Slides 6

 

Mobile Radio Propagation Small-Scale Fading and Multipath CS 515 Mobile and Wireless Networking Fall 2002 İbrahim Körpeoğlu Computer Engineering Department Bilkent University

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Relationship between Bandwidth and Receiver Power  

What happens when two different signals with different bandwidths are sent through the channel? 



What is the receiver power characteristics for both signals?

WeThe mean the bandwith of the isbaseband signal bandwidth of the baseband signal is inversely 

related with its symbol rate.

One symbol

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Bandwidth of Baseband Signals Highbandwidth (Wideband) Signal

Lowbandwidth (Narrowband) Signal

Continuous Wave (CW) Signal t CS 515

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A pulsed probing signal (wideband) Tbb

Transmitter  p(t)

x(t): transmitted signal TREP

T  REP  >> τ max   (τ max : maximum measured excess delay)  x(t ) = Re{ p (t )e

} =  p (t ) cos(2π  f c t )

 j 2π   f c t 

x(t)

Multipath Wireless Channel

p(t)

y(t)

Baseband signals

Bandpass signals CS 515

r(t) Multipath Wireless Channel

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Received Power of Wideband Sİgnals p(t)

r(t) Multipath Wireless Channel

The output r(t) will approximate the channel impulse response since p(t) approximates unit impulses. 1  N −1  jθ i r (t ) = ai e ⋅  p(t  − τ i ) 2 i =0

∑

Assume the multipath components c omponents have random amplitudes and phases at time t.

 N −1  jθ  2   N −1 2  E a ,θ [ P WB ] = E a ,θ  ∑ ai e  = ∑ ai = E [ P WB ]  i=0  i =0 i

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Received Power of Wideband Sİgnals This shows that if all the multipath components of a transmitted signal is resolved at the receiver then: The average small scale received power is simply the sum of  received powers in each multipath component.

In practice, the amplitudes of individual multipath components do not fluctuate widely in a local area (for distance in the order of wavelength or  fraction of wavelength). This means the average received power of a wideband signal do not fluctuate significantly when the receiver is moving in a local area.

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Received Power of Narrowband Sİgnals A CW Signal

x(t): transmitted signal

Transmitter 

c(t) Assume now A CW signal transmitted into the same s ame channel. Let comlex envelope will be:

c(t ) = 2 −

The instantaneous complex envelope of the received signal will be: The instantaneous power will be:

r (t ) =

 N  1

∑

ai e

 jθ i ( t ,τ  )

i =0

r (t )

2

2

 N −1

= ∑ ai e jθ  (t ,τ ) i

i =0

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İbrahim Körpeoğlu

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Received Power of Narrowband Sİgnals

Over a local area (over small distance – wavelengths), the amplitude a multipath component may not change signicantly, but the phase may change a lot. For example: - if receiver moves λ meters then phase change is 2π . In this case the component c omponent may add up posively to the total sum Σ . - if receiver moves λ /4 meters then phase change is π /2 ( 90 degrees) . In this case the component c omponent may add up negatively to the total sum Σ , hence the instantaneous receiver power. Therefore for a CW (continues wave, narrowband narrowband)) signal, the small movements may cause large fluctuations on the instantenous receiver power, which typifies small scale fading for CW signals.

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Wideband versus Narrowband Baseband Signals However, the average received power for a CW signal over a local area is equivalent to the average received power for a wideband signal on the local area. This occurs because the phases of multipath components at different locations over the small-scale region are independently distributed (IID uniform) over [0,2π ].

In summary: 1. Recei Received ved pow power er for CW si signals gnals u under ndergoes goes ra rapid pid fad fades es over sma smallll distances distances 2. Recei Received ved pow power er for wi wideba deband nd sign signals als chan changes ges ver veryy little of sm small all dist distances ances.. 3. Howe However, ver, the local a area rea av averag erage e of bot both h sign signals als ar are e near nearly ly iden identical. tical.

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Small-Scale Multipath Measuremen Measurements ts 

Several Methods 

Direct RF Pulse System







Spread Spectrum Sliding Correlator Channel Sounding Frequency Domain Channel Sounding

These techniques are also called channel sounding techniques

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Direct RF Pulse System Tx f c

Pulse Generator  RF Link

Rx BPF

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Detector 

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Digital Oscilloscope

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Parameters of Mobile Multipath Channels Time Dispersion Parameters 



Grossly quantifies the multipath channel

 

Determined from Power Delay Profile Parameters include   

 

Mean Access Delay RMS Delay Spread Excess Delay Spread (X dB)

Coherence Bandwidth Doppler Spread and Coherence Time

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Measuring PDPs 

Power Delay Profiles 

Are measured by channel sounding techniques





Plots of delay relative received power as a function of  excess They are found by averaging intantenous power  delay measurements over a local area  

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Local area: no greater than 6m outdoor  Local area: no greater than 2m indoor   Samples taken at λ /4 meters approximately  For 450MHz – 6 GHz frequency range.

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Timer Dispersion Parameters Determined from a power delay profile.

Mean excess delay( τ  ):

τ  =

∑

ak 2τ k  a2

∑ τ

):

σ τ 

=

τ 

2

τ 

2

∑ − (τ )

∑ = ∑a k 

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k 

2

∑ = ∑ P (τ  )

 P (τ k  )(τ k 2 )

k 

2 k 

k 

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 P (τ  ) k 

ak 2τ k 2

k 

k 

k 

k 

Rms delay spread ( σ

k 

=

k 

∑ P (τ  )(τ  )

İbrahim Körpeoğlu

k 

k 

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Timer Dispersion Parameters Maximum Excess Delay (X dB):

Defined as the time delay value after which the multipath energy falls to X dB below the maximum multipath energy (not necesarily belonging to the first arriving component). It is also called excess delay spread .

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RMS Delay Spread

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PDP Outdoor 

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PDP Indoor 

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Noise Threshold 



The values of time dispersion parameters also depend on the noise threshold (the level of power below which the signal is considered as noise). If noise threshold is set too low, then the noise will be processed as multipath and thus causing the parameters to be higher.

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Coherence Bandwidth (BC) 

Range of frequencies over which the channel can be considered flat (i.e. channel passes all spectral components with equal gain and linear phase). 



It is a definition that depends on RMS Delay Spread. Two sinusoids with frequency separation greater than B   are affected quite differently by the channel. c

f 1 Receiver  f 2 Multipath Channel

Frequency Separation: |f 1-f 2|

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Coherence Bandwidth Frequency correlation between two sinusoids: 0 S Sym ymbo boll P Per erio iod d

Small-scale Fading (Based on Doppler Spread)

Fast Fading 1. Hig High Do Dopp ppller Sp Spre read ad 2. Co Cohe here renc nce eT Tim ime e < Sy Symb mbol ol Peri Period od 3. Ch Chan anne nell va vari riat atio ions ns fa faste sterr tha than n ba baseb seban and d signal variations

Slow Fading 1. Lo Low w Do Dop pple pler Spre pread 2. Co Cohe here renc nce eT Tim ime e>S Sym ymbo boll Pe Peri riod od 3. Ch Chan anne nell var varia iatition onss sma smallller er th than an ba base seba band nd signal variations

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Flat Fading 

Occurs when the amplitude of the received  received signal signal   changes with time 



For example according to Rayleigh Distribution

Occurs when symbol period of the transmitted signal is much larger than the Delay Spread of the channel 



Bandwidth of the applied signal is narrow.

May cause deep fades. 

Increase the transmit power to combat this situation.

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İbrahim Körpeoğlu

 

Flat Fading s(t)

h(t,τ )  

r(t) τ

0

TS

0 τ

0

TS + τ

Occurs when: BC: Coherence bandwidth BS > σ τ σ τ : Delay Spread

BC σ τ and TS < σ τ

>> TS

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Fast Fading 

Due to Doppler Spread 

  

Rate of change of the channel characteristics  characteristics  is larger than the Rate of change of the transmitted signal The channel changes during a symbol period. The channel changes because of receiver motion. Coherence time of the channel is smaller than the symbol period of the transmitter signal Occurs when: BS < BD and TS > T C

BS: Bandwidth of the signal BD: Doppler Spread TS: Symbol Period TC: Coherence Bandwidth

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Slow Fading 

Due to Doppler Spread 

Rate of change of the channel characteristics characteristics   is much smaller than the Rate of change of the transmitted signal

Occurs when: BS >> BD and TS