march 1, 2005week 7 1 ee521 analog and digital communications james k. beard, ph. d....
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March 1, 2005 Week 7 1
EE521 Analog and Digital CommunicationsJames K. Beard, Ph. D.
Tuesday, March 1, 2005
http://astro.temple.edu/~jkbeard/
Week 7 2March 1, 2005
Attendance
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Week 7 3March 1, 2005
Essentials Text: Bernard Sklar, Digital Communications, Second
Edition SystemView Office
E&A 349 Tuesday afternoons 3:30 PM to 4:30 PM & before class MWF 10:30 AM to 11:30 AM
Spring Break Next Week (March 8) Next quiz March 22 Final Exam Scheduled
Tuesday, May 10, 6:00 PM to 8:00 PM Here in this classroom
Week 7 4March 1, 2005
Today’s Topics
Take-Home Quiz Due Today SystemView Trial Version Installation Term Projects Coherent and non-coherent detection Discussion (as time permits)
Week 7 5March 1, 2005
Quiz Overview
Practice Quiz was from text homeworkProblem 1.1 page 51Problem 2.2 page 101Problem 3.1 page 162
Quiz was similarFrom homework problemsModifications to problem statement and
parameters
Week 7 6March 1, 2005
Quiz timeline
Quiz last weekOpen bookCalculatorNo notes (will allow notes for next quiz & final)
Follow-up quiz announced at end of classTake-homeWill require SystemView to completeWill be deployed on Blackboard this week
Week 7 8March 1, 2005
Scoring TemplateGRADE 0 out of 100
Question Weight Part Weight SP Weight Q Grade WG Q Subt TotalsQuestion 1 0.2 0
Part I 0.25 0a) 0.25 NR 0b) 0.25 NR 0c) 0.25 NR 0d) 0.25 NR 0
0Part II 0.5 0
a) 0.25 NR 0b) 0.25 NR 0c) 0.25 NR 0d) 0.25 NR 0
0Part III 0.25 0
a) 0.25 NR 0b) 0.25 NR 0c) 0.25 NR 0d) 0.25 NR 0
0 0
Question 2 0.4 0Part I 0.25 NR 0Part II 0.25 NR 0Part III 0.5 0
a) 0.2 NR 0 0b) 0.2 NR 0c) 0.2 NR 0d) 0.2 NR 0e) 0.2 NR 0
0
Question 3 0.4 0Part I 0.25 NR 0Part II 0.25 NR 0Part III 0.25 NR 0Part IV 0.25 NR 0Part V 0.25 NR 0
0
TOTAL 0
Week 7 9March 1, 2005
Problem 1 Definitions
Energy vs. power signalsSection 1.2.4 pp 14-16Energy signal – nonzero but finite energyPower signal – nonzero but finite power
Definitions, equations (1.7) and (1.8)
2
xE x t dt
2
2
2
1lim
T
xT
T
P x t dtT
Week 7 10March 1, 2005
Problem 1 Energy Spectra
Section 1.4 pp 19, 20 Fourier transform of energy signal
Energy spectrum
exp , 2xF f x t j t dt f
2*x x x xf F f F f F f
Week 7 11March 1, 2005
Problem 1 Power Spectra
Section 1.4 pp. 19, 20 Autocorrelation of power signal
Power spectrum
2
2
1lim *
T
x TT
R x t x t dtT
exp 2x xf R t j f d
Week 7 12March 1, 2005
Identities
Average power and autocorrelation function
Power spectrum
2
2
10 lim *
T
x x TT
P R x t x t dtT
lim 0xf
f
Week 7 13March 1, 2005
Problem 1 Equations
Part (a)
Part (b)
Part (c)
Part (d)
0( ) cos 2 ,x t A f t t
0 00 0
0
exp 2 for ,2 2
T T kx t A j f t t T
f
exp , 0x t u t A a j b t c j d a
0exp 2 ,x t A j f t t
Week 7 14March 1, 2005
Problem 1 Powers & Energies
0
0
222
0
2
2 22
02
22
0
22 2
2
1lim cos 2
2
exp 2exp 2 2
2
1lim exp 2 exp 2
T
a TT
k
f
bk
f
c
T
d TT
AP A f t dt
T
k AE k A dt
f
A cE k A a t c dt
a
P A dt AT
Week 7 15March 1, 2005
Problem 1a Autocorrelation
22
0 0
2
2 2
0 0
2
2 2
0 0 0
1lim cos cos
1lim cos cos 2
2
cos exp exp2 4
T
a TT
T
TT
R A t t dtT
At dt
T
A Aj t j t
Week 7 16March 1, 2005
Problem 1b Fourier Transform
0
0
2
0
2
0
0
exp exp
exp sinc
k
f
bk
f
F f A j t dt
f fA k
f
Week 7 17March 1, 2005
Problem 1c Fourier Transform
0
0
22
2 2 2
exp exp
exp exp
exp
exp 2
2
c
c c
F f A a j b t c j d j t dt
A c j d a j b t dt
A c j d
a j b
A cP f F f
a b b
Week 7 18March 1, 2005
Problem 1d Autocorrelation
22
0 0
2
22
0
2
20
1lim exp 2 exp exp
1exp 2 lim exp
exp 2 exp 2
T
d TT
T
TT
R A j t j t dtT
A j dtT
A j f
Week 7 19March 1, 2005
Problem 1 Spectra
2
0 0
0
0
2 2 2
2 20 0
4
exp sinc
exp exp 2,
2 2
exp 2 ,
a
b
c c
d d
AG f f f f f
f fF f A k
f
c j d cF f G f
a j b j f a b b
R A j f G f A f f
Week 7 20March 1, 2005
Problem 2, The Block Diagram
Naturally sampled low pass analog
waveform
Local Oscillator
LPF
sx t
exp 2 sj k f t
1x t
Ox t
Week 7 21March 1, 2005
Spectrum of Naturally Sampled Signal
0 sf 2 sf 3 sf
sincsf f gate width
for natural sampling
Shows Part I
Week 7 22March 1, 2005
Problem 2 Part II – The Figure
BW
W
BW – signal bandwidthW – maximum spectral spread
Week 7 23March 1, 2005
Problem 2 Part 2
The signal x1(t) has a power spectrum Shifted left by k.fs The signal x2(t)
Has a power spectrum that is one of the replicas shown in the previous slide
Spectral distortion results from the slope of the natural sampling overall shape
Error and distortion are determined by’ Aliasing into the passband from the other spectral replicas Residual high frequency terms from the LPF stopband
Within these errors, x2(t) is a scaled replica of xs(t) Within this and the PAM quantization, xs(t) is a replica of
the input signal
Week 7 24March 1, 2005
Problem 2 Part III (1 of 2)
The minimum sample rate is 2.WLower sample rates will allow splatter to alias
into the signal bandSignal will still be reproduced, with larger
errors The LPF
Passband extends to BW/2Stopband begins at fs-W/2
Week 7 25March 1, 2005
Problem 2 Part III (2 of 2)
For a natural sampling duty cycle of d The minimum system sample rate for two samples is 2.fs/d Using a system sample rate that is a multiple of fs
Provides the same sampling for every gate Allows accuracy of natural sampling with lower system sample rates
The sample rate Determines the LPF transition band of fs-(W+BW)/2 Higher is better for filter cost/performance trade space
The spectrum aliasing number k Should be significantly smaller than 1/d Avoid selecting spectrum near the null in natural sampling
spectra
Week 7 26March 1, 2005
Question 3 – The Block Diagram
Bandpass signal
Local Oscillator
LPF
Bx t
0exp 2j f t
1x t
Ox t22
2
Week 7 27March 1, 2005
Problem 3 Part I
The output signal xO(t) is the bandpass signal xB(t) shifted down in frequency by f0
For all-analog signals, the LPF Will supplement the last I.F. filter Can provide better performance than a bandpass filter
For sampled signals, the LPF Provides anti-aliasing filtering – suppression of
spectral images May allow decimation to sample rate near BW
Week 7 28March 1, 2005
Question 3, Part II
Considerations are similar to those of Question 2 In Question 2, natural sampling generated an array of
bandpass signals The complex rest of the circuit was a quadrature
demodulator that selected one of the bandpass signals
The duty cycle is not a part of Question 3 Minimum sample rate is 2.W LPF
Bandpass to BW/2 Stopband begins at fs – W/2
Week 7 29March 1, 2005
Problem 3 Part III
Sample rates fs that alias f0 to ±fs/4
Nyquist criteria, including spectral spread
Lowest sample rate is for a k of
04
2 1s
ff
k
2sf W
0 01 1ceiling floor
2 2
f fk
W W
Week 7 30March 1, 2005
Problem III Part IV
Look at numerical values of LPF specsBandpass to BW/2Stopband begins at fs – W/2
Transition band is fs-(BW+W)/2
Shape factor is (2.fs-W)/BW
LPF trade space is better for higher fs
Week 7 31March 1, 2005
Problem 3 Part V
The sample rate at I.F. is 2.W For complex signals, the Nyquist rate is W Allowing for a shape factor for the LPF increases the
sample rate above 2.W Decimation
Minimum is a factor of 2 to produce a sample rate of W complex Aliasing considerations can drive a complex data rate higher
than W Higher sample rates and simpler LPF will allow decimation of 3
or 4 to produce a complex sample rate near W Dual-stage digital LPF can provide a very high performance – a
shape factor only slightly larger than 1
Week 7 32March 1, 2005
SystemView
I have a mini-CD-ROM with the trial version When you install
During business hours When asked for “Regular” or “Professional” select
“Professional” Call Maureen Chisholm at 678-218-4603 to get your
activation code Other resources
The student version will probably carry you another week
The full version is available in E&A 604E – watch for two icons on the desktop and select the Professional version
Week 7 33March 1, 2005
Term Projects
Interpret, plan, model Use SystemView Assignments deployed by email last week Your preferences and comments are
encouragedOffice hoursEmail
Week 7 34March 1, 2005
SystemView Assignment
Objectives Generate test signal over speech band Determine fundamental simulation parameters
SystemView sample rate Run end time Comm system sample rate
Mimics Problem 3 Part V Successful completion is launch of your term
project
Week 7 35March 1, 2005
Term Project
Information
source
FormatSource encode
EncryptChannel encode
Multi-plex
Pulse modulate
Bandpass modulate
Freq-uency spread
Multiple access
X M I T
FormatSource decode
DecryptChannel decode
Demul-tiplex
DetectDemod-ulate & Sample
Freq-uency
despread
Multiple access
R C V
Channel
Information
sink
Bit stream
Synch-ronization
Digital baseband waveform
Digital bandpass waveformDigital
outputˆ im
Digital input
im
ˆiu z T r t
iu ig t is t
Optional
Essential
Legend:
Message symbols
Channel symbols
Channel symbols
From other
sources
To other destinations
Message symbols
Channel impulse
response
ch t
Week 7 37March 1, 2005
Spectrum of Input SignalSystemView
200
200
1.2e+3
1.2e+3
2.2e+3
2.2e+3
3.2e+3
3.2e+3-10
-30
-50
-70
-90
Powe
r Den
sity
Frequency in Hz (dF = 439.5e-3 Hz)
Spectral Density of Input (dBm/Hz 50 ohms)
Week 7 38March 1, 2005
Next Steps
Sample at comm system sample rate Adjust SystemView sample rate
Make it the comm system sample rate times a power of 2
This allows a power of 2 for both SystemView and comm system sampled data for the same run times
Quantize to 16 bits Convert to bitstream Map characters to 2-bit symbols for QPSK or
MSK
Week 7 39March 1, 2005
Sklar Chapter 4
Information
source
FormatSource encode
EncryptChannel encode
Multi-plex
Pulse modulate
Bandpass modulate
Fre-quency spread
Multiple access
X M I T
FormatSource decode
DecryptChannel decode
Demul-tiplex
DetectDemod-ulate & Sample
Freq-uency
despread
Multiple access
R C V
Channel
Information
sink
Bit stream
Synch-ronization
Digital baseband waveform
Digital bandpass waveformDigital
outputˆ im
Digital input
im
ˆiu z T r t
iu ig t is t
Optional
Essential
Legend:
Message symbols
Channel symbols
Channel symbols
From other
sources
To other destinations
Message symbols
Channel impulse
response
ch t
Week 7 41March 1, 2005
Correlator Receiver
ir t s t n t N
0
T
ir t f t dt DECISIONLOGIC
is t
The correlation functions fi(t) may be Signal replicas si(t)
Orthogonal basis functions
With the right decision logic – a maximum likelihood detector
Week 7 42March 1, 2005
Coherent Detection of BPSK
The BPSK basis functions are
Correlate with an orthogonal basis function
1 0
2 0
2cos , 0
2cos , 0
Es t t t T
T
Es t t t T
T
1 0
2cos , 0t t t T
T
Week 7 43March 1, 2005
BPSK Demodulated Output
Output is plus or minus the pulse amplitude, depending on the phase
Coherence in this case lets us set the phase Φ to zero
Not knowing Φ Causes a fundamental ambiguityStill allows us to detect bit changes
Week 7 44March 1, 2005
Coherent MPSK Detection
M-ary PSK signals are
The basis functions are
0
2 2cos , 0 , 1, ,i
E is t t t T i M
T N
1 0
2 0
2cos , 0
2sin , 0
t t t TT
t t t TT
Week 7 45March 1, 2005
MPSK Demodulated Output
Output is a complex numberMagnitude is the pulse amplitudePhase is the modulation phase
Not knowing the phaseCauses a fundamental ambiguityStill allows us to detect phase changes
Week 7 46March 1, 2005
Coherent Detection of FSK
FSK waveforms are
We take the phase as zero, as before Basis functions are
2cos , 0 , 1, ,i i
Es t t t T i M
T
2cos , 0j jt t t T
T
Week 7 47March 1, 2005
Non-Coherent PSK Detection
Differential PSKUnknown phase of signal is a random variablePhases of adjacent received pulses are
compared Performance
Coherent – measure one phaseNon-coherent – measure two phases and
subtract Non-coherent is inherently noisier by 3 dB
Week 7 48March 1, 2005
Non-Coherent FSK
Use a filter bank Use I-Q demodulator Threshold the squared magnitudes
Week 7 49March 1, 2005
Example 4.1 pp. 187-188
Correlation is four-sample summation Waveform set is
Correlation is by summation over k
1
2
, 0
, 0
, 0,1,2,34k
s t A t t T
s t A t t T
Tt k k
Week 7 50March 1, 2005
Example 4.1 (Concluded)
Correlator summation is
What is z2?
2 232
10
14
4 4k
A Az k
Week 7 51March 1, 2005
Example 4.2 pp. 193-194
Phase as a function of propagation delay Phase changes by 360 degrees for each
wavelength of change of path length Wavelength for 1 GHz is about 1 foot Conclusion
Path length uncertainty of 3 inches will cause 90 degrees of phase uncertainty
Coherent detection depends on real-time monitoring of received phase
Phase-locked loops (PLLs) are needed to support coherent detection