1. Chapter 2. Wireless Channels
BASED ON CHAPTERS 4 & 5
OF WIRELESS COMMUNICATIONS PRINCIPLES AND PRACTICE, 2/E, T.S. RAPPPAPORT

2. Characteristics of Wireless Channels
Path loss and white noises
Multipath delay and spread
Fading
Doppler spread
Co-channel and adjacent channel interference
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3. Radio Propagations Depends on Frequency:
Ground wave: frequencies lower than 2MHz can propagate alone the earth ground (because its super long wavelength can make large diffraction)
Sky wave: frequency of 1MHz~30MHz, can be reflected by the ionosphere.
Line-of-sight wave: at >30MHz frequencies, radio traveling in a straight line. Thus a "radio-horizon" exists for these frequencies.
However, with a strong signal source the radio wave can penetrate through thin obstacles such as walls & trees, with around 10-20dB attenuation.
Ground wave
Sky wave
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4. Line-of-Sight Calculation
FM/TV tower height: depends on how far it will cover!
Consider following: (𝑟≈𝑟′ when 𝛼 is small)
𝑟 2 + 𝑅 2 = 𝑅+𝐻 2
𝑟 2 = 𝐻 2 +2𝑅𝐻
For the fact that 𝑟≫𝐻, we have
𝑟= 2𝑅𝐻 or 𝐻= 𝑟 2 2𝑅
Line-of-sight wave H r r' R R 𝛼
Example: R=6400km, we have the radio coverage radius 30km, then 𝐻 = 𝑟2 2𝑅 = km ≈ 70m

5. Radio Horizon From 𝑟= 2𝑅𝐻 = 2×6400× 10 3 ×𝐻 (m) 𝑟≈3.577 𝐻 (km)
This is call optical horizon. Radio frequency can diffract a little bit and distance is longer:
𝑟≈ 𝐻 (km)
𝑟= 𝐾𝐻 km , 𝐾=4/3
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6. Radio Propagation in Free Space
Consider an isotropic antenna which radiates in free space equally to all directions.
The transmitted signal is cos⁡(2𝜋𝑓𝑡)
The electric far field at distance 𝑟 is
It is clear the signal power ( 𝐸 2 ) is inversely proportional to the distance (𝑟) square.
𝐸 𝑓,𝑡,𝑟 = cos⁡[2𝜋𝑓 𝑡− 𝑟 𝑐 ] 𝑟
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7. Radio Propagation in Free Space
The free space power received by a receiver antenna at a distance 𝑑 from transmitting antenna is given by Friis equation:
𝑃𝑡 is the transmitted power, Pr⁡(𝑑) is the received power. 𝐺𝑡, 𝐺𝑟 are transmitter/receiver gains, 𝑑 is the distance, 𝐿 is the system loss factor, and  is the wavelength.
The Gain of an antenna is related to its effective aperture 𝐴 𝑒 :
In practice, Effective Radiated Power (ERP) is used because real antennas are polarized, thus some gain is obtained by polarized antennas and we denote it in 𝑑𝐵𝑖 (to isotropic).
𝑃 𝑟 𝑑 = 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 𝜆 𝜋 2 𝑑 2 𝐿
𝐺= 4𝜋 𝐴 𝑒 𝜆 2
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8. Path Loss
Path loss represents signal attenuation as a positive quantity measured in dB over the radio propagation path.
defined as ratio of effective transmitted power and the received power. In free space, we have
This equation doesn’t hold for 𝑑=0 (i.e., so-called Near Field).
𝑃𝐿 𝑑𝐵 =10log 𝑃 𝑡 𝑃 𝑟 =−10 log 𝐺 𝑡 𝐺 𝑟 𝜆 𝜋 2 𝑑 2 𝐿
In free space, the signal power decreases by the square of distance.
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9. Ground Two-ray Path Loss
The earth is a good conductor/reflector
𝑃 𝑟 (𝑑)= 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 ℎ 𝑡 ℎ 𝑟 𝑑 4
In two-ray ground mode, the signal power decreases by power of 4 of the distance. The detailed derivation can be found in [Schwartz, pp.23-25]. d h t d 1 h r d 2 d’
d’’
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10. Power Calculation
An isotropic antenna radiates 1W in free space. 𝐺 𝑡 = 𝐺 𝑟 =1 (0𝑑𝐵), frequency is 300MHz.
What is the received power in watts at distance of 10m?
What is the received power in watts at distance of 10km?
An dipole antenna (omnidirectional horizontally) radiates 100W from a radio tower. ℎ 𝑡 =30𝑚, ℎ 𝑟 =2𝑚, 𝐺 𝑡 = 𝐺 𝑟 =1 (0𝑑𝐵). Find the answers for the same distances.
As you see, the value becomes very small, therefore we always use decibel values.
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11. Radiation Power Density
Denoted as 𝜌 (mW/ cm 2 ).
An isotropic antenna radiates 1W as the previous example. Find power density at 1m and 100m respectively.
US FCC has specified a safety guideline for cellular radiations.
0.001𝑚𝑊/𝑐 𝑚 2
Typical near a
celluar tower
0.5𝑚𝑊/𝑐 𝑚 2
FCC Public Exposure
Standard (900MHz)
4𝑚𝑊/𝑐 𝑚 2
Unreproduced
Reports of Effects
100𝑚𝑊/𝑐 𝑚 2
Clear Hazards
0.02𝑚𝑊/𝑐 𝑚 2
Maximum near a
celluar tower
1𝑚𝑊/𝑐 𝑚 2
FCC Public Exposure
Standard (2000MHz)
40𝑚𝑊/𝑐 𝑚 2
Reproducible Effects
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12. SAR (Mobile phone)
MMF (Mobile Manufacturer Forum) has adopted SAR (Specific Absorption Rate)
𝑆𝐴𝑅= 𝜎 𝐸 𝑟𝑚𝑠 2 𝑑 , where 𝜎 is conductivity of medium (brain ~ S/m), 𝐸 𝑟𝑚𝑠 is the RMS value of Electric Field and 𝑑 is the density of medium (brain ~1040kg/ 𝑚 3 )
In EU the limit is 2W/kg for human being's head and trunk.
Specific absorption rate (SAR) [W/kg] describes the possible biological effects of RF fields. The high energy of RF field exposure causes thermal effects in biological tissues and generates high SAR values. However, the so-called non-thermal effects, or the biological effects of RF fields at low energy levels have not been clarified yet. The basic concern of the present work is health hazard…… The depth of penetration is more in the child than the adult. The exposure of high intensity EM waves in the UHF (i.e., 300 MHz-3 GHz) range generates heat, which can cause thermal damage to the brain, specially of the children. This temperature may rise up to about 0.1℃ in 1𝑚 𝑚 3 after 33 hrs of continuous phone use. DNA breaks after receiving RF exposure. [Hoque et al, 2013]
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13. Signal Propagation Ranges
Because radio signal power decays by distance, there is a range for correct reception.
Transmission range
Communication range
Low error rate
Detecting range
Detection of the signal is possible, but cannot correctly receive data because error rate is too high
Interferencing range
Signal cannot be detected but acts as a kind of noise to other systems
Interference range
Detection range
Transmission range
Distance from the transmitter. In practice there are irregular circles due to the variation of environment.
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14. Multi-path propagation
In practice the signal coming to the receiver is a combined signal with multiple components caused by reflection/diffraction/scattering, this is called multi-path propagation model.
Two-ray ground model is the simplest multi-path example.
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15. Effects of Multipath Reflection
“Ghost image” on TV.
GPS – incorrect position calculation.
Intersymbol interference (ISI).
Fading.
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16. Intersymbol Interference
Suppose that there are two paths.
The shorter one has length d1, the longer one length d2.
What is the difference in propagation delay between the two paths? 2 3
Symbols received over the shorter path 1 2
Symbols received over the longer path 3  1
Received signal – a combination of the two signals
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17. Multipath delay vs Symbol rate
Calculate:
3 multipath distances are 5km, 10km and 15km respectively, how much delay 𝛿 is between the 1st and 3rd path?
If the symbol rate is 10kbps, how many symbols does 𝛿 equal to? How about the symbol rate is 10Mbps?
Advanced homework: use Matlab to simulate this scenario.
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18. Random Channel Characterization
Caused by the multi-path, the radio signal presents a random feature in both long-term (slow) and short-term (fast) loss. We name this kind of loss as fading.
Fading happens in a random fashion, because it is caused by the random movement of user mobile, and/or uncertain changes of environments.
Received power
Average in long time (slow fading)
Fast fading
time
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19. Fading in Time: Slow Fadings
Long-term fading is caused by the movement of user device so that the signal may come from different reflecting/diffracting/scattering path. This change is slow because the mobile needs to have a relatively long distance to move.
One special long-term fading is called shadowing, caused by the mobile moves into a shadow area of radio.
It is also called slow fading.
Poor signal
Strong signal
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20. Fading in Time: Fast Fadings
Short-term fading is caused by the movement of user mobile (usually in a magnitude of wavelength) so that the combined signal at the receiver changes its phase and magnitude in short time..
It is also called fast fading.
Several mathematical models have been established for short-term fading, they are
Nakagami fading
Weibull fading
Rayleigh fading (open field, non-line-of-sight)
Rician fading (open field, line-of-sight)
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21. Fast Fading: an example
Simplest 2-path scenario:
𝐸 𝑓,𝑡 = cos 2𝜋𝑓 𝑡− 𝑟 𝑐 𝑟 − cos⁡[2𝜋𝑓 𝑡− 2𝑑−𝑟 𝑐 ] 2𝑑−𝑟
reflected 𝑟 𝑑
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22. Fast Fading: an Example
If the mobile is close to the wall, 𝑑≈𝑟, 2𝑑−𝑟≈𝑟
𝐸 𝑓,𝑡 = cos 2𝜋𝑓 𝑡− 𝑟 𝑐 −cos⁡[2𝜋𝑓 𝑡− 2𝑑−𝑟 𝑐 ] 𝑟
The phase difference is
Δ𝜃= 2𝜋𝑓 2𝑑−𝑟 𝑐 +𝜋 − 2𝜋𝑓𝑟 𝑐 = 4𝜋𝑓 𝑐 𝑑−𝑟 +𝜋
If the phase difference Δ𝜃 is a multiple of 2𝜋, two waves add constructively, if it is an odd integer of 𝜋, two waves add distructively. Thus a standing wave is formed, and the distance between a node to an anti-node is Δ𝑟= 𝜆 4 .
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23. Fast Fading: an Example
So, if the mobile terminal moves either towards the Tx tower or towards the wall, it will be encountering nodes and anti-nodes every Δr (which is also called as coherent distance). At an anti-node, the signal fades.
The radio frequency used by cellular system is around 1~2GHz, 𝜆≈ 15~30𝑐𝑚. Therefore, even the mobile terminal moves at a relatively low speed, fast fading occurs.
E.g., 𝑓=2𝐺𝐻𝑧, 𝜆=15𝑐𝑚, mobile velocity 𝑣=2𝑚/𝑠. It will take 𝜆/4 𝑣 = sec. from a node to an antinode.
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24. Fast Fading at High Mobility
If the mobility is high, e,g., on a moving vehicle or train (speed is about 60~200km/h), the time from a node to antinode becomes much smaller.
As a result, fast fading occurs at a time scale of milliseconds, slow fading occurs at a time scale of seconds or minutes.
Fast fading is caused by standingwave, so it occurs only in an environment with strong reflections.
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25. Effects of Fading for digital modulation
BER: the lower the better
Fig. 2.13
SNR: the higher the worse
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26. A Result from WINIQSIM
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27. Result Comparison No multipath, no white noise No multipath,
Gaussian noise
Multipath,
Gaussian noise
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28. Irreducible BER due to fading
Probability of error
Fig. 2.16
Signal-to-Noise Ratio
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29. Irreducible BER due to fading
The lower the mobility, the lower the BER
Fig. 2.16
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30. Fading in Frequency Domain
In frequency domain, fading can be classified as "flat fading" and "selective fading".
Flat fading means fading occurs at the whole frequency band of a communication system. It's typical for most narrow-band communication systems.
Selective fading occurs at certain frequencies or subbands of the whole frequency band of a communication system. It's typically a wideband system feature.
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31. Mitigation
Using diversity channels is a way to mitigate fading results, because fading is random and different channels fade at different time. Diversity can be done in time, frequency, and space. There are several techniques:
Diversity reception and transmission (against fast fading)
OFDM (against ISI, doppler)
Rake receivers (against ISI)
Space–time codes/Interleaving (against fast fading)
MIMO (against fast fading)
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