dept. of ee, ndhu 1 chapter three baseband demodulation/detection
TRANSCRIPT
![Page 1: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/1.jpg)
1Dept. of EE, NDHU
Chapter Three
Baseband Demodulation/Detection
![Page 2: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/2.jpg)
2Dept. of EE, NDHU
Error Probability Performance
• Error probability function
where is the time cross-correlation coefficient between two signals
• Antitpodal signal
– equals to -1, then
• Orthogonal signal
– equals to 0, then
))1(
()2
(00 N
EQ
N
EQP bd
B
)2
(0N
EQP b
B
)(0N
EQP b
B
![Page 3: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/3.jpg)
3Dept. of EE, NDHU
Error Probability of Binary Signaling
• Unipolar signaling
• Detection of unipolar baseband signaling0binary for 0 0)(
1binary for 0 )(
2
1
TttS
TtAtS
TAaa
Ta
TAdttnAAEtsTzETaT
2210
2
2
011
)2/1(2
thresholdoptimal the
,0)(
}))(({)](|)([)(
)(0N
EQP b
B
![Page 4: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/4.jpg)
4Dept. of EE, NDHU
Error Probability of Binary Signaling
• Bipolar signaling
• Detection of bipolar baseband signaling0binary for 0 )(
1binary for 0 )(
2
1
TtAtS
TtAtS
02
thresholdoptimal the 210
21
aa
aa
)2
(0N
EQP b
B
![Page 5: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/5.jpg)
5Dept. of EE, NDHU
Bit Error Performance of Unipolar and Bipolar Signaling
![Page 6: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/6.jpg)
6Dept. of EE, NDHU
Intersymbol Interference in the Detection Process
)()()()( fHfHfHfH rct
![Page 7: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/7.jpg)
7Dept. of EE, NDHU
Nyquist Channels for Zero ISI
![Page 8: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/8.jpg)
8Dept. of EE, NDHU
Pulse Shaping to Reduce ISI
• Goals and Trade-offs
– Compact signaling spectrum is to provide the higher allowable data rate
– Time pulse would become spread in time, which induces ISI
• The Raised-Cosine filter
where W is the absolute bandwidth and W0=1/2T represents the minimum Nyqu
ist bandwidth and the -6 dB bandwidth
Wffor
WfWWforWW
WWfWWffor
fH
0
2 )2
4(cos
2 1
)( 00
02
0
20
000
])(4[1
])(2cos[)2(sin2)(
tWW
tWWtWcWth
![Page 9: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/9.jpg)
9Dept. of EE, NDHU
Raised-Cosine Filter Characteristics
![Page 10: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/10.jpg)
10Dept. of EE, NDHU
Two Types of Error-Perfformance Degradation
![Page 11: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/11.jpg)
11Dept. of EE, NDHU
Example 3.3 Bandwidth Requirements
(a) Find the minimum required bandwidth for the baseband transmission of
a four-level PAM pulse sequence having a data rate of R=2400 bits/s if t
he system transfer characteristic consists of a raised-cosine spectrum wit
h 100% excess bandwidth (r=1)
(b) The same 4-ary PAM sequence is modulated onto a carrier wave, so that
the baseband spectrum is shifted and centered at frequency f0. Find the
minimum required DSB bandwidth for transmitting the modulated PAM
sequence
![Page 12: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/12.jpg)
12Dept. of EE, NDHU
Nyquist Pulse
![Page 13: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/13.jpg)
13Dept. of EE, NDHU
Square-root Nyquist Pulse and Raised-cosine Pulse
![Page 14: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/14.jpg)
14Dept. of EE, NDHU
Equalization
• Maximum-likelihood sequence estimation (MLSE)
– Make measurement of channel response and adjust the receiver to the transmission environment
– Enable the detector to make good estimates from the distorted pulse sequence (ex. Viterbi equaliza
tion)
• Equalization with filtering
– Use filter to compensate the distorted pulse
– Linear filter contains only feedforward elements (ex. transversal equalizers)
– Non-linear filter contains both feedforward and feedback elements (ex. decision feedback equalize
rs)
– Preset or adaptive filter design
– Filter’s resolution and update rate
![Page 15: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/15.jpg)
15Dept. of EE, NDHU
Receiving / Equalizing Filter
• The overall transfer function
• System design goal
then Ht(f) and Hr(f) each have frequency transfer functions that are the square r
oot of the raised cosine.
• Equalizing filter sometimes not only compensates the channel effect but compen
sates the ISI brought by the transmitter and receiver (ex. Gaussian filter)
)()()()()( fHfHfHfHfH erctRC
)()()(
)(
1
)(
1)( )(
fHfHfH
efHfH
fH
rtRC
fj
cce
c
![Page 16: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/16.jpg)
16Dept. of EE, NDHU
Eye Pattern
• Eye pattern is a filtering effect
![Page 17: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/17.jpg)
17Dept. of EE, NDHU
Distorted Pulse Response
![Page 18: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/18.jpg)
18Dept. of EE, NDHU
Transversal Equalizer
• A training sequence (like PN sequence) is needed to estimate the channel freque
ncy response
• A transversal filter is the most popular form of an easily adjustable equal
izing filter consisting of a delay line with T-second tapes
• The main contribution is from a central tap of a transversal filter
• In practice, a finite-length transversal filter is realized to approximate the ideal fi
lter (infinite-length transversal filter)
• Consider there are (2N+1) taps with weights c-N, c-N+1, …,cN, the equalizer output
samples {z(k)}
NNnNNkcnkxkzN
Nnn , 2,2 , )()(
![Page 19: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/19.jpg)
19Dept. of EE, NDHU
Transversal Filter
![Page 20: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/20.jpg)
20Dept. of EE, NDHU
Zero-Forcing Solution
• Relationship among {z(k)}, {x(k)}, and {cn} for the transversal filter
• Disposing the top N the bottom N rows of the matrix X into a square matrix with dimension
of 2N+1 and transform Z vector into a vector of 2N+1
• Rewrite the relationship
• Select the weights {cn} so that the equalizer output is
)(0000
)1()(000
)()1()2()1()(
0)()1(
0000)(
and
)2(
)0(
)2(
0
Nx
NxNx
NxNxNxNxNx
NxNx
Nx
X
c
c
c
c
Nz
z
Nz
z
N
N
zXccXz 1
Nkfor
kforkz
,,2,1 0
0 1)(
![Page 21: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/21.jpg)
21Dept. of EE, NDHU
Example: A Zero-Forcing Equalizer
• Consider a three-taps transversal filter, the given received data {x(k)} are 0.0, 0.2,
0.9, -0.3,0.1. Using the zero-forcing solution to find the weights {c-1, c0, c1}
– For the relationship
1
0
1
1
0
1
9.03.01.0
2.09.03.0
02.09.0
)0()1()2(
)1()0()1(
)2()1()0(
0
1
0
c
c
c
c
c
c
xxx
xxx
xxx
Xcz
3448.0
9631.0
2140.0
1
0
1
c
c
c
![Page 22: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/22.jpg)
22Dept. of EE, NDHU
Minimum MSE Solution
• Minimize the mean-square error (MSE) of all the ISI terms plus the
noise power at the output of the equalizer
• MSE is defined as the expected value of the squared difference between
the desired data symbol and the estimated data symbol
• MSE solution
• Minimum MSE solution is superior to zero-forcing solution
• Minimum MSE is more robust in the presence of noise and large ISI
xzxxxxxz
TT
RRccRR
XcXzX
1
![Page 23: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/23.jpg)
23Dept. of EE, NDHU
Decision Feedback Equalizer
• Limitation of a linear equalizer is that it performs poor on channel
having spectral nulls
• Decision feedback equalizer (DFE) is a non-linear equalizer and uses
previous detector decisions to eliminate the ISI on pulse
• Basic idea is that if the values of the symbols previously detected are
known, then the ISI contributed by these symbols can be cancelled out
• Forward filter and feedback filter are used in the DFE
• The advantage of DFE is that the feedback filter operates on noiseless
quantized levels, and thus its output is free of channel noise
![Page 24: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/24.jpg)
24Dept. of EE, NDHU
Decision Feedback Equalizer
![Page 25: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/25.jpg)
25Dept. of EE, NDHU
Preset and Adaptive Equalization
• The equalizer weights remain fixed during transmission of data, then the
equalization is called preset equalization
• Preset equalization sets the tap weights according to some average
knowledge of the channel (Ex. Voice-grade telephone)
• Adaptive equalization can be implemented to perform tap-weight
adjustments periodically or continually
• Periodic adjustments are accomplished by periodically transmitting a
preamble sequence
• Continually adjustment are performed by the decision directed procedure
![Page 26: Dept. of EE, NDHU 1 Chapter Three Baseband Demodulation/Detection](https://reader037.vdocuments.us/reader037/viewer/2022103005/56649de45503460f94ada950/html5/thumbnails/26.jpg)
26Dept. of EE, NDHU
Preset and Adaptive Equalization
• Disadvantages of preset equalization
– Require an initial training period
– A time-varying channel can degrade system performance
• If the probability of error exceeds one percent (rule of thumb), decision-directed adaptive
equalizer might not converge
• Common solution to the adaptive equalization
– Initialize the equalizer with a preamble to provide good channel-error performance
– Then switch to the decision-directed mode
– Blind equalization algorithm can be used to form initial channel estimates without a
preamble