Wireless Channels

Ada Poon, Bob Brodersen

Berkeley Wireless Research Center

University of California, Berkeley

Earth-Ionospheric Waveguide

3 – 30 kHz,very low frequency (VLF)

Large wavelength (>10 km)

Wave can’t penetrate to the lowest layer of ionosphere.

Long distance telegraphy broadcasting

Navigation systems

Submarine communications

Ionosphere

Earth

Surface Wave Diffraction

30 – 300 kHz,low frequency (LF)

Wave follows the curvature of earth.

Long distance communications

Navigation systems Earth

Ionospheric Reflection & Refraction

3 – 30 MHz,high frequency (HF)

Wave is refracted by the layers of ionosphere and eventually, totally reflected and returns to the earth.

Radio broadcasting

Ionosphere

Earth

Tropospheric Scattering

30 – 300 MHz,very high frequency (VHF)

Wave is scattered by the particles in the troposphere.

Military applications

Multi-channel telephony

Troposphere

Earth

Four Basic Propagation Mechanisms

Waveguide

Diffraction

Reflection & Refraction

Scattering

Cellular Systems

Outdoor environment

0.3 – 3 GHz, ultra high frequency (UHF)

Propagation mechanisms:» Waveguiding along streets» Diffraction around hills» Reflection from buildings» Scattering by plants

Wireless LAN

Indoor environment

3 – 30 GHz, super high frequency (SHF)

Propagation mechanisms:» Waveguiding along corridors» Diffraction around door openings» Reflection from walls» Scattering by furniture

We are studying electrical engineering, but most of us don’t like to get too involved into classic electrodynamics.

Characterization Parameters

Path loss

Delay spread

Doppler shift

Angular spread

Coherence time

Coherence bandwidth

Friis Transmission Formula

PR = PT · ?

In free space, path loss is

d transmitter-receiver separationGR receiver antenna gainGT transmitter antenna gainλ wavelength

How about in a scattering environment?

( )2

2

2

2 41 −∝⋅= dGG

dPP TR

T

R

πλ

Path Loss Exponent, n

In a scattering environment, the path loss is

Typical values inUrban 2.7 – 3.5Sub-urban 3 – 5Indoor LOS 1.6 – 1.8 (< 2, why?)Indoor NLOS 2 – 6

n

T

R dPP −∝

UWB, LOS

802.11a, LOS

802.11b, LOS

UWB, NLOS

802.11a, NLOS

802.11b, NLOS

Multipath Model

iυ

iτ

iκ̂

∑=

− −−=L

ii

N

iii

fjtji eeft

1

22 )ˆˆ()ˆˆ()ˆ,ˆ,,( kkκκΓkκH δδτππυ

ik̂

iΓ

Doppler shift

delay

direction of departure

direction of arrival

polarization

ik̂ iκ̂

v

Maximum Doppler Shift

λυ vf im == max

Frequency spread, fm

For example, if a cell phone is moving at 60 km/hr using a 900 MHz carrier, the maximum Doppler shift is 50 Hz.

v

Delay Spread

Delay spread

1τ 2τ 3τ 4τt

iiiidT ττ minmax −=

Sample Measurements

Delay Spread vs. Frequency

Insensitive to the choice of coordinates

Larger delay spread in the office environment

Delay spread increases with frequency

Delay Power Profiles and Arrival PDFs

Angular Spread

Coordinates:

Transmit elevation spread

Transmit azimuth spread

Receive

Tii

Tii

T θθ minmax −=Θ

( )Ti

Tii φθ ,ˆ =k ( )R

iR

ii φθ ,ˆ =κ

Tii

Tii

T φφ minmax −=Φ

Rii

Rii

R θθ minmax −=Θ Rii

Rii

R φφ minmax −=Φ

Sample Measurements

Angle Power Profiles and Arrival PDFs

∑=

− −−=L

ii

N

iii

fjtji eeft

1

22 )ˆˆ()ˆˆ()ˆ,ˆ,,( kkκκΓkκH δδτππυ

Coherence Bandwidth, Coherence Time

[ ] 0~)ˆ,ˆ,,()ˆ,ˆ,,( * kκHkκH ftfTt c+Ε

Coherence time, Tc

Coherence bandwidth, Wc

ik̂ iκ̂

v

[ ] 0~)ˆ,ˆ,,()ˆ,ˆ,,( * kκHkκH ftWft c+Ε

Change of Domains

)ˆ,ˆ,,( kκH ft

)ˆ,ˆ,,( kκH τt

),,,( TRft rrH

array topology

array topology

),,,( TRt rrH τ

Channel Characterization

(υi, τi, θi)’sextraction

geometry & dielectric

properties of environment

effective scatterer

distribution

distribution

(t, f, rR, rT) correlation

Measurement Ray tracing Abstract modeling

array topology

frequency spreaddelay spread,angular spread

coherence timecoherence bandwidth

),,,( θ∆θτ∆τ

path loss