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Lee’s Macroscopic Macroscopi c Propagation Propagati on Model
Lee model is one of the most popular macroscopic propagation models. mode ls. It is relatively relatively simple, simple, intuitive and once optimized, it provides reasonably accurate predictions. The model was developed as a result of large data collection campaign performed throughout the eighties in the northeastern United States. Due to its simple mathematical formulat formulation, ion, it is is frequent frequently ly used used in in computer simulations and propagation propagation modeling. Initially the model was developed for for propa propagat gation ion in and around around 900MH 900MHzz frequ frequenc ency y band. band. Recent Recently ly,, extens extensiv ivee data data colle collecti ction on and prop propaga agati tion on model model valid validat atio ions ns have have demon demonst stra rate ted d the the model model’s ’s appli applicab cabil ilit ity y for for freq frequen uenci cies es up to 2GHz. The main assumption of the model is that the propagation path loss depends on two types of factors: 1. Factors due to the natural terrain. 2. Factors due to clutter clutter and man made structures. structures. The model tries to separate the impacts of two factors by modeling them through separate paramete parameters. rs.
1.1 1.1
Equatio n of the Mod el
The equation used to implement Lee’s propagation model is given as P LR
= P LRref + m L log
d d L ref
+ ( P T − P LTref ) + C L log
hbs h Lbsref
+ F L log
hm h Lmref
+ DL
(1)
where: P L R
Received signal level in dBm
P LRref
Received signal level at the reference distance for the reference conditions in dBm
m L d d Lref
Slope coefficient in dB/decade Distance between the transmitter and receiver in miles Reference distance in miles
P T P LTref
Transmit power in dBm
hbs
Effective antenna height of the transmitter in feet
h Lbsref
Reference height of the transmitter transmitter in feet
hm
Height of the receiver in feet
Reference Refere nce transmit power in dBm
1
h L mref
Reference height of the receiver in meters/feet
DL C L , F L
Diffraction loses in dB Multiplier coefficients in dB
1.1.1 Reference Conditions Central to the application of Lee’s model is the notion of reference conditions. Examination of (1) shows that all of the parameters of the model are specified relative to standard configuration of the transmitter and receiver. The standard reference conditions are given in Table 1. Table 1. Reference conditions for Lee model1
Parameter
Symbol
Reference Distance Reference ERP Reference BTS Height Reference MS Height
d Lref
Reference Value 1 mile
P LTref
50 dBm
h Lbsref
150 feet
h L mref
10 Feet
If the configuration of the actual system is different than the reference conditions given in Table 1, the received signal level is corrected by appropriate correction. The corrections are given as: Transmit power correction:
∆ P LR = P T − P LTref
(2)
where P T is the actual transmit power (in dBm) and P LTref is the reference transmit power given in Table 1. BTS height correction
h ∆ P LR = C L log bs h Lbsref
(3)
where hbs is the effective base station height 2 and h Lbsref is the reference BS height as given in Table 1. Nominal value for multiplier coefficient is given as C L 1
= 15 .
The reference conditions given in this table reflect WI ZARD ’s implementation of Lee’s model. 2
MS height correction
h ∆ P LR = F L log ms h Lmsref
(4)
where hms is the actual height of the mobile station and h L mref is the reference height from Table 1. Nominal value for multiplier coefficient is given as F L
= 10 .
Example 4.1. Consider the RSL predictions at the distance d = 2.3 miles for the site having following numerical data: P Lref = − 59 dBm, m L = −38.4 dBm, P T = 52 dBm, hbs = 175 feet
and hms
= 10 feet.
Assume that the radio path is not obstructed.
Applying (1) we have: P LR
1.2
2.3 175 10 = −59 − 38.4 ⋅ log + (52 − 50) + 15 ⋅ log + 10 log = −71.89 dBm 1 150 10
Slope and Intercept (Effects of man made structures)
Slope and intercept parameters are used to model the effects of man made structures of the propagation of the radio signal. Intercept is defined relative to some reference distance. Commonly the reference distance is chosen as one mile, and in essence, the intercept can be defined as the RSL of the reference transmitter at the distance of 1 mile. Therefore, the intercept models the average signal attenuation that occurs within one mile from the BTS site. The slope shows the rate at which the signal is decaying as the mobile travels away from the BTS site. Its value is affected by the amount and density of the clutter and man made structure within the propagation environment. The slope becomes greater (signal decays faster), as the density of man made structures become higher. The values for the slope and intercept are determined experimentally from large quantities of measured data collected in different propagation environments. Some typical values for 850MHz propagation conditions are shown in Table 2. Table 2. Typical values for slope and intercept in 850 MHz frequency band
Environment Open Area Suburban Urban Dense Urban 2
One mile intercept Slope [dBm] DB/dec -50.5 -43.5 -59 -38.4 -63 -40 -74 -43.1
A precise definition of the effective antenna height will be provided in Section 1.3. 3
1.3
Effective An tenna Height (Effect of Natural Terrain)
The effective antenna height is used to model the effects of the local terrain slope on the value of the received signal level. The terrain around the bin in which the receiver is located can be sloping down toward or be tilting up at the transmitter antenna. The tilt will cause the received signal to reflect off the ground around the mobile unit differently, thus affecting the RSL. Luckily, it is unnecessary to calculate the reflected angle(s). The effect can be modeled by using the effective antenna height . The effective antenna height is calculated using trigonometry (the slope), and an imaginary line extending into the ground or through the air (depending on whether there is a slope up or down), to the base of the transmitter antenna. From the diagrams below, one can see that the line is a projection of the slope line back to the antenna. BS
Effective Ant enn a Height
Effective Ant enn a Height BS
MS
MS effect of local down slope
effect of local upward slope
Figure 1. Illustration of effective antenna height for a local slope up and local slope down.
The results of this simple trigonometry are incorporated into the modified measurement based model by replacing the base station antenna height, h b, with an effective antenna height hbseff . Calculating the effective antenna height by projecting the local slope back to the base station is only an approximation. The approximation works well for bin sizes larger than 50 meters. For a bin less than 50 meters per side and an 850 MHz signal, one needs a more sophisticated approach that is beyond the scope of this presentation. It is also important to note that the effective antenna height equals the actual antenna height (regardless of local terrain slope) for obstructed cases. In other words, if the line- of-sight path is obstructed, the effective antenna height is set to the actual base station height and the KED equations are used. 1.4
Frequency Dependence of Model Variables
Lee’s model is designed to operate in the frequency range from 200MHz to 2GHz. However its parameters are frequency dependent. In this section we examine the dependence and show how the model can be used for path loss predictions in different frequency bands.
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1.4.1 Frequency Dependency of the Slope The slope ( n ×10 ) in dB/decade is frequency independent when in VHF through upper UHF bands (150 MHz to 2000 MHz) in propagation prediction scenarios. The frequency independence means that whether the model is used to design an AMPS system (~850 MHz) or a GSM system (~1900 MHz), the standard slopes for urban, suburban, and rural areas will work in both frequency ranges. However, below 150 MHz surface waves become a major contributor to overall received signal strength. Above 2000 MHz, atmospheric losses become a significant contributing factor. There are also special ducting effects that can occur above 2200 MHz. These are considerations that must be accounted for throughout additional correction factors. The generic Lee’s model as given in (1) does not accommodate for these additional propagation effects.
1.4.2 5.1.2. Frequency Dependence in 1-Mile Intercept The 1-mile intercept value, P LRref , is frequency dependent.
This frequency dependence can be
seen if one examines the equation for the free space propagation losses. As a general rule, one can use:
f 1 f 2
P1mile ( f 2 ) = P1mile ( f 1 ) + 20 log
(5)
to adjust the 1-mile intercept value observed at one frequency, f 1 (say, 850 MHz), to that at another frequency, f 2 (say, 1900 MHz). Table 3 shows default values for slope and intercept in different propagation environments and for different operating frequencies. Table 3. Slope and 1-mile intercept values to be used for frequencies other than 850 MHz Frequency (MHz) Environment
150
450
850
900
1800
P1mile
Slope
P1mile
Slope
P1mile
Slope
P1mile
Slope
P1mile
Slope
Free Space Open Area Suburban Urban Area Heavy Urban
-30.1 -32.0 -41.0 -46.0 -57.0
20.0 43.5 38.4 40.0 43.1
-39.6 -42.0 -52.0 -56.0 -67.0
20.0 43.5 38.4 40.0 43.1
-45.2 -49.0 -59.0 -63.0 -74.0
20.0 43.5 38.4 40.0 43.1
-45.7 -50.5 -59.5 -63.5 -74.5
20.0 43.5 38.4 40.0 43.1
-51.7 -56.5 -65.5 -69.5 -80.5
20.0 43.5 38.4 40.0 43.1
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