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Rayleigh
fading
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Chapter: Wireless
Channels
Section: Multipath
Fading | 
Delay SpreadBecause of multipath
reflections, the channel impulse response of a wireless channel looks
likes a series of pulses.
Figure: Example of impulse response and
frequency transfer function of a multipath channel.
We can define the local-mean average
received power with excess delay within the interval (T, T
+ dt). This gives the "delay profile" of the channel.
The delay profile determines to what extent the channel fading at two
different frequencies f1 and f2 are correlated.
Some definitions
- The maximum delay time spread is the total time interval during
which reflections with significant energy arrive.
- The rms delay spread TRMS is the standard
deviation (or root-mean-square) value of the delay of reflections,
weighted proportional to the energy in the reflected waves.
For
a digital signal with high bit rate, this dispersion is experienced as
frequency selective fading and intersymbol interference (ISI). No serious
ISI is likely to occur if the symbol duration is longer than, say, ten
times the rms delay spread.
Typical ValuesIn macro-cellular mobile radio, delay spreads are
mostly in the range from TRMS is about 100 nsec to 10
microsec. A typical delay spread of 0.25 microsec corresponds to a coherence
bandwidth of about 640 kHz. Measurements made in the U.S., indicated
that delay spreads are usually less than 0.2 microsec in open areas, about
0.5 microsec in suburban areas, and about 3 micros in urban areas.
Measurements in The Netherlands showed that delay spreads are relatively
large in European-style suburban areas, but rarely exceed 2 microsec.
However, large distant buildings such as apartment flats occasionally
cause reflections with excess delays in the order of 25 microsec.
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Figure: Measured Delay profile in a German urban
environment at 1800 MHz
Delay Spread = 1.2 msec; coherence BW = 1.3 MHz
Source: Research group of Prof. Paul Walter Baier, U. of
Kaiserslautern, Germany.
See also: corresponding scatter plot. |
The Indoor Channel
FIGURE: RMS Delay Spread vs. propagation
distance in the U.C. Berkeley, Cory Hall Building.
In indoor and micro-cellular channels, the delay spread is usually
smaller, and rarely exceed a few hundred nanoseconds. Seidel and Rappaport
reported delay spreads in four European cities of less than 8 microsec in
macro-cellular channels, less than 2 microsec in micro-cellular channels,
and between 50 and 300 ns in pico-cellular channels.
Delay ProfileThe delay profile is the expected power per unit of
time received with a certain excess delay. It is obtained by averaging a
large set of impulse responses.
Figure: Typical delay profile: Exponential
Figure: Typical indoor delay profile:
In an indoor environment, early reflections often arrive with almost
identical power. This gives a fairly flat profile up to some point, and a
tail of weaker reflections with larger excess delay.
Figure: Typical "bad urban" delay profile
Besides the normal reflections from nearby obstacles, remote high rise
buildings cause strong reflections with large excess delay.
From the delay profile, one can compute the correlation
of the fading at different carrier frequencies.
Figure Auto-Covariance of the received
amplitude of two carriers transmitted with certain frequency offset.
Resolvable PathsA wideband signal with symbol duration
Tc (or a direct sequence (DS)-CDMA signal with chip time
Tc), can "resolve" the time dispersion of the channel with
an accuracy of about Tc. For DS-CDMA, the number of
resolvable paths is TDelay
N = round (-------) + 1
Tchip
where round(x) is the largest integer value
smaller than x and TDelay is total length of the
delay profile. A DS-CDMA Rake receiver can
exploit N-fold path diversity.
How do systems handle delay spreads?
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System |
Countermeasure |
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Analog |
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GSM |
- Adaptive channel equalization
- Channel estimation training sequence
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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)
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IS95 Cellular CDMA |
- Rake receiver separately recovers
signals over paths with excessive delays
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Digital Audio
Broadcasting |
- OFDM multi-carrier modulation: The
radio channel is split into many narrowband (ISI- free)
subchannels
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