Lecture 3

� Signal Propagation Overview

� Path Loss Models● Free-space Path Loss● Ray Tracing Models● Simplified Path Loss Model● Empirical Models● Empirical Models

� Log Normal Shadowing

� Combined Path Loss and Shadowing

�Outage Probability

�Model Parameters are Obtained from Empirical Measurements

Propagation Characteristics

� Path Loss (includes average shadowing)

� Shadowing (due to obstructions)

� Multipath Fading� Multipath Fading

Pr/Pt

d=vt

PrPt

d=vt

v Very slow

SlowFast

Lecture 3

� Signal Propagation Overview

� Path Loss Models● Free-space Path Loss● Ray Tracing Models● Simplified Path Loss Model● Empirical Models● Empirical Models

� Log Normal Shadowing

� Combined Path Loss and Shadowing

�Outage Probability

�Model Parameters are Obtained from Empirical Measurements

Path Loss Modeling

� Maxwell’s equations� Complex and impractical

� Free space path loss model� Too simple� Too simple

� Ray tracing models�Requires site-specific information

� Empirical Models�Don’t always generalize to other environments

� Simplified power falloff models�Main characteristics: good for high-level analysis

� Linear path loss

� Path loss in dB

� The dB path gain

Transmit signal

� The transmitted signal

u(t): complex baseband signal

fc: carrier frequency

Free-Space Path Loss

� The received signal

where the product of the transmit and

receive antenna field radiation patterns in

the LOS direction.

LOS: Line-Of-Sight

Free-Space Path Loss

� The ratio between the power of the

received signal and the power of transmit

signal issignal is

Free-Space Path Loss

Free-Space Path Loss

d=vt

� Path loss for unobstructed LOS path

� Power falls off :

� Proportional to d2

� Inversely proportional to λλλλ2 (proportional to f2)

Ray Tracing Approximation

� Represent wavefronts as simple particles

� Geometry determines received signal from each signal componenteach signal component

� Typically includes reflected rays, can also include scattered and defracted rays.

� Requires site parameters

�Geometry

�Dielectric properties

Two Path Model

� Path loss for one LOS path and 1 ground (or reflected) bouncereflected) bounce

� Ground bounce approximately cancels LOS path above critical distance

� Power falls off

� Proportional to d2 (small d)

� Proportional to d4 (d>dc) (dc: critical distance)

� Independent of λ λ λ λ (f)

Two Path Model

General Ray Tracing

� Models all signal components

�Reflections

� Scattering� Scattering

�Diffraction

� Requires detailed geometry and dielectric properties of site� Similar to Maxwell, but easier math.

� Computer packages often used

Simplified Path Loss Model

� Used when path loss dominated by reflections.

� Most important parameter is the path loss exponent γγγγ, determined empirically.

82,0 ≤≤

= γγ

d

dKPP tr

Most important parameter is the path loss exponent γγγγ, determined empirically.

Empirical Models

� Okumura model� Empirically based (site/freq specific)

� Awkward (uses graphs)

� L(fc, d): free space path loss at distance d

� Carrier frequency fc

� Amu(fc, d): median attenuation

�G(ht) base station antenna height gain factor

�G(hr) mobile antenna height gain factor

�GAREA: gain due to the type of environment

Commonly used in cellular system simulations

Empirical Models

� Hata model� Analytical approximation to Okumura model

� COST 231 Model: � Extends Hata model to higher frequency (2 GHz)

Commonly used in cellular system simulations

Empirical Models

� Indoor

� FAF: floor attenuation factorFAF: floor attenuation factor

� PAF: partition attenuation factor

Bài tập

� Under a free space path loss model, find

the transmit power required to obtain a

received power of 1 dBm for a wireless received power of 1 dBm for a wireless

system with isotropic antennas (Gl = 1)

and a carrier frequency f = 5 GHz,

assuming a distance d = 10m. Repeat for d

= 100m

Lecture 3

� Signal Propagation Overview

� Path Loss Models● Free-space Path Loss● Ray Tracing Models● Simplified Path Loss Model● Empirical Models● Empirical Models

� Log Normal Shadowing

� Combined Path Loss and Shadowing

�Outage Probability

�Model Parameters are Obtained from Empirical Measurements

Shadowing

� Models attenuation from obstructionsXc

� Random due to random # and type of obstructions

� Typically follows a log-normal distribution

� dB value of power is normally distributed

� µµµµ=0 (if mean captured in path loss), 4 dB < σσσσ2 < 12 dB (empirical)

� CLT (Central Limit Theorem) used to explain this

model

Shadowing

Xc

� The probability

Lecture 3

� Signal Propagation Overview

� Path Loss Models● Free-space Path Loss● Ray Tracing Models● Simplified Path Loss Model● Empirical Models● Empirical Models

� Log Normal Shadowing

� Combined Path Loss and Shadowing

�Outage Probability

�Model Parameters are Obtained from Empirical Measurements

Combined Path Loss and Shadowing

� Linear Model: ψψψψ lognormal

ψγ

=d

dK

P

P

t

r 0 Slow10logΚΚΚΚ

� dB Model

dPt

),0(~

,log10log10)(

2

01010

ψσψ

ψγ

N

d

dKdB

P

P

dB

dBt

r +

−=

Pr/Pt (dB)

log d

Very slow

-10γγγγ

Lecture 3

� Signal Propagation Overview

� Path Loss Models● Free-space Path Loss● Ray Tracing Models● Simplified Path Loss Model● Empirical Models● Empirical Models

� Log Normal Shadowing

� Combined Path Loss and Shadowing

�Outage Probability

�Model Parameters are Obtained from Empirical Measurements

Outage Probability

� Path loss: circular cells

� Path loss+shadowing: amoeba cells� Tradeoff between coverage and interference

rP

� Outage probability� Probability that received power is below a given minimum

Lecture 3

� Signal Propagation Overview

� Path Loss Models● Free-space Path Loss● Ray Tracing Models● Simplified Path Loss Model● Empirical Models● Empirical Models

� Log Normal Shadowing

� Combined Path Loss and Shadowing

�Outage Probability

�Model Parameters are Obtained from Empirical Measurements

Model Parameters fromEmpirical Measurements

� Fit model to data

� Path loss (K,γγγγ), d0 known:� “Best fit” line through dB data

Pr/Pt(dB)

log(d)10γγγγ

K (dB)

log(d0)

σσσσψψψψ2

� “Best fit” line through dB data� K obtained from measurements at d0.

�Exponent is MMSE (Minimum Mean Square Error) estimate based on data

� Captures mean due to shadowing

� Shadowing variance� Variance of data relative to path loss model (straight line) with MMSE estimate for γγγγ

Main Points

� Path loss models simplify Maxwell’s equations

� Models vary in complexity and accuracy

� Power falloff with distance is proportional to d2 � Power falloff with distance is proportional to d2

in free space, d4 in two path model

� General ray tracing computationally complex

� Empirical models used in 2G simulations

� Main characteristics of path loss captured in

simple model Pr=PtK[d0/d]γγγγ

Main Points

� Random attenuation due to shadowing modeled as log-normal (empirical parameters)

� Shadowing decorrelates over decorrelation distance

� Combined path loss and shadowing leads to outage and amoeba-like cell shapes

� Path loss and shadowing parameters are obtained from empirical measurements