Path Loss and Shadowing

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Path Loss and Shadowing

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We want to understand the following effect(s):

Wireless Communications - Path Loss and Shadowing

Image source: Theodore S. Rappaport, Wireless Communications, 2nd ed., Prentice Hall, 2002

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LOG-DISTANCE PATH-LOSS

MODEL

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Motivation: model extension of what we derived so far

We assume that transmitter and receiver are stationary

 Wave propagation in free space is basically straight (like light)

 According to Friis equation: receive power decreases in a vacuum with 1 / d² (d = distance between transmitter and receiver)

If we assume obstacles in the room, then the reception power will also be influenced by



Shadowing by obstacles



Reflection on large surfaces



Refraction depending on the density of a medium



Scattering on small obstacles



Diffraction on sharp edges

Why is that a problem? We'll take a look at next:



all mentioned effects except shadowing (next slides)



and then we add shadowing (the slides afterwards)

Reflection Scattering Diffraction

Shadowing Refraction

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The multipath propagation problem

Line-of- sight path

Non-line-of-sight path

example shows reflection

(the same applies for all other effects

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Remark: Multipath propagation can also be an advantage

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blocked LOS-Pfad sender

receiver

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Phase reversed Increase distance

Two‐Ray Ground Reflection Model

frey

Sender Receiver

-1 -0.5 0 0.5 1

0 1 2 3 4 5 6

-1 -0.5

0 0.5

1

0 1

2 3

4 5

6 -1

-0.5 0 0.5 1

0 1

2 3

4 5

6 -1 -0.5 0 0.5 1

0 1 2 3 4 5 6

-1 -0.5 0 0.5 1

0 1 2 3 4 5 6

-1 -0.5 0 0.5 1

0 1 2 3 4 5 6

LOS signal

Reflected signal

Complete signal

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Model parameters discussed

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rappaport02wireless: 4.9.1

Reference distance d₀

• has to be in the far field

• should be less than “typical distances” of the considered system

• commonly used values

• 1km for large coverage cellular system

• much smaller (such as 100m or 1m) for microcellular systems Distance dbetween transmitter and receiver

Path loss PL(d₀) at reference distance d₀

• computed either from free space propagation model or

• determined empirically

Path loss exponent n(often also noted as α).

Typical path loss exponents obtained in various mobile radio environments

Image source: Theodore S. Rappaport, Wireless Communications, 2nd ed., Prentice Hall, 2002, page 139

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Empirical path‐loss models

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Okumura‐Hata Path‐Loss Model

Original model after Okumura revised by Hata. Path‐loss model for cellular networks based on empirical data on measurements in Tokyo.

For urban areas :

L

_dB,urban

(d) = 69.55 + 26.16 log

₁₀

f

_c

– 13.82 log

₁₀

h

_t

– a(h

_r

) + (44.9 – 6.55 log h

_t

) log

₁₀

d

f

_c

= carrier frequency in MHz (100 to 1500 MHz)

h

_t

= height of the transmitting antenna (base station) in m (30 to 200 m) h

_r

= height of the receiving antenna (mobile unit) in m (1 to 10 m)

d = distance between the antennas in km (1 to 20 km)

a(h

_r

) = correction factor for mobile antenna height based on the size of the

coverage area

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Okumura‐Hata Path‐Loss Model

The correction factor a(h _r ) for small to medium sized cities:

a(h _r ) = (1.1 log ₁₀ f _c – 0.7) h _r – (1.56 log ₁₀ f _c – 0.8) dB

The correction factor a(h _r ) for larger cities:

a(h _r ) = 8.29 [log ₁₀ (1.54 h _r )] ² – 1.1 dB for f _c <= 300 MHz

a(h _r ) = 3.2 [log ₁₀ (11.75 h _r )] ² – 4.97 dB for f _c > 300 MHz

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Okumura‐Hata Path‐Loss Model

For suburban areas:

L dB,suburban (d) = L _dB,urban (d) – 2 [log ₁₀ (f _c / 28)] ² – 5.4 For rural areas:

L _dB,rural (d) = L _dB,urban (d) – 4.78 (log ₁₀ f _c ) ² – 18.733 (log ₁₀ f _c ) – K

where K ranges from 35.94 (countryside) to 40.94 (desert)

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Log‐normal shadowing

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Empirical Evidence (Example)

saunders07wireless: 9.2

Driving around a base station at a constant distance.

Depicted is the local mean after subtracting the median (50%) level in decibles.

The typical shape of the probability density function of shadowing compared to the PDF of the log-normal distribution.

Image source: Saunders, S., & Aragón-Zavala, A. (2007). Antennas and Propagation for Wireless Communication Systems (2nd Edition). Wiley (Fig. 9.2 and Fig. 9.3)

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Summarized

schwarz04wireless: 2.2 “shadow fading”

P

_r

dBm

d [m]

average received power due to path loss

• described by log-distance path loss model

• just depends on transmitter receiver separation

• called area mean

average received power when taking shadow fading into account

• called local mean

• depends on actual transmitter and receiver position

• however does not change rapidly when node positions are changed slightly

• variation typically in the order of many wavelengths

• decribed by log-normal shadowing model for an arbitrary transmitter receiver pair

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Empirical Data for the Log-Normal-Shadowing Model

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Determining PL(d ₀ ), n and  from empirical data

Choose a suitable d

₀

 in the far field

 Transmitter-receiver distance usually > = d₀

Determine PL(d

₀

)

 e.g. theoretically according to Friis equation or

 Empirical by means of many independent

measurements at distance d₀

Determine independent

empirical measurement data for growing distance

For empirical measurement data, determine the best n and  (e.g., linear

regression method (i.e., mean squared deviation of measurement data and

model data is minimal) for n, and then sample variance

PL of area mean is linear here since distance is plotted logarithmically

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Simplified example (see Rappaport p. 143)

Distance to Sender Received power 100 m (reference distance) 0 dBm

200 m -20 dBm

1000 m -35 dBm

3000 m -70 dBm

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Example: typical parameters for lognormal shadowing model for near ground communication at 800-1000 MHz

Lognormal shadowing model is characterized by

, 

²

, PL(1m) (path loss at reference distance d

₀

)

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FURTHER DISCUSSIONS

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Signal propagation areas

distance sender

communication

detection interference

Communication region



communication possible



low error rate Detection region



signal detection possible



no communication possible Interference region



signal can not be detected



signal contributes to

the background noise

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Side note: ray tracing as an alternative to modeling signal propagation

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Recap

So far, we have only considered the problem of attenuation and overlapping waves of one symbol

Multipath propagation also leads to another problem

Inter symbol interference (ISI): Interference with neighboring symbols

signal at sender

signal at receiver LOS pulses multipath

pulses

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Recap

Another fact that complicates wireless communication:

Signals often consist of many sinusoids of different frequencies (see discussion on Fourier transformation and the subject of modulation) The treated effects are usually also frequency selective

This means that the effects have different effects on the frequency spectrum of the signal; which additionally distorts the signal

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Path Loss and Shadowing