Wireless Communication Systems · – Slow fading (shadowing) is caused by large obstructions...

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1: The Wireless Channel

Wireless Communication Systems


Ayman Naguib

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Course OutlinePart I: Basics

1. The Wireless Channel

2. Diversity

3. Multiple Access and Interference Management

4. Capacity of Wireless Channels

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Background Requirements:

• Basic digital communications principles.• Basic signals and systems• Basic math, linear algebra and probability.



1. The Wireless Channel

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Wireless Channels

Remote Dominant Reflector

Remote DominantReflector

Co-Channel Mobile

Local Scatterersto Mobile

Local Scatterersto Base

Local Scatterersto Base

Base Station

Local ScatteringMultipath PropagationMobile MotionCellular Spectrum Reuse

FadingIntersymbol InterferenceTime Varying ChannelCo-channel Interference

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Signal Level in Wireless Channels

• Three partially separableseparable effects:–– Slow fadingSlow fading (shadowing) is caused by large obstructions between transmitter

and receiver.–– Fast fadingFast fading is due to scattering of the signal by object near transmitter.–– Path lossPath loss is proportional to 1/rα, α is called path loss exponent. α =2 for free

space and is normally between 2.5 and 5 depending on the actual typography.

Mean Path Loss

Long Term Fading

Short Term Fading

Distance (dB)

Sig

nal L

evel

(dB)

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Propagation Path Loss

•• DefinitionDefinition: ratio between received and transmitted power.

LP

Ptr

t

=

hr

ht

θθ

d

d̀

`

r

r



Propagation Pass Loss ...

• Received signal power:2

2

1 2 1 22 2

2

2

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2 1 1

jr t t r

t r t r

r r

r

P PG G R ed

h h h hd d

ZRZ

Z

φλπ

πφ

λ

θθε θ ε

ε θ

Δ⎛ ⎞= +⎝ ⎠

⎡ ⎤⎡ ⎤ ⎡ ⎤+ −⎛ ⎞ ⎛ ⎞⎢ ⎥Δ = + − +⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦−

=+

⎧ −⎪= ⎨⎪ −⎩

/ /

sinsin

cos /

cos

for vertical polarizationfor horizontal polarization

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•• For large For large dd :

• Also, for fc > 100 MHz and θ ≤ 10°, R tends to -1.• In this case the received power is:

• In general:

Propagation Pass Loss ...

P PG Gh h

dr t t rt r= FHGIKJ2

2

for

for

d d L d

d d L dc t

c t

< ∝> ∝

: /

: /

1

1

2

4

Δφ πλ

≈ ≈ −4

1h h

dRt r ,



Propagation Pass Loss ...•• Measurements:Measurements:

– @ 100 MHz (Okumura): 1/d2 + additional loss that depends on the environment.

– @ 910 MHz (Cox): slope is steeper than 1/d2 but not as steep as 1/d4.

– @800 MHz (Bertoni): two slopes model, dc.depends on the terrains.

•• DilectricDilectric Canyon or tenCanyon or ten--ray model:ray model:– Urban areas with rectilinear streets.– Receiver and transmitter are well below roof tops.– Path loss exponent is insensitive to antenna heights as long

as antennas are well below roof tops, almost proportional to 1/d2.

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Large-scale fading• Also called slow fading or shadowing.• Due to obstructions between Tx and Rx. Local Local

meanmean will vary depending on the changing sizechanging sizeand geometrygeometry of of surrounding buildings and obstacles Detailed modeling complicated.

• Time constants associated with variations are very long as the mobile moves, many seconds or minutes.

• More important for cell site planning.• most measurements show that slow-fading S, is

approximately loglog--normalnormal, that is:

210

2

10 log ~ ( , )

4 12and dBs s

s t s

S N

L

μ σ

μ σ∝ ∈ −



Large-scale fading (Shadowing) ...•• Why logWhy log--normal ? normal ?

11 ,

n

i ii i i

a ra r

i i n os s e s s e =− Δ

− Δ−

∑= ⋅ = ⋅

Δr1 Δr2 Δr3 ΔrnTx Rx

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•• Correlation behavior is not known in general:Correlation behavior is not known in general:– Measurements (Gudmundson (Ericsson)) suggest

that slow fading can be modeled as a first order first order MarkovMarkov process in suburban areassuburban areas with very few high rises (Stockholm suburbs):

– In densedense environments (NYC for example) slow fading is non-stationary (Cox) (too much diffractiontoo much diffraction). Independent incrementIndependent increment process model is more accurate.

Slow Fading (Shadowing) ...

ρ τ σ τs s cv X( ) exp | |/= −2 b g

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Small-scale multipath (fast) fading• Wireless communication typically happens at very high

carrier frequency. (eg. fc = 900 MHz or 1.9 GHz for cellular)

• Multipath fading due to constructive and destructiveinterference of the transmitted waves.

• Channel varies when mobile moves a distance of the order of the carrier wavelength. This is about 0.3 m for 900 Mhz cellular.

• For vehicular speeds, this translates to channel variation of the order of 100 Hz.

• Primary driver behind wireless communication system design.

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Small-scale multipath fading …

Local Scattering Structure

Mobile

Dominant Reflector #1Dominant Reflector #2

Dominant Reflector #3

Base Station Antenna

v

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Wireless Channel Modeling• We wish to understand how physical parameters such as

– carrier frequency– mobile speed– bandwidth– delay spread

impact how a wireless channel behaves from the communication system point of view.

• We start with deterministic physical model and progress towards statistical models, which are more useful for design and performance evaluation.

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Physical Models• Wireless channels can be modeled as linear time-

varying systems:

where ai(t) and τi(t) are the gain and delay of path i.• The time-varying impulse response is:

• Consider first the special case when the channel is time-invariant:

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Passband to Baseband Conversion• Communication takes place at• Processing takes place at baseband

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Complex Baseband Equivalent Channel

• The frequency response of the system is shifted from the passband to the baseband.

• Each path is associated with a delay and a complex gain.

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Modulation and Sampling

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Multipath ResolutionSampled baseband-equivalent channel model:

where hl is the l th complex channel tap.

and the sum is over all paths that fall in the delay bin

System resolves the multipaths up to delays of 1/W .

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Flat and Frequency-Selective Fading• Fading occurs when there is destructive interference of

the multipaths that contribute to a tap.

Delay spreadCoherence bandwidth

single tap, flat fading

multiple taps, frequency selective

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Effective channel depends on both physical environment and bandwidth!

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Time Variations

Doppler shift of the i th path

Doppler spread

Coherence time

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Two-path Examplev= 60 km/hr, fc = 900 MHz:

direct path has Doppler shift of -50 Hzreflected path has shift of +50 HzDoppler spread = 100 Hz

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Doppler Spread

Doppler spread is proportional to:• the carrier frequency fc;• the angular spread of arriving paths.

where θi is the angle the direction of motion makes with the i th path.

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Types of Channels

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Typical Channels are Underspread• Coherence time Tc depends on carrier frequency

and vehicular speed, of the order of milliseconds or more.

• Delay spread Td depends on distance to scatterers, of the order of nanoseconds (indoor) to microseconds (outdoor).

• Channel can be considered as time-invariant over a long time scale.

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Statistical Models

• Design and performance analysis based on statistical ensemble of channels rather than specific physicalchannel.

• Rayleigh flat fading model: many small scattered paths

Complex circular symmetric Gaussian . Squared magnitude is exponentially distributed.• Rician model: 1 line-of-sight plus scattered paths

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Correlation over Time• Specified by autocorrelation

function and power spectral density of fading process.

• Example: Clarke’s (or Jake’s) model.

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Additive Gaussian Noise• Complete baseband-equivalent channel model:

• Special case: flat fading:

• Will use this throughout the course.

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Wireless Channel Models: Wrap-up

• A wireless Channel Model.

• Fade amplitude, phase, time delay, and the number of resolvable paths will change with time as the mobile moves in the environment.

•• A channel modelA channel model: model and distribution of L, τ, α, and φ.

( )

1 1( , ) ( ) ( ) ( ) ( )i

L Lj t

i i i ii i

h t a t t e φτ δ τ τ α δ τ τ= =

= − = −∑ ∑

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Wireless Channel Models: Wrap-up …

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Cellular Channels•• Macro Cells:Macro Cells:

– Base stations on roof tops, cover several miles.–– Urban:Urban:

• High desnity of scatterers, heavy shadowing, delay spread up to 1-1.5 μs, no direct path, signal is due diffraction and scattering due to structures near the mobile.

• Number of resolvable paths depends on the signal bandwidth, signal is well modeled by the Rayleigh fading model.

–– Suburban:Suburban:• Lower density of strong scatterers, less shadowing, a direct path may exist,

delay spreads up to 1-1.5 μs and sometimes up to 15-20 μs due to large scatterers such as mountains or city skylines.

• Number of resolvable paths depends on the specific terrain, signal is well modeled by the Nakagami fading model with m from 1 to 15.

–– Rural:Rural:• Very few scatterers, either low or no shadowing at all, delay spreads up to 0.1-

0.3 μs, mostly one peak.• Well modeled by Nakagami fading with m up to 100.



Cellular Channels ...

•• Micro Cell:Micro Cell:– Small cells (few hundred meters) with high user density

(business etc.). Base stations well below roof tops.– LOS propagation modeled by the dielectric canyon model

with delay spreads up to 1.5 μs.– None LOS propagation due to coupling with side streets

and reflections from buildings. Delay spreads up to 500 ns.

– Uses ray tracing to model the propagation environment.

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Cellular Channels ...

•• Pico or Indoor Cells:Pico or Indoor Cells:– 3D well diffused scattering process, impulse response

similar to micro-cells.– LOS propagation: a strong direct path and few

smaller components due to reflections within 50-100 ns.

– None LOS propagation: many indirect paths from all directions within 100-150 ns.

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Wireless Channels: 2nd Look

Local Scattering Structure

Mobile




Base Station Antenna Array

vt

vr

ΔΔ

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Wireless Channels: 2nd Look …

• Tx and/or Rx may have more than one antenna• Channel from different Tx and to different Rx

antennas are in different in general:– Depends on the angle spread, angle of arrival,

normalized distances between antennas (w.r.t. wavelength), etc.

• Antennas are very close to each other: channels are strongly correlated• Antennas are far apart: channels are un-correlated.•• Coherence Distance.Coherence Distance.

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Space-Time Fading

10lo

g 10h(

t,z)

Distance (in wavelength •)Time ms

Angle Spread Θd = 0°, Doppler Spread fd = 200 Hz

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Space-Time Fading ….

Time ms

Distance (in wavelength •)

10lo

g 10h(

t,z)

Angle Spread Θd = 5°, Doppler Spread fd = 200 Hz

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ChannelSpread

ChannelSelectivity

Measure ofSelectivity

Delay Spread Frequency Selective Coherence Bandwidth

Doppler Spread Time Selective Coherence Time

Angle Spread Space Selective Coherence Distance

The Three Spreads

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Summary• We have understood how time and frequency

selectivity of wireless channels depend on key physical parameters.

• We have come up with statistical channel models that are useful for analysis and design.

Wireless Communication Systems · – Slow fading (shadowing) is caused by large obstructions...

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