(f,d) (dB)
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Correction Factor = GAREA(dB)
35 30 25 20 15 10 5 GAREA(dB) 103 frequency (MHz) suburban area quasi open area open area
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3.10.4 Hata Model: empirical model of graphical path loss data from
Okumura - predicts median path loss for different channels - valid over UHF/VHF band from 150MHz-1.5GHz - charts used to characterize factors affecting mobile land propagation - standard formulas for approximating urban propagation loss - correction factors for some situations - compares closely with Okumura model as d > 1km large mobile systems
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L50 (urban)(dB) = A + B log10d
Parameter Comment L50 50th % value (median) propagation path loss (urban) fc frequency from 150MHz-1.5GHz hte, hre Base Station and Mobile antenna height (hre) correction factor for hre , affected by coverage area d Tx-Rx separation (3.82) L50 (urban)(dB) = A + B log10d A= log10(fc) – log10(hte) – (hre) represents fixed loss – approximately 2.6 power law dependence on fc dependence on antenna heights is proportional to hre1.382 B= log10(hte) represents path loss exponent, worst case ≈ 4.5 L50 (urban)(dB) = log10 fc – log10 hte – (hre) + ( hte)log10 d
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(1.1log10 fc - 0.7)hre – (1.56log10 fc - 0.8)dB
Mobile Antenna Height Correction Factor for Hata Model (hre) Comment (1.1log10 fc - 0.7)hre – (1.56log10 fc - 0.8)dB Medium City 3.83 8.29(log hre)2 – 1.1 dB Large City (fc 300MHz) 3.84a 3.2(log hre)2 – 4.97 dB Large City (fc > 300MHz) 3.84b Hata Model for Rural and Suburban Regions represent reductions in fixed losses for less demanding environments L50 (dB) Comment L50 (urban) - 2[log10 (fc/28)]2 – 5.4 Suburban Area 3.85 L50 (urban) (log10 fc) log10 fc Rural Area 3.86
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Valid Range for Parameters
150MHz < fc < 1GHz 30m < hb < 200m 1m < hm < 10m 1km < r < 20km Propagation losses increase with frequency in built up areas
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Example Tables for Okumura-Hata Model
Path Loss (dB) Range (km) 180 170 160 150 140 130 120 110 100 900 MHz 700 MHz hte = 30m hre = 1m Terrain Legend Urban Suburban Open Path Loss (dB) hte (m) 160 155 150 145 140 135 130 125 120 20km 10km 5km fc = 700MHz
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3.10.5 PCS Extension to Hata Model
European Co-operative Scientific & Technical (EUROCOST) formed COST-231 extend Hatas model to 2GHz L50 (urban)(dB) = logfc – loghte – (hre) + ( hte)logd + CM (hre) defined in 3.83, 3.84a, 3.84b CM = 0dB for medium sized cities CM = 3dB metropolitan centers fc = frequency from 1500MHz - 2 GHz hte = 30m-200m hre = 1m-10m d = 1km-20km
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3.10.6 Walfisch & Bertoni Model
path loss: S = P0Q2P (3.89) P0 = (3.90) P0 = free space path loss between isotropic antennas Q2 = reduction in rooftop signal due to row of buildings that immediately shadow hill P1 = based on diffraction determines signal loss from roof top to street S (dB) = L0 + Lrts + Lms (3.91) L0 = free space loss Lrts = roof-to-street diffraction & scatter loss Lms = multi-screen diffraction loss from rows of building
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3.10.7 Wideband PCS Microcell Model
Feuerstien Measured cellular systems in Bay Area - 20MHz pulsed transmitter at 1900 MHz - base station antenna heights 3.7m, 8.5m, 13.3m - mobile antenna heights 1.7m assume flat ground reflection model let df = 1st Fresnel zone clearance df = (3.92a) Model for Average Path Loss - LOS channel double regression model with regression breakpoint at 1st Fresnel zone clearance fits measured data well model assumes omni-directional vertical antennas
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Average Path Loss – PCS Microcell
(3.92b) p1 = = path loss in dB at reference distance d0 = 1m d = T-R separation distance n1, n2 = path loss exponents relates to antenna heights e.g. at 1900MHz p1 = 38.0dB
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Transmit Antenna Height
= 10nlog(d) + p1 (3.92c) n = OBS path loss exponent – related to transmitter height = log normal shadowing component from distance dependent mean (3.10.2) Transmit Antenna Height 1900 MHz LOS n n2 (dB) 1900 MHz OBS n (dB) low (3.7m) med (8.5m) high(13.3m)
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3.11 Indoor Propagation Model
smaller Tx-Rx separation distances than outdoors higher environmental variability for much small Tx-Rx separation - conditions vary from: doors open/closed, antenna position, - variable far field radiation for receiver locations & antenna types strongly influenced by building features, layout, materials Dominated by same mechanisms as outdoor propagation (reflection, refraction, scattering) Classified as either LOS or OBS Surveyed by [Mol91], [Has93] - Partition Losses – Same Floor - Partition Losses – Different Floor - Log-distance path loss model - Ericsson Multiple Breakpoint Model - Attenuation Factor Model
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Partition Losses – Same Floor
hard partitions: immovable, part of building soft partitions: movable, lower than the ceiling Partition Losses – Different Floor: dependent on external building dimensions, structural characteristics & materials Log-distance path loss model: accurate for many indoor paths PL(dB) = (3.93) n depends on surroundings and building type = normal random variable in dB having std deviation identical to log normal shadowing mode (3.69)
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(1) Ericsson Multiple Breakpoint Model: measurements in multi-floor office building
uses uniform distribution to generate path loss values between minimum &maximum range, relative to distance 4 breakpoints consider upper and lower bound on path loss assumes 30dB attenutation at d0 = 1m - accurate for f = 900MHz & unity gain anntenae provides deterministic limit on range of path loss at given distance 20dB 30 50 70 90 110 attenuation (dB) meters
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primary ray tracing = single ray drawn between Tx & Rx
(2) Attenuation Factor Model (Seidel92b) includes effect of building type & variations caused by obstacles reduces std deviation for path loss to 4dB std deviation for path loss with log distance model 13dB 3.94 nSF = exponent value for same floor measurement – must be accurate FAF = floor attenuation factor for different floor PAF = partition attenuation factor for obstruction encountered by primary ray tracing primary ray tracing = single ray drawn between Tx & Rx yields good accuracy with good computational efficiency FAF PAF(1) PAF(2) Rx Tx
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Replace FAF with nMF = exponent for multiple floor loss
3.95 decreases as average region becomes smaller-more specific Building Path Loss obeys free space + loss factor () (Dev90b) loss factor increases exponentially with d (dB/m) = attenuation constant for channel 3.96 4-story bldg 2-story bldg f 850MHz 0.62 1.7GHz 0.57 f 850MHz 0.48 1.7GHz 0.35
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Path Loss Exponent & Standard Deviation for Typical Building
Location n σ (dB) number of points same floor 2.76 12.9 501 through 1 floor 4.19 5.1 73 through 2 floor 5.04 6.5 30 through 3 floor 5.22 6.7
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(3) Simple Indoor Path Loss Model
Lp (dB) = (dB) + 2.47 r = distance between transmitter & receiver r0 = nominal reference distance (typically 1m) WAF(p) is wall attenuation factor, for P floors FAF(q) is floor attenuation factor, for Q floors n 2 for close distances, larger for greater distances material loss at 900MHz loss at 1700MHz plaster wall 5dB 11dB concrete wall 10dB 17dB more accurate when P and Q are small model neglects angle of incidence & effect of distance on n
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3.12 Signal Penetration into Buildings
no exact models signal strength increases with height lower levels are affected by ground clutter (attenuation & penetration) higher floors may have LOS channel stronger incident signal on walls RF Penetration affected by - frequency - height within building - antenna pattern in elevation plain
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penetration loss decreases with increased frequency loss in front of windows is 6dB greater than without windows penetration loss decreases 1.9dB with each floor when < 15th floor increased attenuation at >15 floors – shadowing affects from taller buildings metallic tints result in 3dB to 30dB attenuation penetration impacted by angle of incidence
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Penetration Loss vs Frequency for two different building
(1) (2) Frequency (MHz) Attenuation (dB) 441 16.4 896.5 11.6 1400 7.6 Frequency (MHz) Attenuation (dB) 900 14.2 1800 13.4 2300 12.8 Ray Tracing & Site Specific Models rapid acceleration of computer & visualization capabilities SISP – site specific propagation models GIS – graphical information systems - support ray tracing - augmented with aerial photos & architectural drawings
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