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(1)

Blackboard Notes

Theoretical Evidence

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 76

saunders07wireless: 9.3

(2)

Summarized

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 77

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

This is called large-scale fading, slow fading, shadow fading or log-normal fading

(3)

Correlated Shadowing

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 78

(4)

Motivation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 79

frey

When used in a Simulation:

For arbitrary non related transmitter receiver pairs.

Use log-normal shadowing model to generate average received power (i.e. local mean) for each pair

• compute the area mean from log-distance path loss model

• add independent Gaussian random value with mean zero and variance and variance σ

• (or just generate independent Gaussian value with mean set to area mean and variance σ) Be careful if transmitter receiver pairs t1,r1 and t2,r2 are statistically dependent!

The Gaussian values are no longer independent! (due to slow fading)  see the

following discussion

(5)

Blackboard Notes

Motivation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 80

frey

(6)

Blackboard Notes

Correlated Shadowing Models

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 81

saunders07wireless: 9.6

(7)

Blackboard Notes

Serial Correlation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 82

saunders07wireless: 9.6.1

(8)

Blackboard Notes

Serial Correlation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 83

saunders07wireless: 9.6.1

(9)

Blackboard Notes

How to generate two correlated Gaussian distributed random variables?

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 84

(10)

Blackboard Notes

Simulating a whole correlated shadowing process…

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 85

saunders07wireless: 9.6.1

(11)

Example Plot

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 86

saunders07wireless: 9.6.1

Image source: Saunders, S., & Aragón-Zavala, A. (2007). Antennas and Propagation for Wireless Communication Systems (2nd Edition). Wiley (Fig. 9.14)

(12)

Blackboard Notes

Site‐to‐Site Correlation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 87

saunders07wireless: 9.6.2

(13)

Blackboard Notes

Site‐to‐Site Correlation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 88

saunders07wireless: 9.6.2

(14)

Blackboard Notes

Site‐to‐Site Correlation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 89

saunders07wireless: 9.6.2

(15)

Blackboard Notes

Site‐to‐Site Correlation

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 90

saunders07wireless: 9.6.2

(16)

Blackboard Notes

Adapting Serial Correlation to two Mobile Nodes

WS 18/19 Drahtlose Kommunikation - Technische Grundlagen 91

agrawal09correlated‐twc: III.A

Referenzen

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