1. EE 6331, Spring, 2009 Advanced Telecommunication
                                                           
Zhu Han
Department of Electrical and Computer Engineering
Class 13
Mar. 3rd, 2009

2. Outline Exam Review Geometric representation of modulation signals
ADC/DAC
PCM
Geometric representation of modulation signals
Linear modulation
BPSK, DPSK; QPSK, offset QPSK, /4 QPSK
Constant envelope modulation
BFSK, MSK, GMSK
Combined linear and constant envelope modulation
MPSK
QAM
MFSK and OFDM
ECE6331 Spring 2009

3. PAM, PWM, PPM, PCM
ECE6331 Spring 2009

4. Quantization Scalar Quantizer Block Diagram Mid-tread Mid-rise
ECE6331 Spring 2009

5. Equations
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6. Quantization Noise
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7. Example
SNR for varying number of representation levels for sinusoidal modulation X dB, example 3.1
Number of representation level L
Number of Bits per Sample, R
SNR (dB) 32 5
31.8 64 6
37.8
128 7
43.8
256 8
49.8
ECE6331 Spring 2009

8. Conditions for Optimality of Scalar Quantizers
Let m(t) be a message signal drawn from a stationary process M(t)
-A  m  A
m1= -A
mL+1=A
mk  mk+1 for k=1,2,…., L
The kth partition cell is defined as
Jk: mk< m  mk+1 for k=1,2,…., L
d(m,vk): distortion measure for using vk to represent values inside Jk.
ECE6331 Spring 2009

9. Condition for Optimal Quantizer
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10. Condition One
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11. Condition Two
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12. Vector Quantization image and voice compression, voice recognition
statistical pattern recognition
volume rendering
ECE6331 Spring 2009

13. Numbers passed from ADC to computer to represent analogue voltage
PCM
0000
1111
1110
1101
1100
1011
1010
1001
0001
0010
0011
0100
0101
0110
0111
Resolution=
1 part in 2n
0000
0110
0111
0011
1100
1001
1011
Numbers passed from ADC to computer to represent analogue voltage
ECE6331 Spring 2009

14. Non-uniform Quantizer
F: nonlinear compressing function
F-1: nonlinear expanding function
F and F-1: nonlinear compander y y ^ F Q
F-1 x ^ x
Example
F: y=log(x) F-1: x=exp(x)
We will study nonuniform quantization by PCM example next
A law and  law
ECE6331 Spring 2009

15.  Law/A Law
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16. Geometric Representation of Modulation Signal
Digital Modulation involves
Choosing a particular signal waveform for transmission for a particular symbol or signal
For M possible signals, the set of all signal waveforms are:
For binary modulation, each bit is mapped to a signal from a set of signal set S that has two signals
We can view the elements of S as points in vector space
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17. Geometric Representation of Modulation Signal
Vector space
We can represented the elements of S as linear combination of basis signals.
The number of basis signals are the dimension of the vector space.
Basis signals are orthogonal to each-other.
Each basis is normalized to have unit energy:
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18. Example Two signal waveforms to be used for transmission
The basis signal Q I
Constellation Diagram
Dimension = 1
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19. Constellation Diagram
Properties of Modulation Scheme can be inferred from Constellation Diagram
Bandwidth occupied by the modulation increases as the dimension of the modulated signal increases
Bandwidth occupied by the modulation decreases as the signal points per dimension increases (getting more dense)
Probability of bit error is proportional to the distance between the closest points in the constellation.
Bit error decreases as the distance increases (sparse).
Equation
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20. Concept of a constellation diagram
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21. Example of samples of matched filter output for some bandpass modulation schemes
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22. Linear Modulation Techniques
Classify digital modulation techniques as:
Linear
The amplitude of the transmitted signal varies linearly with the modulating digital signal, m(t).
They usually do not have constant envelope.
More spectral efficient.
Poor power efficiency
Example: BPSK, QPSK.
Non-linear
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23. Binary Phase Shift Keying
Use alternative sine wave phase to encode bits
Phases are separated by 180 degrees.
Simple to implement, inefficient use of bandwidth.
Very robust, used extensively in satellite communication. Q
State 1
State
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24. BPSK Example 1 1 0 1 0 1 Data Carrier Carrier+ p BPSK waveform 24
Data
Carrier
Carrier+ p
BPSK waveform
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25. BPSK Virtue of pulse shaping
equations
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26. BPSK Coherent demodulator
6.72
6.73
6.74
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27. Differential PSK encoding
Differential BPSK
0 = same phase as last signal element
1 = 180º shift from last signal element
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28. DPSK modulation and demodulation
6.75,
3dB loss
EE 542/452 Spring 2008
EE 552/452 Spring 2007 28

29. Quadrature Phase Shift Keying
Multilevel Modulation Technique: 2 bits per symbol
More spectrally efficient, more complex receiver.
Two times more bandwidth efficient than BPSK Q
11 State
01 State
00 State
10 State
Phase of Carrier: p/4, 2p/4, 5p/4, 7p/4
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30. 4 different waveforms cos+sin -cos+sin 11 01 00 10 cos-sin -cos-sin 30
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31. QPSK Example
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32. QPSK Virtue of pulse shaping
6.80
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33. QPSK modulation
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34. QPSK receiver
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35. Differential Coherent
DBPSK
3dB loss
QPSK BER 6.79, the same as BPSK
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36. Offset QPSK waveforms
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37. Offset OQPSK QPSK can have 180 degree jump, amplitude fluctuation
By offsetting the timing of the odd and even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time.
90 degree jump
ECE6331 Spring 2009

38. Pi/4 QPSK signaling 135 degree Non-coherent detection 38
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39. Pi/4 QPSK transmitter
Example 6.9
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40. I. Differential detection of pi/4 QPSK
Example 6.10
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41. II. IF Differential Detection
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42. III. FM Discriminator detector
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43. Constant Envelope Modulation
Amplitude of the carrier is constant, regardless of the variation in the modulating signal
Better immunity to fluctuations due to fading.
Better random noise immunity
Power efficient
They occupy larger bandwidth
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44. Frequency Shift Keying (FSK)
The frequency of the carrier is changed according to the message state (high (1) or low (0)).
One frequency encodes a 0 while another frequency encodes a 1 (a form of frequency modulation)
Integral of m(x) is continues.
Continues FSK
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45. FSK Bandwidth Limiting factor: Physical capabilities of the carrier
Not susceptible to noise as much as ASK
Applications
On voice-grade lines, used up to 1200bps
Used for high-frequency (3 to 30 MHz) radio transmission
used at higher frequencies on LANs that use coaxial cable
ECE6331 Spring 2009

46. Multiple Frequency-Shift Keying (MFSK)
More than two frequencies are used
More bandwidth efficient but more susceptible to error
f i = f c + (2i – 1 – M)f d
f c = the carrier frequency
f d = the difference frequency
M = number of different signal elements = 2 L
L = number of bits per signal element
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47. FSK Coherent Detection
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48. Noncoherent FSK
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49. MSK modulation
Equation 6.104, 6.105
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50. MSK reception
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51. Minimum Shift Keying spectra
6.107
6.108
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52. GMSK spectral shaping
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53. GMSK spectra shaping
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54. Simple GMSK modulation and demodulation
ECE6331 Spring 2009
EE 552/452 Spring 2007 54

55. Digital GMSK demodulator
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56. 8-PSK Signal Constellation
Equation
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57. Pulse Shaped M-PSK
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58. QAM – Quadrature Amplitude Modulation
Modulation technique used in the cable/video networking world
Instead of a single signal change representing only 1 bps – multiple bits can be represented buy a single signal change
Combination of phase shifting and amplitude shifting (8 phases, 2 amplitudes)
ECE6331 Spring 2009

59. QAM
QAM
As an example of QAM, 12 different phases are combined with two different amplitudes
Since only 4 phase angles have 2 different amplitudes, there are a total of 16 combinations
With 16 signal combinations, each baud equals 4 bits of information (2 ^ 4 = 16)
Combine ASK and PSK such that each signal corresponds to multiple bits
More phases than amplitudes
Minimum bandwidth requirement same as ASK or PSK
ECE6331 Spring 2009

60. 16-QAM Signal Constellation
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61. QAM vs. MFSK
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62. Orthogonal frequency-division multiplexing
Special form of Multi-Carrier Transmission.
Multi-Carrier Modulation.
Divide a high bit-rate digital stream into several low bit-rate schemes and transmit in parallel (using Sub-Carriers)
ECE6331 Spring 2009

63. Comparison of Digital Modulation
ECE6331 Spring 2009

64. Comparison of Digital Modulation
ECE6331 Spring 2009

65. Spectral Efficiencies in practical radios
GSM- Digital Cellular
Data Rate = 270kb/s, bandwidth = 200kHz
Bandwidth Efficiency = 270/200 =1.35bits/sec/Hz
Modulation: Gaussian Minimum Shift Keying (FSK with orthogonal frequencies).
“Gaussian” refers to filter response.
IS-54 North American Digital Cellular
Data Rate = 48kb/s, bandwidth = 30kHz
Bandwidth Efficiency = 48/30 =1.6bits/sec/Hz
Modulation: pi/4 DQPSK
ECE6331 Spring 2009

66. Modulation Summary
Phase Shift Keying is often used, as it provides a highly bandwidth efficient modulation scheme.
QPSK, modulation is very robust, but requires some form of linear amplification. OQPSK and p/4-QPSK can be implemented, and reduce the envelope variations of the signal.
High level M-ary schemes (such as 64-QAM) are very bandwidth efficient, but more susceptible to noise and require linear amplification.
Constant envelope schemes (such as GMSK) can be employed since an efficient, non-linear amplifier can be used.
Coherent reception provides better performance than differential, but requires a more complex receiver.
ECE6331 Spring 2009