1. Telecommunications Engineering Topic 2: Modulation and FDMA
James K Beard, Ph.D.
(215)
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2. Topics Homework Amplitude Modulation BPSK QPSK Summary Assignment
References
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3. Modulation Text section 3.2 Defined as encoding data onto a carrier
Transmitter signal
Single frequency, or carrier, without modulation
Spectrum about carrier frequency with modulation
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4. Modulation Issues Spectrum Multiple access
Bandwidth of transmitted spectrum and bit rate are related
Efficiency is a function of the modulation
Multiple access
Enables more than one user per channel
Modulation concept is integrated with multiple access concept
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5. Linear and Nonlinear Modulation
Sum of two modulated transmitters is same as modulation from sum of signals
Multiplying input by a constant results in the output of the modulator scaled by that constant
Nonlinear – when either condition does not hold
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6. Analog and Digital Modulation
Analog modulation
Signal is time-continuous
Transmitted spectrum is, in general, a continuous spectrum
Digital modulation
Signal is discontinuous bit stream
Transmitted spectrum falls off as 1/f or 1/f2
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7. Amplitude and Angle Modulation
Amplitude modulation
The transmit signal is the carrier multiplied by a linear function of the signal
The phase of the transmitted signal is constant
Angle modulation
The phase or frequency of the carrier is varied in the modulation process
The amplitude of the transmitted signal is constant
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8. Amplitude Modulation Text Section 3.3.1 Definition
Transmitted signal is product of
Carrier signal – unmodulated transmitter signal
Data signal plus offset
Offset is to make signal factor nonnegative
Transmitted signal components
Carrier – from offset
Sum and difference signals – from data
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9. BPSK Text section 3.3.2 BPSK == Binary Phase-Shift Keying
Modulation is phase inversions
Spectrum is splattered quite a bit
Spectral lines separated by bit rate frequency
Shape of spectral lines follows sinc function
The sinc function spectrum
Parameterized for pi/2 increments
Result is 1/f envelope on lines
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10. QPSK Text section 3.3.3 QPSK == Quadraphase-Shift Keying
Similar to BPSK except four phases instead of two
Variation – Offset QPSK, or OQPSK
Phase transitions confined to pi/4
Elimination of pi/2 phase shifts improves spectrum
Offset is related to mapping of code to waveform
Chip rate doubles to implement code-waveform mapping
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11. Spectral Efficiency Spectral efficiency means
High percentage of signal spectrum in band
Better pulse shape reproduction in receivers
More accurate decoding at a given SNR
Less crosstalk and cross-interference
Higher spectral efficiency
The first goal of the waveform designer
Gains in efficiency with little added complexity
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12. Improved Spectral Efficiency
Baseline is square pulse
Sinc function spectrum
Rolloff is 1/f
First cut is raised cosine
Square spectrum with cosine transition
Pulse is inverse Fourier transform
Root raised cosine
Square root of raised cosine in transmitter and receiver
Transmitted pulse is inverse Fourier transform of square root of spectrum
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13. Raised-Cosine Spectra
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14. Raised-Cosine Pulses
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15. Root Raised-Cosine Spectra
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16. Root Raised-Cosine Pulses
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17. RRC for (0,1,1,0,0)
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18. Topics Continuous-phase modulation – minimum shift keying (MSK)
Power spectra of MSK signal
Gaussian-filtered MSK
Frequency division multiple access (FDMA)
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19. Continuous-Phase Modulation
Also called Minimum Shift Keying
FSK with phase continuity between pulses
Allows rolloff of 1/f4 as opposed to 1/f
Define the difference in the number of cycles between the two frequencies over a pulse time as the deviation ratio h:
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20. Special Values of h When h is pi When h is pi/2
Phase is the same at the end of each pulse
Starting phase is the same every time
When h is pi/2
Minimum for good spectral efficiency
Starting phase can “walk” pi/2 per pulse
Back to same phase every two pulses
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21. Power Spectra of MSK Signal
Fourier transform of signal shows 1/f4 rolloff
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22. Gaussian-Filtered MSK
Gaussian shape
Represents a parabola on a dB plot
Good first-order fit to many single-lobe curves
Simple filters
Main lobe of beam pattern
Simple to work with
Produces pulse as it would be transmitted
Some spreading in time
Good performance
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23. Frequency Division Multiple Access
FDMA
Closely-spaced frequency channels in transmission band
Cross-channel modulation controlled
Waveform design
Guard band
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24. Summary Modulation Spectral efficiency
Puts signal data on a carrier for transmission
Linear or nonlinear
Amplitude or angle
Spectral efficiency
Simple RC and RRC show first cut
Gains are apparent using first principles
MPSK provides good channel efficiency
FDMA provides good multiplexing alternative
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25. Assignment
Read Text 3.4.1, , 3.8
Read Bit Error Rate (BER), section 3.12
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26. Bit Error Rates Examined here for simple receivers Purpose is to show
BPSK, QPSK, MSK, etc.
No pulse shaping filters
Purpose is to show
Differences between fundamental modulation types
The effect of the channel
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27. High SNR Bit Error Rate General equations in Table 3.4 p. 159
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28. AWGN Bit Error Rates
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29. High SNR AWGN Bit Error Rates
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30. Rayleigh Fading Bit Error Rates
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31. BER Conclusions AWGN BER Fading BPSK/QPSK/MSK provide best performance
Others are close enough to be useful
Select best spectral control for best achievable BER
Fading
Low SNR area of fading pdf drives BER
Significant variable fading forces high BER
Houston, we have a problem
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32. Study Problems and Reading Assignments
Study examples and problems
Problem 3.30, p. 177, Adjacent channel interference
Problem 3.35 p. 178, look at part (a); part (b) was done in class
Problem 3.36 p. 178, an intermediate difficulty problem in bit error rate using MSK
Reading assignments
Review Sections 4.1, 4.2 (EE300 material)
Read Sections 4.3, 4.4
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33. Okumrua-Hata Empirical Model
Chapter 2, Theme Example 1, p. 82
Equation for propagation loss in urban environments
Example of empirical model
Look at measured data
Estimate form that measurement variations might take
Do RMS fits of different equations to the data
Select the ones that seem to work best
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34. Parameters Range, valid from 1 km to 20 km
Base station height, valid from 30 m to 200 m
Receiver height, valid from 1 m to 10 m
Operating frequency, valid from 150 MHz to 1 GHz
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35. Forms of equations Base equation is Fit is to A, B, C
Note that B is 10 times the propagation exponent
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36. Results
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37. Practice Quiz What are the three layers and their functions?
Problem 2.22 p. 81, Link Budget
Example 2.21 p. 83, Base Station Antenna Height using Okumrua-Hata model
Problem 3.17 p. 173
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