1. Propagation Characteristics
Lecture 2

2. Frequencies for communication

3. Frequencies and regulations

4. Signal propagation
Propagation in free space always like light (straight line)
Receiving power proportional to 1/d² (d = distance between sender and receiver)
Receiving power additionally influenced by
Fading (frequency dependent)
Shadowing
Reflection at large obstacles
Refraction depending on the density of a medium
Scattering at small obstacles
Diffraction at edges

5. Signal propagation

6. Real world example

7. Free space loss, ideal isotropic antenna
Pt = signal power at transmitting antenna
Pr = signal power at receiving antenna
λ = carrier wavelength
d = propagation distance between antennas
c = speed of light (3x108 m/s)
where d and λ are in the same units (e.g., meters)

8. Free Space Loss
Free space loss equation can be rewritten:

9. Free Space Loss Free space loss accounting for gain of other antennas
Isotropic ant : Gt=1, Gr=1
Gt = gain of transmitting antenna
Gr = gain of receiving antenna
At = effective area of transmitting antenna
Ar = effective area of receiving antenna

10. Free Space Loss
Free space loss accounting for gain of other antennas can be recast as

11. Propagation model Path loss: function of distance between TX and RX
d0 : close-in distance, received power reference point, commonly 1Km used
d :T-R separation: distance
n: path loss exponent
Log-normal shadowing: amplitude has a log-normal PDF
Addition of random variable
Xσ : zero-mean Gaussian distributed random variable (in dB) with standard deviation σ

12. Path loss model parameter

13. Path loss model parameter
Two values are
computed from
measured data,
using linear
regression method

14. Empirical Models Okumura model Hata model Cost 231 Model:
Empirically based (site/freq specific)
Awkward (uses graphs)
Hata model
Analytical approximation to Okumura model
Cost 231 Model:
Extends Hata model to higher frequency (2 GHz)
Walfish/Bertoni:
Cost 231 extension to include diffraction from rooftops
Commonly used in cellular system simulations

15. (Okumura) model

16. Hata model

17. Propagation Characteristics
Path Loss (includes average shadowing)
Shadowing (due to obstructions):
reflection, refraction, diffraction
Multipath Fading
Pr/Pt
d=vt Pr Pt v
Very slow
Slow
Fast

18. Channel characteristics
Channel characteristics change over time and location
signal paths change
different delay variations of different signal parts
different phases of signal parts
quick changes in the power received
(short term fading)
Additional changes in
distance to sender
obstacles further away
slow changes in the average power
slow changes in the average term fading received (long term fading)

19. Combined Path Loss & Fading

20. Path Loss Modeling Maxwell’s equations Free space path loss model
Complex and impractical
Free space path loss model
Too simple
Ray tracing models
Requires site-specific information
Simplified power falloff models
Main characteristics: good for high-level analysis
Empirical Models
Don’t always generalize to other environments

21. Small Scale fading
Variations due to shadowing occur over relatively large distances– often many meters
Signals in multipath environments also undergo small scale fading – variations that occur over the wavelength of the signal
This is due to the different multipath components combining either constructively or destructively

22. Small-scale fading (2)
Offset of only a fraction of a wavelength can lead to large change in signal level:

23. Multipath propagation
Signal can take many different paths between sender and receiver
due to reflection, scattering, diffraction
Time dispersion: signal is dispersed over time
interference with “neighbor” symbols Inter Symbol Interference (ISI)
The signal reaches a receiver directly and phase shifted
distorted signal depending on the phases of the different parts

24. The Effects of Multipath Propagation
• Due to the different paths taken by the multipath components, they may arrive at different times
• If the symbol period TS is smaller than the delay spread, i.e. TS < Tm, Inter-Symbol Interference (ISI) will occur
• The receiver cannot determine which symbol each multipath component belongs to:

25. The Effects of Multipath Propagation

26. Delay Spread
The Delay Spread Tm is defined as the difference between times-of arrival
of the first and last multipath components Typical values are as follows:

27. (Doppler shift)

28. Fading

29. Coherence Bandwidth
The Coherence Bandwidth Bc is a statistical measure of the range of frequencies over which the attenuation of the channel is approximately constant
Two frequency components f1 and f2 will experience similar attenuation if (f1 – f2) << Bc
Coherence Bandwidth is approximately related to the Delay Spread by:
Bc (Hz) = 1/Tm
e.g. in a particular factory environment,
Tm = 120ns, Bc = 1/(120 x 10-9) = 8.33 MHz

30. Coherence Bandwidth (2)
If the transmitted signal has a bandwidth (Bu) much smaller than the Coherence Bandwidth(Bc), i.e. Bu << Bc, all frequency components will be attenuated similarly.
This is called Flat Fading
Else, it will undergo Frequency-selective fading, with different components attenuated differently. This causes distortion of the signal