Transcript Properties of Mobile Radio Propagation Channel

Properties of the Mobile Radio
Propagation Channel
Jean-Paul M.G. Linnartz
Nat.Lab., Philips Research
Mobile Radio Propagation Channel
Statistical Description of Multipath Fading
The basic Rayleigh / Ricean model gives the PDF of envelope
 But: how fast does the signal fade?
 How wide in bandwidth are fades?
Typical system engineering questions:
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What is an appropriate packet duration, to avoid fades?
How much ISI will occur?
For frequency diversity, how far should one separate carriers?
How far should one separate antennas for diversity?
What is good a interleaving depth?
What bit rates work well?
Why can't I connect an ordinary modem to a cellular phone?
The models discussed in the following sheets
will provide insight in these issues
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Multipath fading
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Mobile Radio Propagation Channel
The Mobile Radio Propagation Channel
A wireless channel exhibits severe fluctuations for small
displacements of the antenna or small carrier frequency offsets.
Channel Amplitude in dB versus location (= time*velocity) and frequency
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Multipath fading
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Mobile Radio Propagation Channel
Some buzz words about Time Dispersion and Frequency Dispersion
Time Dispersion
Frequency Dispersion
Time Domain
Interpretation
Channel variations
Fast Fading
Correlation Distance
Delay spread
InterSymbol Interference
Channel equalization
Frequency
Domain
Interpretation
Doppler spectrum
Intercarrier Interference
Frequency selective fading
Coherence bandwidth
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Mobile Radio Propagation Channel
Fading is characterised by two distinct mechanisms
• 1. Time dispersion
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Time variations of the channel are caused by motion of the antenna
Channel changes every half a wavelength
Moving antenna gives Doppler spread
Fast fading requires short packet durations, thus high bit rates
Time dispersion poses requirements on synchronization and rate of
convergence of channel estimation
 Interleaving may help to avoid burst errors
• 2. Frequency dispersion
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Delayed reflections cause intersymbol interference
Channel Equalization may be needed.
Frequency selective fading
Multipath delay spreads require long symbol times
Frequency diversity or spread spectrum may help
Multipath fading
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Mobile Radio Propagation Channel
Time dispersion of narrowband signal (single frequency)
Transmit: cos(2p fc t)
Receive: I(t) cos(2p fc t) + Q(t) sin(2p fc t)
= R(t) cos(2p fc t + f)
I-Q phase trajectory
•
As a function of time, I(t) and Q(t) follow a random trajectory through
the complex plane
•
Intuitive conclusion:
Deep amplitude fades coincide with large phase rotations
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Mobile Radio Propagation Channel
Doppler shift
• All reflected waves arrive from a different angle
• All waves have a different Doppler shift
v
f cos f
c c
The Doppler shift of a particular wave is
f 0=
Maximum Doppler shift:
fD = fc v / c
Joint Signal Model
• Infinite number of waves
• Uniform distribution of angle of arrival f: fF(f) = 1/2p
• First find distribution of angle of arrival the compute distribution of Doppler shifts
• Line spectrum goes into continuous spectrum
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Doppler
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Mobile Radio Propagation Channel
Doppler Spectrum
If one transmits a sinusoid, …
what are the frequency components in the received signal?
 Power density spectrum versus received frequency
 Probability density of Doppler shift versus received
frequency
 The Doppler spectrum has a characteristic U-shape.
 Note the similarity with sampling a randomly-phased
sinusoid
 No components fall outside interval [fc- fD, fc+ fD]
 Components of + fD or -fD appear relatively often
 Fades are not entirely “memory-less”
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Doppler
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Mobile Radio Propagation Channel
Autocorrelation of the signal
We now know the Doppler spectrum.
But how fast does the channel change?
Wiener-Kinchine Theorem:
 Power density spectrum of a random signal is the Fourier Transform of
its autocorrelation
 Inverse Fourier Transform of Doppler spectrum gives autocorrelation of
I(t) and Q(t)
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Autocorrelation
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Mobile Radio Propagation Channel
Autocovariance of amplitude
2
=
C J0 ( 2 p f D t )
J0 is zero-order Bessel function of first kind.
Note that the correlation is a function of
distance or time offset:
f Dt =
f
v
c t =
c
d

where
d is the antenna displacement during t, with d = v t
 is the carrier wavelength (30 cm at 1 GHz)
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Autocorrelation
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Mobile Radio Propagation Channel
How to handle fast multipath fading?
Analog
 User must speak slowly
GSM
 Blocks of data shorter than average non-fade
period
 Error correction and interleaving to avoid
burst errors
 Error detection and speech decoding
 Fade margins in cell planning
DECT
 Diversity reception at base station
IS95
 Wideband transmission averages channel
behaviour
 This avoids burst errors and deep fades
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Mobile Radio Propagation Channel
Frequency Dispersion
• Frequency dispersion is caused by the
delay spread of the channel
• Frequency dispersion has no relation to
the velocity of the antenna
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Mobile Radio Propagation Channel
Frequency Dispersion: Delay Profile
Typical sample of impulse response h(t)
If we transmit a pulse (t) we receive h(t)
Delay profile: PDF of received power: "average h2(t)"
Local-mean power in delay bin t isp
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Multipath fading
ft(t)t
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Mobile Radio Propagation Channel
Typical Delay Spreads
Macrocells TRMS < 8 sec
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GSM (256 kbit/s) uses an equalizer
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IS-54 (48 kbit/s): no equalizer
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In mountanous regions delays of 8 sec and more
occur
GSM has some problems in Switzerland
Microcells
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TRMS < 2 sec
Low antennas (below tops of buildings)
Picocells
TRMS < 50 nsec - 300 nsec
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Indoor: often 50 nsec is assumed
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DECT (1 Mbit/s) works well up to 90 nsec
Outdoors, DECT has problem if range > 200 .. 500 m
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Multipath fading
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Mobile Radio Propagation Channel
Channel Parameters at 1800 MHz
Environment Delay Spread Angle spread Max. Doppler shift
Macrocellular:
Rural flat
0.5 ms
1 degree
200 Hz
Macrocellular:
Urban
5 ms
20 degrees
120 Hz
Macrocellular:
Hilly
20 ms
30 degrees
200 Hz
Microcellular:
Factory, Mall
0.3 ms
120 degrees
10 Hz
Microcellular:
Indoors, Office
0.1 ms
360 degrees
2..6 Hz
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Mobile Radio Propagation Channel
Typical Delay Profiles
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1)
Exponential
2)
Uniform Delay Profile
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Experienced on some indoor
channels
Often approximated by N-Ray
Channel
3)
Bad Urban
Multipath fading
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Mobile Radio Propagation Channel
How do systems handle delay spreads?
Analog
 Narrowband transmission
GSM
 Adaptive channel equalization
 Channel estimation training sequence
DECT
 Use the handset only in small cells with small delay spreads
 Diversity and channel selection can help a little bit
“pick a channel where late reflections are in a fade”
IS95
 Rake receiver separately recovers signals over paths with excessive delays
Digital Audio Broacasting
 OFDM multi-carrier modulation
The radio channel is split into many narrowband (ISI-free) subchannels
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Mobile Radio Propagation Channel
Frequency and Time Dispersion
Model: Each wave has its own angle and excess delay
 Antenna motion changes phase
 changing carrier frequency changes phase
The scattering environment is defined by
 angles of arrival
 excess delays in each path
 power of each path
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Mobile Radio Propagation Channel
Scatter Function of a Multipath Mobile Channel
Gives power as function of
 Doppler Shift (derived from angle f )

Excess Delay
Example of a scatter plot
Horizontal axes:
 x-axis:
Excess delay time
 y-axis:Doppler shift
Vertical axis
 z-axis:
received power
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Mobile Radio Propagation Channel
Scatter Function of a Multipath Mobile Channel
Example of
a scatter plot
Excess Delay
Doppler Shift
derived from angle f
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Mobile Radio Propagation Channel
Correlation of Fading vs. Frequency Separation
 When do we experience frequency-selective fading?
 How to choose a good bit rate?
 Where is frequency diversity effective?
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Multipath fading
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Mobile Radio Propagation Channel
Consider two (random) sinusoidal signals
 Sample 1 at frequency f1 at time t1
 Sample 2 at frequency f2 at time t2
Covariance of amplitudes
C R 1,R 2  
2
J 02 (2p
=
v

t)
1 + 4 p 2 ( f 1 - f 2 )2 T RMS 2
Special cases
 Zero displacement / motion: t = 0
 Zero frequency separation: f = 0
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Mobile Radio Propagation Channel
Coherence Bandwidth
Definition: Coherence. Bandwidth is the frequency separation for which the
correlation coefficient is down from 1 to 0.5 Thus 1 = 2p(f1 - f2) TRMS
 so Coherence Bandwidth BW = 1 (2p TRMS)
 We derived this for an exponential delay profile
Another rule of thumb:
 ISI affects BER if Tb > 0.1TRMS
Conclusion:
 Either keep transmission bandwidth much smaller than the coherence
bandwidth of the channel, or
 use signal processing to overcome ISI, e.g.
 Equalization
 DS-CDMA with rake
 OFDM
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Effects of fading on
modulated radio signals
Mobile Radio Propagation Channel
Effects of Multipath (I)
Time
Time
Frequency
OFDM
Time
Wideband
Narrowband
Frequency
Frequency
Mobile Radio Propagation Channel
Effects of Multipath (II)
Frequency
+
Frequency
MC-CDMA
Time
+
+
+
+
Frequency
Hopping
Time
Time
DS-CDMA
+ -
+ -
-
+ -
+
-
+ -
+
Frequency
Time Dispersion Revisited
The duration of fades and
the optimum packet length
Mobile Radio Propagation Channel
Time Dispersion Revisited: Duration of Fades
In the next slides we study the temporal behavior of fades.
Outline:
 # of level crossings per second
 Model for level crossings
 Average non-fade duration
 Effective throughput and optimum packet length
 Average fade-duration
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Mobile Radio Propagation Channel
Two-State Model
Very simple mode: channel has two-states
 Good state: Signal above “threshold”, BER is virtually zero
 Poor state: “Signal outage”, BER is 1/2, receiver falls out of sync, etc
Markov model approach:
 Exponential distribution of sojourn time Prob(T >T0) = exp(-T0/Tave)
 Memory-less transitions
This model may be sufficiently realistic for many investigations
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Mobile Radio Propagation Channel
Average Fade / Nonfade Duration
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Fade duration
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Mobile Radio Propagation Channel
Average nonfade duration
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Fade duration
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Mobile Radio Propagation Channel
How to handle long fades when the user is stationary?
Analog
 Disconnect user
GSM
 Slow frequency hopping
 Handover, if appropriate
 Power control
DECT
 Diversity at base station
 Best channel selection by handset
IS95
 Wide band transmission avoids most deep fades (at least in macro-cells)
 Power control
Wireless LANs
 Frequency Hopping, Antenna Diversity
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Fade duration
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Mobile Radio Propagation Channel
Optimal Packet length
We want to optimize
#User bits
Effective throughput = ---------------- Prob(success)
#Packet bits
This requires a trade off between
 Short packets:
much overhead (headers, sync. words etc).
 Long packets:
may experience fade before end of packet.
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Fade duration
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Mobile Radio Propagation Channel
Optimal Packet length
fc = 900 MHz
72 km/h (v=20 m/s)
fade margin 10 dB
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Fade duration
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Mobile Radio Propagation Channel
Derivation of Optimal Packet length
 Assume exponential, memoryless nonfade durations
(This is an approximation: In reality many nonfade periods have
duration of /2, due to U-shaped Doppler spectrum)
 Successful reception if
1) Above threshold at start of packet
2) No fade starts before packet ends
Formula:
 1 2p f D T L 
 1 T 
P( succ ) = exp - - L  = exp - 
  T NF 

 

with TL packet duration
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Fade duration
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Mobile Radio Propagation Channel
Average fade duration
 1 
TF=
exp   - 1
2π f D   η  
η
 AFD is inversely proportional to Doppler spread
 Fade durations rapidly reduce with increasing margin, but time between fades
increases much slower
 Experiments: For large fade margins: exponentially distributed fade durations
 Relevant to find length of error bursts and design of interleaving
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Fade duration
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Mobile Radio Propagation Channel
Conclusion
• The multipath channel is characterized by two effects:
Time and Frequency Dispersion
• Time Dispersion effects are proportional to speed and
carrier frequency
• System designer needs to anticipate for channel anomalies
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