Channel Fading

EC744 Wireless Communication Fall 2008

Mohamed Essam KhedrDepartment of Electronics and Communications

Wireless Communication Fading Channel Overview

Syllabus

• Tentatively

Channel coding techniquesWeek 6

Mid Term exam (take home), Diversity techniquesWeek 7

Equalization techniquesWeek 8

Spread spectrum, MIMO and OFDMWeek 9

Wireless networking: 802.11, 802.16, UWBWeek 10

Hot topicsWeek 11

PresentationsWeek 12


Final ExamWeek 15


Source coding techniquesWeek 5

Modulation techniquesDemodulation techniques (coherent and non-coherent)

Week 4

Channel characteristics (AWGN, fading)Week 3

Digital Communication fundamentalsWeek 2

Overview wireless communications, Probabilities Week 1

Fading � Is due to multipath propagation.

With respect to a stationary base station, multipath propagation creates a stochastic standing wave pattern, through which the mobile station moves.

�Caused by shadowing:when the propagation environment is changing significantly, but this fading is typically much slower than the multipath fading.

Multipath Propagation - Fading

AntennaAntennaab y = a + b

a & b are in phase a & b are out of phase by π

Complete fading when 2πd/λ = nπ, d is the path difference

Diffractedwave Reflected

wave

No direct patha b

AntennaAntennab y = 0a

Fading - Types• Slow (Long) Term

0 5 10 15 20 25 Distance (λ)

Sign

al s

tren

gth

rela

tive

to 1

uV (d

b)

0

10

20

30

Slow fading

Fast fading

Exact representation of fading characteristics is not possible, because of infinite number of situation.

Exact representation of fading characteristics is not possible, because of infinite number of situation.

•Fast (Short) Term (Also known as Rayleigh fading)

Fading - Slow (Long) Term� Slower variation in mean signal strength (distance 1-2 km)� Produced by movement over much longer distances� Caused by:

�Terrain configuration (hill, flat area etc.):Results in local mean (long term fading) attenuationand fluctuation.�The built environment (rural and urban areas etc.), between base station and the mobile unit:Results in local mean attenuation

Fading - Slow (Long) Term

Transmitterτn,1

Receiver

τk,1

τ or d

τn,3τn,2

τk,2

τk,3

τk,4 one subpath

LOS

path k

path n

d(t)

vmR(t)

θn

C. D. Charalambous et al

Fading- Fast (Short) Term� Describes the constant amplitude fluctuations in the received

signal as the mobile moves.� Caused by multipath reflection of transmitted signal by local

scatters (houses, building etc.)� Observed over distances = λ/2� Signal variation up to 30 dB.� Is a frequency selective phenomenon.� Can be described using Rayleigh statistics, (no line of sight).� Can be described using Rician statistics, (line of sight).� Causes random fluctuations in the received power, and also

distorts the pulse carrying the information.

Fading- Fast (Short) Term - contd.

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Or

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)sin()2sin()(cos)2cos()(

In-phase Quadrature

Fading- Fast (Short) Term - contd.The phaseφi can be assumed to be uniformly distributed inthe range (0, 2π), provided the locations of buildings etc. are completely random.

This for large N, the amplitude of the received signal is:

)2sin()2cos()( tfYtfXtS ccr π−π=

where ��==

==N

iii

N

iii aYaX

11

)sin(),(cos φφ

X and Y are independent, identically distributed Gaussian random variables.

Fading- Fast (Short) Term - contd.The envelope of the received signal is:

5022 .)( YXA += Which will be Rayleigh distributed.

Rayleigh

Exponential

A or power P

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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

Measuring PDPs

• Power Delay Profiles– Are measured by channel sounding techniques– Plots of relative received power as a function of

excess delay – They are found by averaging intantenous power

delay measurements over a local area– 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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Mean excess delay( ):

Rms delay spread (σ(σ(σ(σττττ):):):):

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Timer Dispersion ParametersMaximum Excess Delay (X dB):

Defined as the time delay value after which the multipath energyfalls to X dB below the maximum multipath energy (not necesarily belongingto the first arriving component).

It is also called excess delay spread.

RMS Delay Spread

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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 Bc are affected quite differently by the channel.

Receiver

f1

f2

Multipath Channel Frequency Separation: |f1-f2|

Coherence Bandwidth

σ501=CB

Frequency correlation between two sinusoids: 0 <= Cr1, r2 <= 1.

If we define Coherence Bandwidth (BC) as the range of frequencies over which the frequency correlation is above 0.9, then

If we define Coherence Bandwidth as the range of frequencies over which the frequency correlation is above 0.5, then

σ51=CB

σ is rms delay spread.

This is called 50% coherence bandwidth.

Coherence Bandwidth

• Example: • For a multipath channel, σ is given as 1.37µs.• The 50% coherence bandwidth is given as: 1/5σ =

146kHz. – This means that, for a good transmission from a transmitter

to a receiver, the range of transmission frequency (channel bandwidth) should not exceed 146kHz, so that all frequencies in this band experience the same channel characteristics.

– Equalizers are needed in order to use transmission frequencies that are separated larger than this value.

– This coherence bandwidth is enough for an AMPS channel (30kHz band needed for a channel), but is not enough for a GSM channel (200kHz needed per channel).

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Coherence Time

• Delay spread and Coherence bandwidthdescribe the time dispersive nature of the channel in a local area.

• They don’t offer information about the time varying nature of the channel caused by relative motion of transmitter and receiver.

• Doppler Spread and Coherence time are parameters which describe the time varying nature of the channel in a small-scale region.

Doppler Spread

• Measure of spectral broadening caused by motion

• We know how to compute Doppler shift: fd

• Doppler spread, BD, is defined as the maximum Doppler shift: fm = v/λ

• If the baseband signal bandwidth is much greater than BD then effect of Doppler spread is negligible at the receiver.

Coherence time is the time duration over which the channel impulse responseis essentially invariant.

If the symbol period of the baseband signal (reciprocal of the baseband signal bandwidth) is greater the coherence time, than the signal will distort, sincechannel will change during the transmission of the signal .

Coherence Time

mfCT 1≈

Coherence time (TC) is defined as: TS

TC

Coherence time is also defined as:

mfC f

Tm

423.0216

9 =≈π

Coherence time definition implies that two signals arriving with a time separation greater than TC are affected differently by the channel.

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Types of Small-scale FadingSmall-scale Fading

(Based on Multipath T�me Delay Spread)

Flat Fading

1. BW Signal < BW of Channel 2. Delay Spread < Symbol Period

Frequency Selective Fading

1. BW Signal > Bw of Channel2. Delay Spread > Symbol Period

Small-scale Fading(Based on Doppler Spread)

Fast Fading

1. High Doppler Spread2. Coherence Time < Symbol Period3. Channel variations faster than baseband

signal variations

Slow Fading

1. Low Doppler Spread2. Coherence Time > Symbol Period3. Channel variations smaller than baseband

signal variations

Channel ClassificationBased on Time-Spreading

Flat Fading1. BS < BC �� Tm < Ts2. Rayleigh, Ricean distrib.3. Spectral chara. of transmitted

signal preserved

Frequency Selective1. BS > BC �� Tm > Ts2. Intersymbol Interference3. Spectral chara. of transmitted

signal not preserved4. Multipath components resolved

Signal

Channel

freq.BS

BC freq.BC

BS

Channel

Signal

C. D. Charalambous et al

Fading in Digital Mobile Communications

• If Bs>> Bc, then a notch appears in the spectrum. Thus resulting in inter-symbol interference (ISI).

- To overcome this, an adaptive equaliser (AE) with inverse response may be used at the receiver. Training sequences are transmitted to update AE.

• If Bs<< Bc, then flat fading occurs, resulting in a burst of error.

- Error correction coding is used to overcome this problem.

Mitigation Techniques for the Multipath Fading Channel

• Space diversity –– Signals at the same frequency using two or three antennas located several

wavelengths a part. – Antennas are connected to two or three radio receivers.– The receiver will the strongest signal is elected– Disadvantage: Uses two or more antennas, therefore the need for a

large site.• Frequency diversity –

– Signals at different frequencies received by the same antenna very rarely fade simultaneously. Thus the use of several carrier frequencies or the use of a wideband signal to combat fading.

– A single aerial connected to a number receiver, each tuned to a different frequency, whose outputs are connected in parallel. The receiver with the strongest instantaneous signal will provide the output.

– Disadvantage: Uses two or more frequencies to transmit the same signal.

Mitigation Techniques for the Multipath Fading Channel

• Time diversity – Spread out the effects of errors through interleaving and coding

• Multipath diversity – Consider the tapped delay line model of a channel

shown previously– If multipaths can be put together coherently at the

receiver, diversity improvement results– This is what the RAKE receiver does (see next

viewgraph)

RAKE Multipath Signal Processing

R.E. Ziemer 2002

Flat Fadingh(t,τ)s(t) r(t)

0 TS 0 τ 0 TS+τ

τ << TS

Occurs when:BS << BC

andTS >> στ

BC: Coherence bandwidthBS: Signal bandwidthTS: Symbol periodστ: Delay Spread

Frequency Selective Fadingh(t,τ)s(t) r(t)

0 TS 0 τ 0 TS+τ

τ >> TS

TS

Causes distortion of the received baseband signal

Causes Inter-Symbol Interference (ISI)

Occurs when:BS > BC

andTS < στ

As a rule of thumb: TS < στ

Fast Fading• Due to Doppler Spread

• Rate of change of the channel characteristicsis 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

andTS > TC

BS: Bandwidth of the signalBD: Doppler SpreadTS: Symbol PeriodTC: Coherence Bandwidth

Slow Fading

• Due to Doppler Spread• Rate of change of the channel characteristics

is much smaller than theRate of change of the transmitted signalOccurs when:

BS >> BDand

TS << TC

BS: Bandwidth of the signalBD: Doppler SpreadTS: Symbol PeriodTC: Coherence Bandwidth

Different Types of Fading

Transmitted Symbol Period

Symbol Period ofTransmitting Signal

TS

TS

TC

στ

Flat SlowFading

Flat Fast Fading

Frequency SelectiveSlow Fading

Frequency Selective Fast Fading

With Respect To SYMBOL PERIOD

Different Types of Fading

Transmitted Baseband Signal BandwidthBS

BD

Flat Fast Fading

Frequency SelectiveSlow Fading

Frequency Selective Fast Fading

BS

Transmitted Baseband

Signal Bandwidth

Flat Slow Fading

BC

With Respect To BASEBAND SIGNAL BANDWIDTH

Average Fade DurationDefined as the average period of time for which the received signal isbelow a specified level R.

For Rayleigh distributed fading signal, it is given by:

( )

rmsm

RR

rR

fe

eN

RrN

=−=

−=≤= −

ρπρ

τ

τ

ρ

ρ

,21

11

]Pr[1

2

2

Fading Model –Gilbert-Elliot Model

Fade Period

Time t

SignalAmplitude

Threshold

Good(Non-fade)

Bad(Fade)

Gilbert-Elliot Model

Good(Non-fade)

Bad(Fade)

1/ANFD

1/AFD

The channel is modeled as a Two-State Markov Chain. Each state duration is memory-less and exponentially distributed.

The rate going from Good to Bad state is: 1/AFD (AFD: Avg Fade Duration)The rate going from Bad to Good state is: 1/ANFD (ANFD: Avg Non-Fade

Duration)

Documents

Channel Fading