Transcript Small scale fading

EE 6332, Spring, 2014
Wireless Communication
Zhu Han
Department of Electrical and Computer Engineering
Class 3
Jan. 22nd, 2014
Outline

Review
– Large scale models: Chapter 2



Log-distance path loss model
log-normal shadowing
Small Scale Fading: Chapter 3
– Small-scale Multipath Propagation
– Impulse Response Model of a Multipath Channel
– Small-scale Multipath Measurements
Multiply Three Effects
ECE6331 Spring 2009
Free Space Path Loss

Path Loss is a measure of attenuation based only on the distance
to the transmitter

Free space model only valid in far-field;
– Path loss models typically define a “close-in” point d0 and
reference other points from there:
d 
Pr (d ) Pr (d0 ) 0 
d 

2
PL (d )  [ Pr (d )] dB
d 
 PL (d 0 )  2  
 d 0  dB
Log-distance generalizes path loss to account for other
environmental factors
d 
PL (d )  PL (d 0 )    
– Choose a d0 in the far field.
d 0  dB

– Measure PL(d ) or calculate Free Space Path Loss.
0
– Take measurements and derive  empirically.
Typical large-scale path loss
Log-Normal Shadowing Model

Shadowing occurs when objects block LOS between transmitter
and receiver

A simple statistical model can account for unpredictable
“shadowing”
– PL(d)(dB)=PL(d)+X0,
– Add a 0-mean Gaussian RV to Log-Distance PL
– Variance  is usually from 3 to 12.
– Reason for Gaussian
Measured large-scale path loss

Determine n and  by mean and variance
Small-Scale Fading

Rapid fluctuations of radio signal amplitude, phase, or delays

Occurs or short time period or short travel distance

Large-scale path loss effects can be ignored

Caused by arrival of two or more waves from the source
combining at the receiver

Resultant detected signal varies widely in amplitudes and phase

Bandwidth of transmitted signal is important factor
Experimental record of received signal envelope
in an urban area
Multipathradio propagation in urban areas
Determining the impulse response of a channel

Transmit a narrowband pulse into the channel

Measure replicas of the pulse that traverse different paths
between transmitter and receiver
Doppler Shift
Comparison of the BER for a fading
and non-fading channel
Parameters of Mobile Multipath Channels

Time Dispersion Parameters
– Grossly quantifies the multipath channel
– Determined from Power Delay Profile (average over different
time, a function of delay)
– Parameters include



Mean Access Delay
RMS Delay Spread
Excess Delay Spread (X dB)

Coherence Bandwidth

Doppler Spread and Coherence Time
Power Delay Profiles

Power delay profiles are generally represented as plots of
relative received power as a function of excess delay with
respect to a fixed time delay reference.

Power delay profiles are found by averaging instantaneous
power delay profile measurements over a local area.
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 l/4 meters approximately
For 450MHz – 6 GHz frequency range.
Impulse Response Model of a Multipath Channel
PDP Outdoor
PDP Indoor
Time Dispersion Parameters

The mean excess delay, rms delay spread, and excess delay spread (X dB)
are multipath channel parameters that can be determined form a power delay
profile.

The mean excess delay is the first moment of the power delay profile and is
defined as
 ak2  k
 
k
 ak
2
 P ( k ) k
k

 P ( k )
k
k

The rms delay spread is the square root of the second central moment of the
power delay profile, where
    2  ( ) 2
 ak2  k2
2 
k
 ak
2
k

 P (  k )  k2

k
 P ( k )
k
Typical values of rms delay spread are on the order of microseconds in
outdoor mobile radio channel and on the order of nanoseconds in indoor
radio channel
Maximum Excess Delay (X dB)




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 belongingto the first arriving
component). It is also called excess delay spread.
The maximum excess delay is defined as (x - 0), where 0 is the first
arriving signal and x is the maximum delay at which a multipath
component is within X dB of the strongest arriving multipath signal.
The value of x is sometimes called the excess delay spread of a
power delay profile.
In practice, values depend on the choice of noise threshold used to
process P(). The noise threshold is used to differentiate between
multipath components and thermal noise.
Noise Thresholds
– 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.
RMS Delay Spread
Effect of delay spread
Effect on error rate
Coherent bandwidth

Analogous to the delay spread parameters in the time domain,
coherence bandwidth is used to characterize the channel in the
frequency domain.

Coherence bandwidth is a statistical measure of the range of
frequencies over which the channel can be considered flat.

Two sinusoids with frequency separation greater than Bc are affected
quite differently by the channel.
f1
Receiver
f2
Multipath Channel
Frequency Separation: |f1-f2|
Coherence Bandwidth

Frequency correlation between two sinusoids: 0 <= Cr1, r2 <= 1.

Coherence bandwidth is the range of frequencies over which
two frequency components have a strong potential for
amplitude correlation.
1
–  is rms delay spread
BC 
50
– If correlation is above 0.9, then
1
– If correlation is above 0.5, then BC 
5
– This is called 50% coherence bandwidth
Example

For a multipath channel,  is given as 1.37ms.

The 50% coherence bandwidth is given as: 1/5 = 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).
Coherence Time

Delay spread and Coherence bandwidth describe 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, the time rate
of change of the mobile radio channel, and is defined as the
range of frequencies over which the received Doppler spectrum
is essentially non-zero.

We know how to compute Doppler shift: fd

Doppler spread, BD, is defined as the maximum Doppler shift:
fm = v/l

If the baseband signal bandwidth is much less than BD then
effect of Doppler spread is negligible at the receiver.
Coherence Time

Coherence time is the time duration over which the channel
impulse response is 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, since channel will change during the
transmission of the signal .
TS
Coherence time (TC) is defined as:
TC 
TC
f2
f1
t1
Dt=t2 - t1
t2
1
fm
Coherence Time


0.423

Coherence time is also defined as: TC 
fm
Coherence time definition implies that two signals arriving with
a time separation greater than TC are affected differently by the
channel.
9
16f m2

Coherence time Tc is the time domain dual of Doppler spread
and is used to characterize the time varying nature of the
frequency dispersive-ness of the channel in the time domain.

If the coherence time is defined as the time over which the time
correlation function is above 0.5, then the coherence time is
approximately, T  9
where f m  v
c
16f m
l
Types of Small-scale Fading
Small-scale Fading
(Based on Multipath Tİme Delay Spread)
Flat Fading
Frequency Selective Fading
1. BW Signal < BW of Channel
1.
2.
2. Delay Spread < Symbol Period
BW Signal > Bw of Channel
Delay Spread > Symbol Period
Small-scale Fading
(Based on Doppler Spread)
Fast Fading
1.
2.
3.
High Doppler Spread
Coherence Time < Symbol Period
Channel variations faster than baseband
signal variations
Slow Fading
1.
2.
3.
Low Doppler Spread
Coherence Time > Symbol Period
Channel variations smaller than baseband
signal variations
Flat Fading

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.
– If Bs  Bc , and Ts    Flat fading

May cause deep fades.
– require 20 or 30 dB more power to achieve low BER during times of
deep fades.
– Increase the transmit power to combat this situation.

The spectral characteristics of the transmitted signals are preserved at the
receiver, however the strength of the received signal changes with time.
Flat fading channels are known as amplitude varying channels or narrowband channels.
Radio channel has a constant gain and linear phase response over a
bandwidth which is greater than the bandwidth of the transmitted signal.
It is the most common type of fading described in the technical literature.



Flat Fading
s(t)
h(t,)
r(t)
  TS
0
TS
Occurs when:
BS << BC
and
TS >> 
0

0
TS+
BC: Coherence bandwidth
BS: Signal bandwidth
TS: Symbol period
: Delay Spread
Frequency Selective Fading

Occurs when channel multipath delay spread is greater than the symbol
period.
– Symbols face time dispersion
– Channel induces Intersymbol Interference (ISI)

Bandwidth of the signal s(t) is wider than the channel impulse response.
Radio channel has a constant gain and linear phase response over a
bandwidth which is smaller than the bandwidth of the transmitted signal.
Frequency selective fading is due to time dispersion of the transmitted
symbols within the channel. Thus the channel induces inter-symbolinterference.
Statistical impulse response model and computer generated impulse
responses are used for analyzing frequency selective small-scale fading.
Frequency selective fading channels are known as wideband channels since
the BW of the signal is wider than the BW of the channel impulse response.
As time varies, the channel varies in gain and amplitude across the spectrum
of s(t), resulting in time varying distortion in the received signal r(t).
If Bs  Bc , and 0.1Ts    Frequency selective fading






Frequency Selective Fading
s(t)
r(t)
h(t,)
  TS
0 TS
0

0 TS
TS+
Causes distortion of the received baseband signal
Causes Inter-Symbol Interference (ISI)
Occurs when:
BS > BC
and
TS < 
As a rule of thumb: TS < 
Fast Fading

Due to Doppler Spread
BS: Bandwidth of
– Rate of change of the channel characteristics is larger than the
the signal
Rate of change of the transmitted signal
Occurs when: BD: Doppler
– The channel changes during a symbol period.
Spread
BS < BD
– The channel changes because of receiver motion.
TS: Symbol
and
Period
– Coherence time of the channel is smaller than
TS > TC
TC: Coherence
the symbol period of the transmitter signal
Bandwidth
– It causes frequency dispersion due to Doppler spread and leads to
distortion.
– Note that, when a channel is specified as a fast or slow fading channel, it
does not specify whether the channel is flat or frequency selective
 A flat, fast fading channel  the amplitude of the delta function
varies faster than the rate of change of the transmitted
baseband signal.
 A frequency selective, fast fading channel  the amplitudes,
phases, and time delays of any one of the multipath
components varies faster than the rate of change of the
transmitted baseband signal.
Slow Fading

Due to Doppler Spread
– Rate of change of the channel characteristics is much smaller
than the rate of change of the transmitted signal
Occurs when:
BS >> BD
and
TS << TC
BS: Bandwidth of the signal
BD: Doppler Spread
TS: Symbol Period
TC: Coherence Bandwidth
Different Types of Fading

With Respect To SYMBOL PERIOD
TS
Flat Fast
Fading
Flat Slow
Fading
Symbol Period of
Transmitting Signal

Frequency Selective
Fast Fading
Frequency Selective
Slow Fading
TC
TS
Transmitted Symbol Period
Different Types of Fading

With Respect To BASEBAND SIGNAL BANDWIDTH
BS
Frequency Selective
Fast Fading
Frequency Selective
Slow Fading
Transmitted
Baseband
BC
Signal Bandwidth
Flat Fast
Fading
Flat Slow
Fading
BD
Transmitted Baseband Signal Bandwidth
BS