Final Exam Review Professor Deepa Kundur University of Toronto Professor Deepa Kundur (University of Toronto) Final Exam Review 1 / 67 Final Exam Review Reference: Sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 4.1, 4.2, 4.3, 4.4, 4.6, 4.7, 4.8 5.1, 5.2, 5.3, 5.4, 5.5 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8 10.1, 10.2 of S. Haykin and M. Moher, Introduction to Analog & Digital Communications, 2nd ed., John Wiley & Sons, Inc., 2007. ISBN-13 978-0-471-43222-7. Professor Deepa Kundur (University of Toronto) Final Exam Review 2 / 67 Chapter 3: Amplitude Modulation Professor Deepa Kundur (University of Toronto) Final Exam Review 3 / 67 Amplitude Modulation I In modulation need two things: 1. a modulated signal: carrier signal: c (t ) 2. a modulating signal: message signal: m(t ) I carrier: I c (t )= A c cos(2πf c t ); phase φ c = 0 is assumed. I message: I m(t ) (information-bearing signal) I assume bandwidth/max freq of m(t ) is W Professor Deepa Kundur (University of Toronto) Final Exam Review 4 / 67
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Final Exam Review
Professor Deepa Kundur
University of Toronto
Professor Deepa Kundur (University of Toronto) Final Exam Review 1 / 67
Professor Deepa Kundur (University of Toronto) Final Exam Review 38 / 67
Encoder: Example
Professor Deepa Kundur (University of Toronto) Final Exam Review 39 / 67
PCM: Transmission Path
PCM Data Sequence
ChannelOutput
Transmitter ReceiverTranmissionPathSO
URC
E
DES
TIN
ATIO
N
ChannelOutput
TranmissionLine
RegenerativeRepeater
TranmissionLine
RegenerativeRepeater
TranmissionLine
...PCM Data Shaped for Transmission
Decision-making
DeviceAmpli�er-Equalizer
TimingCircuit
DistortedPCMWave
RegeneratedPCMWave
Professor Deepa Kundur (University of Toronto) Final Exam Review 40 / 67
PCM: Regenerative RepeaterDecision-making
DeviceAmpli�er-Equalizer
TimingCircuit
DistortedPCMWave
RegeneratedPCMWave
t
t
t
t
t
THRESHOLD
BIT ERROR
“0” “0” “0”“1” “1” “1”
Original PCM Wave
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PCM: Receiver
Two Stages:
1. Decoding and Expanding:
1.1 regenerate the pulse one last time1.2 group into code words1.3 interpret as quantization level1.4 pass through expander (opposite of compressor)
2. Reconstruction:
2.1 pass expander output through low-pass reconstruction filter(cutoff is equal to message bandwidth) to estimate originalmessage m(t)
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Chapter 6: Baseband Data Transmission
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Baseband Transmission of Digital Data
ThresholdBinary input sequence
LineEncoder
0011100010Source
Threshold
Decision-Making Device
Sampleat time
DestinationTransmit-Filter G(f )
ChannelH(f )
Receive-�lter Q(f )
Outputbinary data
Threshold
Decision-Making Device
Sampleat time
Pulse Spectrum P(f )
bk = {0, 1} and ak =
{+1 if bk is symbol 1−1 if bk is symbol 0
s(t) =∞∑
k=−∞
akg(t − kTb)
x(t) = s(t) ? h(t)
y(t) = x(t) ? q(t) = s(t) ? h(t) ? q(t)
=∞∑
k=−∞
akg(t − kTb) ? h(t) ? q(t) =∞∑
k=−∞
akp(t − kTb)
Professor Deepa Kundur (University of Toronto) Final Exam Review 44 / 67
Baseband Transmission of Digital Data
ThresholdBinary input sequence
LineEncoder
0011100010Source
Threshold
Decision-Making Device
Sampleat time
DestinationTransmit-Filter G(f )
ChannelH(f )
Receive-�lter Q(f )
Outputbinary data
Threshold
Decision-Making Device
Sampleat time
Pulse Spectrum P(f )
∴ y(t) =∞∑
k=−∞
akp(t − kTb)
where p(t) = g(t) ∗ h(t) ∗ q(t)
P(f ) = G (f ) · H(f ) · Q(f ).
Professor Deepa Kundur (University of Toronto) Final Exam Review 45 / 67
Baseband Transmission of Digital Data
Threshold
Decision-Making Device
Sampleat time
Transmit-Filter G(f )
ChannelH(f )
Receive-�lter Q(f )
ThresholdBinary input sequence
LineEncoder
0011100010Source Destination
Outputbinary data
Threshold
Decision-Making Device
Sampleat time
Pulse Spectrum P(f )
P(f ) = G(f )H(f )Q(f )
Professor Deepa Kundur (University of Toronto) Final Exam Review 46 / 67
Baseband Transmission of Digital Data
Threshold
Decision-Making Device
Sampleat time
Pulse Spectrum P(f )
P(f ) = G(f )H(f )Q(f )
yi = y(iTb) and pi = p(iTb)
yi =√Eai︸ ︷︷ ︸
signal to detect
+∞∑
k=−∞,k 6=i
akpi−k︸ ︷︷ ︸intersymbol interference
for i ∈ Z
To avoid intersymbol interference (ISI), we need pi = 0 for i 6= 0.
Professor Deepa Kundur (University of Toronto) Final Exam Review 47 / 67
The Nyquist Channel
I Minimum bandwidth channel
I Optimum pulse shape:
popt(t) =√E sinc(2B0t)
Popt(f ) =
{ √E
2B0−B0 < f < B0
0 otherwise, B0 =
1
2Tb
Note: No ISI.
pi = p(iTb) =√E sinc(2B0iTb)
√E sinc
(2 · 1
2TbiTb
)=√E sinc(i) = 0.
Disadvantages: (1) physically unrealizable (sharp transition in freq domain); (2)
slow rate of decay leaving no margin of error for sampling times.
Professor Deepa Kundur (University of Toronto) Final Exam Review 48 / 67
Raised-Cosine Pulse Spectrum
I has a more graceful transition in the frequency domain
I more practical pulse shape:
p(t) =√E sinc(2B0t)
(cos(2παB0t)
1− 16α2B02t2
)
P(f ) =
√E
2B00 ≤ |f | < f1
√E
4B0
{1 + cos
[π(|f |−f1)(B0−f1)
]}f1 < f < 2B0 − f1
0 2B0 − f1 ≤ |f |
α = 1− f1B0
BT = B0(1 + α) where B0 =1
2Tband fv = αB0
Note: No ISI. ∵ pi = 0.Professor Deepa Kundur (University of Toronto) Final Exam Review 49 / 67
Raised-Cosine Pulse Spectrum
f (kHz)
A= sqrt(E)/2B
A/2
0
0B0-B 02B0-2B0B /2 0B /2 0B /2 0B /2
Raised-Cosine
NyquistPulse
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The Eye Pattern
Slope dictates sensitivityto timing error
Best samplingtime
Distortion at sampling time
NO
ISE
MA
RGIN
Time interval over which waveis best sampled.
ZERO-CROSSINGDISTORTION
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Chapter 7: Digital Band-Pass ModulationTechniques
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Binary Modulation Schemes
c(t) = Ac cos(2πfct + φc)
I Binary amplitude-shift keying (BASK): carrier amplitude is keyed between
two possible values (typically√Eb and 0 to represent 1 and 0, respectively);
carrier phase and frequency are held constant.
I Binary phase-shift keying (BPSK):carrier phase is keyed between twopossible values (typically 0 and π to represent 1 and 0, respectively); carrieramplitude and frequency are held constant.
I Binary frequency-shift keying (BFSK): carrier frequency is keyed betweentwo possible values (typically f1 and f2 to represent 1 and 0, respectively);carrier amplitude and phase are held constant.
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Preliminaries
c(t) = Ac cos(2πfct + φc)
I Tb represents the bit duration
I Eb represents the energy of the transmitted signal per bit
I In digital communications the carrier amplitude is normalized to have unitenergy in one bit duration; thus we set
Ac =
√2
Tb
I The carrier frequency fc = kTb
for k ∈ Z to ensure an integer number ofcarrier cycles in a bit duration.
Professor Deepa Kundur (University of Toronto) Final Exam Review 54 / 67
Carrier for Digital Communications
Therefore
c(t) =
√2
Tbcos(2πfct + φc).
For k = 4
0t
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Binary Amplitude-Shift Keying (BASK)
Let φc = 0 and the carrier frequency is fc .
b(t) =
{ √Eb for binary symbol 1
0 for binary symbol 0
c(t) =
√2
Tbcos(2πfct + φc) =
√2
Tbcos(2πfct)
s(t) = b(t) · c(t)
=
{ √2Eb
Tbcos(2πfct) for symbol 1
0 for symbol 0
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BASK Transmitter and Receiver
Transmitter
BASKTransmittedSignal
LevelEncoding
ProductModulator
carrier
EnvelopeDetector
Low-passFilterBASK
wave
Output+
-
Threshold
Decision-Making Device
Binary inputsequence
t0011100010
Sampleat time
Receiver
EnvelopeDetector
Low-passFilterBASK
wave
Output+
-
Threshold
Decision-Making Device
BASKTransmittedSignal
LevelEncoding
ProductModulator
carrier
Binary inputsequence
t0011100010
Sampleat time
Professor Deepa Kundur (University of Toronto) Final Exam Review 57 / 67
Binary Phase-Shift Keying (BPSK)
si(t) =
√
2Eb
Tbcos(2πfct) for symbol 1 (i = 1)√
2Eb
Tbcos(2πfct + π) for symbol 0 (i = 2)
=
√
2Eb
Tbcos(2πfct) for symbol 1 (i = 1)
−√
2Eb
Tbcos(2πfct) for symbol 0 (i = 2)
Professor Deepa Kundur (University of Toronto) Final Exam Review 58 / 67
BPSK Transmitter and Receiver
Transmitter
Low-passFilter
Threshold
Decision-Making Device
Sampleat time
BPSKTransmittedSignal
Binary inputsequence
LevelEncoding
ProductModulator
carrier
ProductModulator
local carrierfrom PLL
(Non-return-to zero)
t0011100010
Receiver
Low-passFilter
Threshold
Decision-Making Device
Sampleat time
BPSKTransmittedSignal
Binary inputsequence
LevelEncoding
ProductModulator
carrier
ProductModulator
local carrierfrom PLL
(Non-return-to zero)
t0011100010
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