1. 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

2. 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) =

3. 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

4. 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

5. 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 

6. 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 =

7. 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

8. 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

9. 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) <  ] =

10. 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)

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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)

21. Correction Factor = GAREA(dB)35 30 25 20 15 10 5
GAREA(dB)
 103
frequency (MHz)
suburban area
quasi open area
open area

22. 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

23. 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

24. (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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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)

32. 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

33. 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)

34. (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

35. 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

36. 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

37. 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

38. (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

39. 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

40. 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

41. 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