1. EE521 Analog and Digital Communications
James K. Beard, Ph. D.
Tuesday, March 1, 2005
March 1, 2005
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2. Attendance
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3. 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
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4. Today’s Topics Take-Home Quiz Due Today
SystemView Trial Version Installation
Term Projects
Coherent and non-coherent detection
Discussion (as time permits)
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5. Quiz Overview Practice Quiz was from text homework Quiz was similar
Problem 1.1 page 51
Problem 2.2 page 101
Problem 3.1 page 162
Quiz was similar
From homework problems
Modifications to problem statement and parameters
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6. Quiz timeline Quiz last week Follow-up quiz announced at end of class
Open book
Calculator
No notes (will allow notes for next quiz & final)
Follow-up quiz announced at end of class
Take-home
Will require SystemView to complete
Will be deployed on Blackboard this week
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7. The Curve
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8. Scoring Template
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9. Problem 1 Definitions Energy vs. power signals
Section pp 14-16
Energy signal – nonzero but finite energy
Power signal – nonzero but finite power
Definitions, equations (1.7) and (1.8)
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10. Problem 1 Energy Spectra
Section 1.4 pp 19, 20
Fourier transform of energy signal
Energy spectrum
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11. Problem 1 Power Spectra Section 1.4 pp. 19, 20
Autocorrelation of power signal
Power spectrum
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12. Identities Average power and autocorrelation function Power spectrum
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13. Problem 1 Equations Part (a) Part (b) Part (c) Part (d) March 1, 2005
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14. Problem 1 Powers & Energies
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15. Problem 1a Autocorrelation
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16. Problem 1b Fourier Transform
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17. Problem 1c Fourier Transform
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18. Problem 1d Autocorrelation
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19. Problem 1 Spectra
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20. Problem 2, The Block Diagram
Naturally sampled low pass analog waveform
Local Oscillator
LPF
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21. Spectrum of Naturally Sampled Signal
Shows Part I
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22. Problem 2 Part II – The FigureBW
BW – signal bandwidth
W – maximum spectral spread W
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23. 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
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24. Problem 2 Part III (1 of 2) The minimum sample rate is 2.W The LPF
Lower sample rates will allow splatter to alias into the signal band
Signal will still be reproduced, with larger errors
The LPF
Passband extends to BW/2
Stopband begins at fs-W/2
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25. 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
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26. Question 3 – The Block Diagram
Bandpass signal
Local Oscillator
LPF 2
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27. 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
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28. 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
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29. 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
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30. Problem III Part IV Look at numerical values of LPF specs
Bandpass to BW/2
Stopband 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
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31. 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
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32. 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 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
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33. Term Projects Interpret, plan, model Use SystemView
Assignments deployed by last week
Your preferences and comments are encouraged
Office hours
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34. 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
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35. Term Project Legend: From other sources Essential Information source
Message symbols
Optional
Channel symbols
X M I T
Format
Source encode
Encrypt
Channel encode
Multi-plex
Pulse modulate
Bandpass modulate
Freq-uency spread
Multiple access
Digital input
Channel impulse response
Bit stream
Synch-ronization
Digital baseband waveform
Digital bandpass waveform
Channel
Digital output
R C V
Format
Source decode
Decrypt
Channel decode
Demul-tiplex
Detect
Demod-ulate & Sample
Freq-uency despread
Multiple access
To other destinations
Channel symbols
Information
sink
Message symbols
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36. System
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37. Spectrum of Input Signal
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38. 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
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39. Sklar Chapter 4 Legend: From other sources Essential Information
Message symbols
Optional
Channel symbols
X M I T
Format
Source encode
Encrypt
Channel encode
Multi-plex
Pulse modulate
Bandpass modulate
Fre-quency spread
Multiple access
Digital input
Channel impulse response
Bit stream
Synch-ronization
Digital baseband waveform
Digital bandpass waveform
Channel
Digital output
R C V
Format
Source decode
Decrypt
Channel decode
Demul-tiplex
Detect
Demod-ulate & Sample
Freq-uency despread
Multiple access
To other destinations
Channel symbols
Information
sink
Message symbols
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40. Detection Coherent Non-coherent BPSK MPSK FSK Differential PSK
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41. Correlator Receiver The correlation functions fi(t) may be
DECISION
LOGIC
The correlation functions fi(t) may be
Signal replicas si(t)
Orthogonal basis functions
With the right decision logic – a maximum likelihood detector
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42. Coherent Detection of BPSK
The BPSK basis functions are
Correlate with an orthogonal basis function
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43. 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 ambiguity
Still allows us to detect bit changes
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44. Coherent MPSK Detection
M-ary PSK signals are
The basis functions are
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45. MPSK Demodulated Output
Output is a complex number
Magnitude is the pulse amplitude
Phase is the modulation phase
Not knowing the phase
Causes a fundamental ambiguity
Still allows us to detect phase changes
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46. Coherent Detection of FSK
FSK waveforms are
We take the phase as zero, as before
Basis functions are
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47. Non-Coherent PSK Detection
Differential PSK
Unknown phase of signal is a random variable
Phases of adjacent received pulses are compared
Performance
Coherent – measure one phase
Non-coherent – measure two phases and subtract
Non-coherent is inherently noisier by 3 dB
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48. Non-Coherent FSK Use a filter bank Use I-Q demodulator
Threshold the squared magnitudes
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49. Example 4.1 pp. 187-188 Correlation is four-sample summation
Waveform set is
Correlation is by summation over k
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50. Example 4.1 (Concluded) Correlator summation is What is z2?
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51. 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
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52. Assignment Add quantization and the ADC to your term project
Read Skar, sections 4.6, 4.7, 4.8, and 4.9
Look at symbol mapping for QPSK and MSK for your term project
Back-up quiz grades will be given by because next week is Spring Break
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