1. EEE 441 Wireless And Mobile Communications
Lecture 07
EEE 441 Wireless And Mobile Communications

2. Quiz2 soln

3. Propagation of Radio Waves: Large-Scale Path Loss

4. Radio Wave Propagation
Large-scale path loss
Observed at receiver distances that are large compared to the wavelength of the carrier signal
Free-space propagation loss
The 3 basic propagation mechanisms of reflection, diffraction and scattering
Small-scale path loss
Rapid fluctuations that occur over small movements in receiver position (a few wavelengths)
Also known as fading

5. Small-Scale and Large-Scale Fading
Received Power (dBm)
-30
-40
-50
-60
This figure is just an illustration to show the concept. It is not based on read data.
-70
T-R Separation (meters)

6. Unit for Power Loss
The decibel, dB
A logarithmic unit that is used to describe a ratio
Given two power values P1 and P2, the difference (as a ratio) is expressed in dB as:
10 log (P1/P2) (dB)
Example
Tx Power P1 = 100W, Rx Power P2 = 1W
The loss = 10 log(100/1) = 20 dB

7. Decibel (dB)
versus
Power Ratio
Comparison of
two Sound Systems

8. Decibel milli
Used to denote a power level with respect to 1mW as the reference power level
Example: Tx power is P1 = 100W
Loss = 10 log(100W/1mW) = 10 log (100,000) = 50 dBm

9. Decibel Watt
Used to denote a power level with respect to 1W as the reference power level
Example: Tx power is P2 = 100W
Loss = 10 log(100W/1W) = 10 log (100) = 20 dBW

10. Radio Wave Propagation
At VLF, LF, and MF bands, radio
waves follow the ground. AM radio
broadcasting uses MF band
reflection
At HF bands, the ground
waves tend to be absorbed by the
earth. The waves that reach ionosphere
( km above earth surface),
are reflected and sent back to
earth.
Ionosphere
absorption

11. Radio Wave Propagation (cont’d)
VHF Transmission
LOS path
Reflected Wave
When directional antennas are used, waves follow more direct paths
- LOS: Line-of-Sight Communication
- Reflected wave interfere with the original signal

12. Coverage Environment Line-of-Sight (LOS) between Tx/Rx
Waves obstructed and absorbed by buildings, foliage, rain …
Velocity of Rx leads to Doppler effects

13. Free-Space Propagation Model

14. Free-Space Propagation Model
Used to predict the received signal strength when Transmitter and Receiver have clear, unobstructed LOS path between them
The Rx power decays as a function of the T-R separation distance raised to some power

15. Friis Free-Space Equation
Free space power received after a distance d is given by Friis free-space equation:
Pr(d) = (PtGtGrl2) / ((4p)2d2L)
Pt is transmitted power
Pr is received power
Gt is transmitter antenna gain (dimensionless quantity)
Gr is receiver antenna gain (dimensionless quantity)
d is T-R separation distance (in meters)
L is system loss factor not related to propagation (L >= 1)
l is wavelength (in meters)

16. Antenna Gain
The gain of an antenna G is related to its affective aperture Ae by:
G = 4pAe / l2
The effective aperture of Ae is related to the physical dimensions of the antenna

17. Isotropic Antennas and Effective Gain
An isotropic radiator is an ideal antenna that radiates power with unit gain uniformly in all directions
Antenna gains are given in units of dBi
(dB gain with respect to an isotropic antenna)

18. Path Loss Path Loss signal attenuation, measured in dB:
PL(dB) = 10 log (Pt/Pr) = -10log[(GtGrl2)/(4p)2d2]
If antennas have unity gains (exclude them):
PL(dB) = 10 log (Pt/Pr) = -10log[l2/(4p)2d2]

19. Long Distance Path-Loss Model
The average large-scale path loss is expressed as a function of distance
The value of n depends on the propagation environment:
n=2 for free space, higher when obstructions are present

20. Path-Loss Exponent for Different Environments
Path Loss Exponent, n
Free space 2
Urban area cellular radio
2.7 to 3.5
Shadowed urban cellular radio
3 to 5
In building line-of-sight
1.6 to 1.8
Obstructed in building
4 to 6
Obstructed in factories
2 to 3

21. What Scale is “Large-Scale”?
For Friis free-space equation to hold, d should be in the far-field of the Tx antenna
The far-field, or Fraunhofer region, is given by:
df = 2D2/l
D is largest physical dimension of the antenna
Additionally, df >> D and df >> l

22. Reference Distance, d0 Free-space equation does not hold for d = 0
We use a small distance d0 as the reference point
d0 should be > df
d0 should be < any practical distance d where we wish to measure the power of a mobile receiver
Received power Pr(d), at a distance d > d0 from a transmitter, is related to Pr at d0, Pr(d0), by:
Pr(d) = Pr(d0)(d0/d)2 given that d >= d0 >= df

23. Reference Distance d0 (cont’d)
Expressing the received power in dBm and dBW:
Pr(d) (dBm) = 10 log [Pr(d0)/0.001W] + 20log(d0/d) where Pr(d0) is in Watts
Pr(d) (dBW) = 10 log [Pr(d0)/1W] + 20log(d0/d) where Pr(d0) is in Watts

24. Selection of Reference Distance d0
In large coverage cellular systems
About 1km
In microcellular systems
About 1m ~ 100m
Must be in the far-field of the antenna, so that near-field effects do not result

25. Fraunhofer Region
For Friis equation to hold, distance d should be in the far-field of the Tx antenna
The far-field, or Fraunhofer region, of a transmitting antenna is defined as:
df = 2D2/l
D is the largest physical dimension of the antenna.
Additionally, df >> D and df >> l

26. Notices
Reading
Rappaport, Ch 4.1 – 4.2 (selections)