EE104: Lecture 25 Outline
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Announcements
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Review of Last Lecture
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Probability of Bit Error in ASK/PSK
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Course Summary
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Hot Topics in Communications
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Next-Generation Systems
Announcements
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HW 7 due Monday at 9 pm (no late HWs)
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Final Exam is Th., 3/20, 8:30am in Gates B03 (basement)
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Solutions will be posted then.
Exam is open book/notes, covers through today’s lecture.
Emphasis is on material after midterm, similar to practice finals
SCPD student must make remote arrangements w/me by this Friday
Practice finals posted on class website
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10 bonus points if turned in by 3/20 at 8:30am (Joice has solutions)
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Final Review: Monday 7-8pm (room 380-380Y)
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Extra Office Hours
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My extra hours: M 4:30-6:30, TW 12-2, and by appointment
Jaron: W 4-6 (Bytes), Nikola: after review and T 5-7pm (110 Packard)
tbp will be done at end of class (10 bonus points)
Review of Last Lecture
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Passband Digital Modulation



ASK/PSK special cases of DSBSC
FSK special case of FM
ASK/PSK Demodulator:
Decision Device
nTb
Tb
s(t)

 ()dt
0
cos(2pfct)



r(nTb)
r1
r0+N
“1” or “0”
DN
r0
Decision devices finds if r(iTb) is closer to r0 or r1
Noise immunity DN is half the distance between r0 and r1
Bit errors occur when noise exceeds this immunity
Noise in ASK/PSK
N(t)
nTb
r1
Tb
s(t)
+
Channel

cos(2pfct)
r(nTb)+N(nTb)

r0
0
“1” or “0”
DN

Probability of bit error: Pb=p(|N(nTb)|>DN=.5|r1-r0|)

N(nTb) is a Gaussian RV: N~N(m=0,s2=.25NoTb)
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For x~N(0,1), Define Q(z)=p(x>z)
 ASK: Pb  p( N  .25 AcTb )  Q


 PSK: Pb  p( N  .5 AcTb )  Q

 
  Q



.25 Ac2Tb
N0
Ac2Tb
N0
Q


2 Eb
N0
Eb
N0
Eb is average
energy per bit
Course Summary

Communication System Block Diagram

Fourier Series and Transforms

Sampling

Power Spectral Density and Autocorrelation

Random Signals and White Noise
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AM Modulation
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FM Modulation
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Digital Modulation
Communication System
Block Diagram
Text
Images
Video
b1b2 ...
m (t )
Source
Encoder
Transmitter
bˆ1bˆ2 ...
mˆ ( t )
sˆ(t )
s(t )
Channel
Receiver
Source
Decoder
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Source encoder converts message into a message signal or bits.
Source decoder converts back to original format.
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Transmitter converts message signal or bits into a transmitted
signal at some carrier frequency.
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Modulation, may also include SS, OFDM, precoding.
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Channel introduces distortion, noise, and interference.

Receiver converts back to message signal or bits.

Demodulation (for SS and OFDM too), may also include equalization.
Main Focus of This Class
b1b2 ...
m (t )
n(t)
Analog or Digital
Modulator
Transmitter
s(t )
h(t)
Channel
+
sˆ(t )  n(t )
Analog or Digital
Demodulator
bˆ1bˆ2 ...
mˆ ( t )
Receiver

Modulation encodes message or bits into the
amplitude, phase, or frequency of carrier signal.

Channel filters signal and introduces noise

Demodulator recovers information from carrier
Need tools for manipulating and filtering signals and noise
Fourier Series

Exponentials are basis functions for periodic signals

Can represent periodic signal in terms of FS coefficients

Complex coefficients are frequency components of signal
x p (t ) 

c e
n  
1
 j 2pnf 0 t
cn 
x
(
t
)
e
dt
p

T0 T0
j 2pnf 0 t
n
xp(t)
c-2
c-1
c0
c1
c2
c-3
-.5T
-T0
.5T
0
T0
2T0
t
c3
-1/T0
c-4
f
0 1/T0 2/T0
c4
Fourier Transform

Represents spectral components of a signal

Signal uniquely represented in time or frequency
domain

These coefficients
are frequency components
of signal


j 2pft
 j 2pnft
x
(
t
)

X
(
f
)
e
df
X ( f )   x (t )e
dt



A
-.5T
.5T
t
f
Timelimited signals have infinite frequency content
Bandlimited signals are infinite duration
Key Properties of FTs

Frequency shifting (modulation)

Multiplying signal by cosine shifts it by fc in frequency.

Multiplication in time Convolution in Frequency

Convolution in time Multiplication in Frequency
Filtering

Convolution defines output of LTI filters

Convolution (time) Multiplication (freq.)

Easier to analyze filters in frequency domain
 Filters characterized by time or freq. response
 Exponentials are eigenfunctions of LTI filters
LTI Filter
x(t)
ej2pfct
X(f)
h(t)
y(t)=h(t)*x(t)
H(f)
Y(f)=H(f)X(f)
H(fc)ej2pfct
Sampling

Sampling (Time):
nd(t-nTs)
x(t)
0

=
0
xs(t)
0
Sampling (Frequency)
X(f)
0
*
nd(t-n/Ts)
0
=
Xs(f)
0
Nyquist Sampling Theorem

A bandlimited signal [-B,B] is completely
described by samples every .5/B secs.


Nyquist rate is 2B samples/sec
Recreate signal from its samples by using a low
pass filter in the frequency domain


Sinc interpolation in time domain
Undersampling creates aliasing
X(f)
X(f)
-B
B
-B
Xs(f)
B
Power Spectral Density

Distribution of signal power over frequency
Sx(f)
P  lim T 
1
2
|
x
(
t
)
|
dt   S x ( f )df

2T
f
PSD/autocorrelation FT pairs: Rx(t Sx(f)
 Useful for filter and modulation analysis

Sx(f)
H(f)
|H(f)|2Sx(f)
cos(2pfct)
Sx(f)
.25[Sx(f-fc)+ Sx(f+fc)]
X
Assumes Sx(f) bandlimited [-B,B], B << fc
Random Signals

Not deterministic (no Fourier transform)

Signal contained in some set of possible realizations
Experiment

Characterize by average PSD Sn(f)

Autocorrelation Rn(t) Sn(f) is the correlation of
the random signal after time t.

Measures how fast random signal changes
Filtering and Modulation

Same PSD effect as for deterministic signals
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Filtering
Sn(f)

H(f)
|H(f)|2Sn(f)
Modulation (no bandwidth constraint on Sn)
cos(2pfct)
Sn(f)
.25[Sn(f-fc)+ Sn(f+fc)]
X
White Noise
Rn(t)
Sn(f)
.5N0d(t)
.5N0
f
t

Signal changes very fast
 Uncorrelated after infinitesimally small delay

Good approximation in practice

Filtering white noise: introduces correlation
Sw(f)=.5N0
H(f)
.5N0|H(f)|2
Amplitude Modulation
ka
1
X
+
cos(2pfct)
s(t)=Ac[1+kam(t)]cos2pfct
m(t)

X
Constant added to signal m(t)

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Simplifies demodulation if 1>|kam(t)|
Constant is wasteful of power

Modulated signal has twice the BW of m(t)

Simple modulators use nonlinear devices
Detection of AM Waves

Entails tradeoff between performance and
complexity (cost)

Square law detector squares signal and then passes
it through a LPF

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Residual distortion proportional to m2(t)
Noncoherent (carrier phase not needed in receiver)
Envelope detector detects envelope of s(t)
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Simple circuit (resistors, capacitor, diode)
Only works when |kam(t)|<1 (poor SNR), no distortion.
Noncoherent
Double Sideband Suppressed
Carrier (DSBSC)

Modulated signal is s(t)=Accos(2pfct)m(t)

Generated by a product or ring modulator

m(t)
Requires coherent detection (f2f1)
 Costas Loop
Product
Modulator
Accos(2pfct+f1
s(t)
Channel
Product
Modulator
Accos(2pfct+f2
m´(t)
LPF
Noise in DSBSC Receivers
n(t)
s(t)=Accos(2pfct+fm(t)
+
LPF
Product
Modulator
1
m´(t)+ n´(t)
Accos(2pfct+f

Power in m´(t) is .25Ac2P

Sn´(f)=.25[Sn(f-fc)+Sn(f+fc)]|H(f)|2

For AWGN, Sn´(f)=.25[.5N0+.5N0], |f|<B.

SNR=Ac2P/(2N0B)
Single Sideband

Transmits upper or lower sideband of DSBSC
USB
LSB

Reduces bandwidth by factor of 2

Uses same demodulator as DSBSC
 Coherent
detection required.
FM Modulation

Information signal encoded in carrier
frequency (or phase)

Modulated signal is s(t)=Accos(q(t))
 q(t)=f(m(t))

Standard FM: q(t)=2pfct+2pkf m(t)dt
 Instantaneous
frequency: fi=fc+kfm(t)
 Signal robust to amplitude variations
 Robust to signal reflections and refractions
FM Bandwidth and Carson’s Rule

Frequency Deviation: Df=kf max|m(t)|
 Maximum

deviation of fi from fc: fi=fc+kfm(t)
Carson’s Rule:
B2Df+2Bm
B
depends on maximum deviation from fc
AND how fast fi changes

Narrowband FM: Df<<BmB2Bm

Wideband FM: Df>>Bm  B2Df
Generating FM Signals

NBFM
 Circuit

based on product modulator
WBFM
 Direct
Method: Modulate a VCO with m(t)
 Indirect Method: Use a NBFM modulator,
followed by a nonlinear device and BPF
FM Generation and Detection

Differentiator/Discriminator and Env. Detector
t
s(t )  Ac [2pf c  2pk f m(t )] sin[ 2pf c t  2pk f  m(t )dt ]
0

Zero Crossing Detector


Uses rate of zero crossings to estimate fi
Phase Lock Loop (PLL)

Uses VCO and feedback to extract m(t)
ASK, PSK, and FSK

Amplitude Shift Keying (ASK)
1
0
1
1
m(t)
 Ac cos(2pf ct ) m(nTb )  1
s(t )  m(t ) Ac cos(2pf ct )  
0
m(nTb )  0

AM Modulation

Phase Shift Keying (PSK)
1
0
1
1
m(t)
m(nTb )  1
 A cos( 2pf ct )
s(t )  Ac m(t ) cos( 2pf ct )   c
 Ac cos( 2pf ct  p ) m(nTb )  1

Frequency Shift Keying
AM Modulation
1
0
1
1
 Ac cos( 2pf1t ) m(nTb )  1
s(t )  
 Ac cos( 2pf 2t ) m(nTb )  1
FM Modulation
ASK/PSK Demodulation
N(t)
nTb
r1
Tb
s(t)
+
Channel

cos(2pfct)
r(nTb)+N(nTb)

DN
r0
0
“1” or “0”

Probability of bit error: Pb=p(|N(nTb)|>DN=.5|r1-r0|)

N(nTb) is a Gaussian RV: N~N(m=0,s2=.25NoTb)

For x~N(0,1), Define Q(z)=p(x>z)=.5erfc(z/2 )
 ASK: Pb  p( N  .25 AcTb )  Q


 PSK: Pb  p( N  .5 AcTb )  Q

 
  Q



.25 Ac2Tb
N0
Ac2Tb
N0
Q


2 Eb
N0
Eb
N0
Eb is average
energy per bit
FSK Demodulation (HW 7)
Tb

s(t)+n(t)
cos(2pf1t)

nTb
cos(2pf2t)

r1(nTb)+N1
“1” or “0”
0
Tb

nTb
Comparator
r2(nTb)+N2
0

Comparator outputs “1” if r1>r2, “0” if r2>r1

Pb=p(|N1-N2|>.5AcTb)=Q(Eb/N0) (same as PSK)

Minimum frequency separation required to differentiate
 |f1-f2|.5/Tb (MSK uses this minimum separation)
Megathemes in EE104

Fourier analysis simplifies the study of communication
systems

Modulation encodes information in phase, frequency, or
amplitude of carrier

Noise and distortion introduced by the channel makes it
difficult to recover signal

The communication system designer must design clever
techniques to compensate for channel impairments or
make signal robust to these impairments.

Ultimate goal is to get high data rates with good quality
and low cost.
Hot Topics in Communications
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All-optical networks
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Advanced Radios
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Components (routers, switches) hard to build
Need very good lasers
Communication schemes very basic
Evolving to more sophisticated techniques
Adaptive techniques for multimedia
Direct conversion radios
Software radios
Low Power (last years on a battery)
Ultra wideband
Wireless Communications
Future Wireless Systems
Ubiquitous Communication Among People and Devices
Nth Generation Cellular
Wireless Internet (802.11)
Wireless Video/Music
Wireless Ad Hoc Networks
Sensor Networks
Smart Homes/Appliances
Automated Vehicle Networks
All this and more…
The End
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Good luck on the final
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Have a great spring break