dept. of ee, ndhu 1 chapter 15 fading channels. dept. of ee, ndhu 2 digital communication systems
TRANSCRIPT
3Dept. of EE, NDHU
Challenges of Communicating Over Fading Channels
• Sources of noise degrade the system performance
– AWGN (ex. Thermal noise)
– Man-made and natural noise
– Interferences
• Band-limiting filter induces the ISI effect
• Radio channel results in propagation loss
– Signal attenuation versus distance over free space. For example,
– Multi-path fading cause fluctuations in the received amplitude, phase, angle of
arrival
2)4
()(d
dLs
4Dept. of EE, NDHU
Characterizing Mobile-radio Propagation
• Large-scale fading
– Signal power attenuation due to motion over large area
– Is caused by the prominent terrain (ex. hills, forest, billboard…)
between the transmitter and the receiver
– Statistics of path loss over the large-scale fading
+ Mean-path loss (nth-power law)
+ Log-normal distributed variation about the mean
– Is evaluated by averaging the received signal over 10 to 30
wavelengths
5Dept. of EE, NDHU
Characterizing Mobile-radio Propagation
• Small-scale fading
– Time-spreading of the signal
+ Time delays of multi-path arrival
– Time-variant behavior of the channel
+ Motion between the transmitter and the receiver results in propagation path chang
es
– Statistics of envelop over the small-scale fading
+ Rayleigh fading if there are large number of reflective paths, and if there is no lin
e-of –sight signal components
+ Rician pdf while a line-of-sight propagation path is added to the multiple reflectiv
e paths
6Dept. of EE, NDHU
Basic Mechanisms for Signal Propagation
• Reflection
– Electromagnetic wave impinges on a smooth surface with very large
dimensions relative to the RF wavelength
• Diffraction
– Propagation path between the transmitter and the receiver is obstructed by a
dense body, causing secondary waves to be formed behind the obstructing
body
• Scattering
– A radio wave impinges on either a large, rough surface or any surface whose
dimensions are on the order of or less, causing the energy to be spread out
8Dept. of EE, NDHU
Baseband Waveform in A Fading Channel
• A transmitted signal can be represented by
• The complex envelop of s(t) is represented by
• In a fading channel, the modified baseband waveform is
component. fading-scale-small thecalled is )( and
envelop, theofcomponent fading-scale-large thecalled is )( where,
)()()()()(
by drepresente becan envelop the
)()(
0
0
)(
tr
tm
tRtrtmtRt
tget tj
})(Re{)( 2 tfj cetgts
)()( )()()( tjtj etRetgtg
11Dept. of EE, NDHU
Large-scale Fading
• Channel model
– Okumura made some of the path-loss measurements for a wide range of ante
nna heights and coverage distance
– Hata transformed Okumura’s data into parametric formulas
• The mean path-loss is a function of distance between a transmitter a
nd receiver
– n-th power of d
– n is equal to 2 in free space, n can be lower while a very strong guided wave
is present, and n can be larger while obstructions are present
)(dLp
)log(10)( )()( )( )( )(0
00 d
dndBdLdBdL
d
ddL sp
np
12Dept. of EE, NDHU
Large-scale Fading
• Path-loss variations
–
– denotes a zero-mean, Gaussian random variable (in decibels)
with standard deviation
– The choice of the value for is often based on measurements
– It is not unusual for to take on values as height as 6 to 10 dB
X
)()log(10)( )()( )(0
0 dBXd
dndBdLdBdL sp
X
X
14Dept. of EE, NDHU
Small-Scale Fading
• Assumptions
– Antenna remains within a limited trajectory, so that the effect of large-scale
fading is a constant
– Antenna is traveling and there are multiple scatter paths with a time-variant
propagation delay , and a time-variant multiplicative factor
– Noise is free
• Derive the bandpass signal within a small-scale fading channel
)(tn )(tn
)()()(2
)]([2
)()()()(
is signal baseband equivalent
)})]([)(Re({)(
)]([)()(
tj
n
tnjn
n
tncfjn
tntcfj
nnn
nnn
etetettz
ettgttr
ttsttr
15Dept. of EE, NDHU
Multi-path Reflected Signal On A Desired Signal
)()()()( tnjnnn ettjytx
pdfRician otherwise 0
0,0for )(]2
)(exp[)(
)()()(
020
02
220
20
0
220
ArAr
IArr
rp
tytxtr rr
order zero and kindfirst theoffunction Bessel modified theis )( and
component signal faded-non theof magnitudepeak thedenotes
0 I
A
16Dept. of EE, NDHU
Multi-path Reflected Signal Without A Desired Signal
pdfRayleigh otherwise 0
0for ]2
exp[)( 02
20
20
0
rrr
rp
•As the magnitude of the line-of sight component approaches zero,
the Rician pdf approaches a Rayleigh pdf. That is,
17Dept. of EE, NDHU
Response of A Multi-path Channel As A Function of Position
0.4 is positions antennabetween interval The
19Dept. of EE, NDHU
Signal Time-Spreading
• Signal time-spreading viewed in the Time-Delay Domain
– Wide-sense stationary uncorrelated scattering (WSSUS) model
– The model treats signal arriving at a receive antenna with different delays as
uncorrelated
– Multi-path-intensity profile describes the average received signal power as a function
of the time delay
– Multi-path-intensity profile usually consists multiple discrete multi-path components
– The time between the first and the last received component represents the maximum
excess delay
– The threshold level relative to the strongest component might be chosen 10 dB or 20
dB
20Dept. of EE, NDHU
Signal Time-Spreading
• Degradation Categories viewed in the Time-Delay Domain
– Frequency selective fading
+ The maximum excess delay time is larger than the symbol time
+ The received multi-path components of a symbol extend beyond the symbol’s duration
+ Yield inter-symbol interference (ISI) distortion that is the same as the ISI caused by an electronic filter
+ Mitigate the ISI distortion is possible because many of the multi-path components are resolvable by the recei
ver
– Frequency non-selective fading or flat fading
+ The maximum excess delay time is smaller than the symbol time
+ All of the received multi-path components of a symbol arrive within a symbol time
+ No ISI induces
+ Performance degradation due to the un-resolvable phasor components can add up destructively to reduce SN
R
+ Signal diversity and using error-correction coding is the most efficient way to improve the performance
sm TT
sm TT
21Dept. of EE, NDHU
Signal Time-Spreading
• Signal time-spreading viewed in the frequency Domain
– Obtain the Fourier transform of
+ Correlation between the channel’s response to two signals as a function of the frequency diff
erence between the two signals
– Coherent bandwidth
+ A statistical measure of the range of the frequencies over which the channel passes all spectr
al components with approximately equal gain and linear phase
+ Approximately, the coherent bandwidth and the excess delay spread are reciprocally
related
+ The relationship between the coherent bandwidth and the root-mean-squared (rms) delay spr
ead depends on the correlation of the channel’s frequency response (ex. while the
correlation of at least 0.5)
)(S )(function n correlatiofrequency -spaced fR
0f
mT0f
mTf /10
276.0
0 f
23Dept. of EE, NDHU
Frequency Response And Transmitted Signal
Wf 0
Wf 0
center) band signalat occursfunction
transfer-frequency Channel of (Null
0 Wf
24Dept. of EE, NDHU
Time-History Examples For Channel Conditions
Frequency-nonselective fading
Frequency-selective fading;
(Inter-chip interference induced)
Frequency-selective fading;
(Inter-chip interference induced)
26Dept. of EE, NDHU
Time Variance Of The Channel
• Time variance viewed in the time Domain
– Space-time correlation function
+ Correlation between the channel’s response to a sinusoidal sent at time t1 and the
channel’s response to a sinusoidal sent at time t2
– Coherent time
+ A measure of the expected time duration over which the channel’s response is ess
entially invariant
+ Provide knowledge about the fading rapidity of the channel
+ Using the dense-scatter channel model, the normalized correlation function with a
n unmodulated CW signal is described by
/2 and , traverseddistance theis
function Besselorder -zero theis )( where, )()( 00
ktV
JtkVJtR
27Dept. of EE, NDHU
Degradation Categories Viewed in Time Domain
• Fast fading
– The channel coherence time is less than the time duration of a transmission symbol
– Channel will change several times during the time span of a symbol
– Mobile moves fast
– Result in an irreducible error rate
– It is difficult to adequately design a match filter
• Slow fading
– Symbol period is less than the coherence time
– On can expect the channel state to virtually remain unchanged during the symbol time
– Mobile moves slowly
– The primary degradation in a slow-fading, as with flat-fading, is the loss in SNR
28Dept. of EE, NDHU
Time Variance Viewed In Doppler-shift Domain
• Signal spectrum at the antenna terminal
– The spectrum shape is the result of the dense-scatter channel model
– The maximum Doppler-shift is
– is the Fourier transform of
– Yields knowledge about the spectral spreading of a transmitted sinusoidal in the Doppler-shift domain
• Doppler spread and coherence time are reciprocally related
– example: the velocity=120km/hr, and the carrier frequency=900MHz, then the fading rate is approximately 100Hz
and the coherence time is approximately 5 ms
dd
d
cd
fvf
ffv
f
vS
re whe
)(1
1)(
2
V
fd
)(vS )( tR
fd 0T
dd ffT
423.0
16
920
33Dept. of EE, NDHU
Performance Over Fading Channel
• Demodulated signal over a discrete multi-path channel
• Assume the channel exhibits flat fading
phase its is )( and ,maganitude envelope theis )()( where
)]([)()( )()(2
ttgtR
ettRettzn
ntjn
tncfjn
variablerandom ddistributeRayleigh a is
)()()()( 0)]()([
TneTRTTz TTj
37Dept. of EE, NDHU
Mitigation To Combat Frequency Selective Fading
• Equalization can mitigate the effects of channel-induced ISI
• Can help modify the system performance from “awful” to
“bad”
• Gather the dispersed symbol energy back into its original
time interval
• Equalizer is an inverse filter of the channel
• Equalizer filter must also change or adapt to the time-
varying channel characteristics
38Dept. of EE, NDHU
Mitigation To Combat Frequency Selective Fading
• Decision feedback equalizer (DFE)
– Once an information symbol has been detected, the ISI that it induces on fut
ure symbols can be estimated and subtracted before the detection of subsequ
ent symbols
• Maximum-likelihood sequence estimation (MLSE) equalizer
– Test all the possible data sequence and choose the most probable of all the c
andidates
– Implemented by using Viterbi decoding algorithm
– MLSE is optimal in the sense that it minimizes the probability of a sequence
error
39Dept. of EE, NDHU
Mitigation To Combat Frequency Selective Fading
• Direct-sequence spread spectrum (DS/SS) techniques
– Mitigate frequency-selective ISI distortion
– Effectively eliminate the multi-path interference by its code correlation receiver
– RAKE receiver coherently combines the multi-path energy
• Frequency hopping spread spectrum (FH/SS) technique
– Frequency diversity
• OFDM
– Avoid the use of equalizer by lengthening the symbol duration
– DAB, DVBT systems
• Pilot signal
40Dept. of EE, NDHU
Mitigation To Combat Fast Fading
• Robust modulation techniques
– Non-coherent scheme or differential scheme
– Not require phase tracking
• Increase the symbol rate by adding the signal redundancy
• Error-correction coding
41Dept. of EE, NDHU
Mitigation To Combat Loss in SNR
• Diversity methods to move the performance “bad” to “good”
– “Diversity” is used to provide the receiver with uncorrelated renditions of the signal of
interest
• Time diversity
– Transmit the signal on L different time slots with time separation of at least T0
– Interleaving with coding technique
• Frequency diversity
– Transmit the signal on L different carriers with frequency separation of at least f0
– The signal bandwidth W is expanded and the frequency diversity order is achieved by
W/f0
– There is the potential for the frequency-selective fading unless the equalizer is used
42Dept. of EE, NDHU
Mitigation to Combat Loss in SNR
• Spread-spectrum systems
• Frequency hopping spread spectrum
• Spatial diversity
– Multiple receive antennas, separated by a distance of at least 10
wavelengths
– Coherently combine all the antenna outputs
• Polarization diversity
• Space-time coding technique
43Dept. of EE, NDHU
Diversity Techniques
• The goal is to utilize additional independent (or at least uncorrelated) signal paths to
improve the received SNR
• Error performance improvement
Mi
MM
ii
iii
ii
i
i
b
bBBB
p
p
ddpp
p
Mi
NExx
xp
NExxxPdxxpxPP
)]exp(1[1)(
)]exp(1[),(
)exp(1)exp(1
)()(
0 , )exp(1
)(
SNR sinstanteouan has ,,,2,1 branch,diversity each If
SNR averaged theis / ,0 ),exp(1
)(
ddistribute squared-chi is d,distributeRayleigh is
,/ and SNRat y probabiliterror -bit theis )( where,)()(
,,21
00
02
2
02
0
44Dept. of EE, NDHU
Diversity Combining Techniques
• Selection
– The sampling of M antenna signals and sending the largest one to the demodulator
– Relatively easy to implement
– Not optimal
• Feedback
– The M signals are scanned in a fixed sequence until one that exceeds a given threshold is found
– The error performance is somewhat inferior to the other methods
– Feedback diversity is quite simple to implement
• Maximal ratio combining
– The signal are weighted according to their individual SNR
– The individual signals must be co-phase before being summed
– Produce an average SNR by
MM
i
M
iiM
11
45Dept. of EE, NDHU
Modulation Types For Fading Channels
• Amplitude-based signal modulation (e.g. QAM) is vulnerabl
e to performance degradation in a fading channel
• Frequency or phase-based modulation is the preferred choice
in a fading channel
• The use of MFSK is more useful than binary signal
• In a slow Rayleigh fading channel, binary DPSK performs w
ell
46Dept. of EE, NDHU
Interleaver
• The primary benefit of an interleaver is to provide time diversity
• The larger the time span, the greater chance that of achieving effective diversity
• The interleaver time span is usually larger than the conerence time
• In a real-time communication system, too large interleaver time ( e.g.
) is not feasible since the inherent time delay would be excessive
• The interleaver provides no benefit against multi-path unless there is motion bet
ween the transmitter and the receiver
• As the motion increases in velocity, so does the benefit of a given interleaver to t
he error performance
10000/ 0 TTIL
ILT 0T
50Dept. of EE, NDHU
Key Parameters for Fading Channels
• Fast-fading distortion
–
– Mitigation
+ Choose a modulation/demodulation technique that is most robust under fast-fadin
g channel
+ For example, avoiding scheme that require PLLs
+ Sufficient redundancy that the symbol rate exceeds the fading rate and does not e
xceed the coherent bandwidth
+ Pilot signal
+ Error-correction coding
dfWf 0
51Dept. of EE, NDHU
Key Parameters for Fading Channels
• Frequency-selective fading distortion
–
– Mitigation
+ Adaptive equalization, spread-spectrum, OFDM
+ Viterbi algorithm
+ Once the distortion effects have been reduced, diversity technique, error-correctio
n coding should be introduced to approach AWGN performance
• Fast-fading and frequency-selective fading distortion
+
dfWf 0
dfWf 0