13

Lecture 2: Wireless Channel Propagation & Modulation Techniques

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Police Radar

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Basics IRandom variable X

If a probability distribution has density f(x), then intuitively the infinitesimal interval [x, x + dx] has probability f(x) dx. Cumulative distribution function Mean:

Variance:

Ex: Gaussian distribution

( ) ( )x

F x f x dx−∞

= ∫( ) ( )E X xf x dx

∞

−∞

= ∫

2 2( ( )) ( )x E x f x dxσ∞

−∞

= −∫

2

22

1 ( )( ) exp( )2

xf x µσπσ

−= −

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Basics II

Time domain Frequency domain

Period T

1/T

-1/T

( ) ( ) exp( 2 )F s f x i xs dxπ∞

−∞

= −∫Fourier Transformation

( ) ( ) exp( 2 )f x F s i xs dsπ∞

−∞

= ∫

τ

1/τ

R: reflection

D: diffraction

S: Scattering

/C fλ =Ex: 3e8/2.4e9 = 12.5cm

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Propagation Model

Large-scale propagation model: the average received signal strength at a given distance from the transmitter

Useful for estimating the radio coverage areaSmall-scale propagation model: the variability of the signal strength in close spatial proximity to a particular location or short time durations

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Free-space ModelFriis free space equation:

are the antenna gains at the transmitter and receiverλ is the wavelengthd is the distanceL is a loss factor not related to propagation

2

2 2( )(4 )

t t rr

PG GP dd Lλ

π=

,t rG G

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Free Space ModelPath loss

Only valid beyond far-field distance, D is the transmitter antenna aperture

2

2 2( ) 10 log 10log(4 )

t t r

r

P G GPL dBP d

λπ

⎡ ⎤= = − ⎢ ⎥

⎣ ⎦

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,

f

f f

Dd

d D dλ

λ

=

200 0( ) ( )( ) ,r r f

dP d P d d d dd

= ≥ ≥

dB

dBm

dBW

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Ground Reflection (Two-Ray) Model

2 2 2 2 2" ' ( ) ( ) ,

when d is large compared to

t rt r t r

t r

h hd d h h d h h dd

h h

∆ = − = + + − − + ≈

+

2 2

4

20, for d > 3

t r t rr t t r

h h h hP PG Gd

πλ

=

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Log-normal Shadowing

00

( )[ ] ( ) ( ) 10 log( )dPL d dB PL d X PL d n Xdσ σ= + = + +

Xσ is a zero-mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB)

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Small-scale FadingFactors that contribute to small-scale fading

Multi-path propagationSpeed of the mobileSpeed of surrounding objectsThe transmission bandwidth of the signal

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Parameters of Mobile Multipath ChannelsTime Dispersion (relative to direct line-of-sight)

Mean excess delayRMS delay spreadExcess delay spread (X dB)Coherence bandwidth

Measures the range of frequencies where the channel can be considered “flat”∝ 1/RMS delay spread

Frequency dispersionTD ∝ fm

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Doppler Shift Geometry

1 cos2d

vftφ θ

π λ∆

= =∆

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Police Radar

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Two independent fading issues

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Flat-fading (non-freq. Selective)Amplitude varying channel/narrowband channels

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Rayleigh fading

2

2 2( ) exp( )2

r rp rσ σ

= −

Models a flat fading channel or an individual multipath component

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Frequency selective fadingIntroduce inter-symbol interference

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Digital Communication Systems

Modulation: to translate a base-band message signal to a bandpass signal which is suitable for transmission

AmplitudeFrequencyPhaseSpread spectrum modulation

Analog

Digital (Base band) Analog (bandpass)