Week04 l10 Pam
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Transcript of Week04 l10 Pam
ENGN3226 Digital Communications1
LECTURE 10
Pulse Amplitude Modulation Salman Durrani
Research School of Engineering, The Australian National University.
http://users.cecs.anu.edu.au/~Salman.Durrani/
ENGN3226 Digital Communications2
Research Questions1.
What is signal space analysis [L07-08]?
2.
Why is it necessary to use a carrier for the wireless transmission of digital baseband signals. [L09]
3.
How can we efficiently transmit digital information over AWGN communication channels ? •
Binary Modulations [ L09]•
PAM [L10]
QPSK [L11]
QAM [L12]
4.
How can we convert the received waveform
r(t) into an
N-dimensional
vector
r which can be used for optimum detection? [13]
5.
What are the statistics of the correlator output r ? [13]6.
How can we prove that no information is lost in considering correlator output r for detection, rather than the received signal r(t) ? [13]
7.
How can we select optimum detection levels for binary receiver decision voltages in presence of AWGN noise? [14]
8.
How can we generalise binary decision criterion for multiple transmitted signals? [15]
9.
How can we simplify the general decision criterion into maximum correlation metrics for detection in AWGN channels? [15]
10.
How can we compare the performance of different modulation schemes? [16]
ENGN3226 Digital Communications3
Outline
3. How can we efficiently transmit digital information over AWGN communication channels ?•
Binary Modulations
•
PAM•
BPSK, QPSK
•
QAM
ENGN3226 Digital Communications4
• Binary Pulse Amplitude Modulation (also called Amplitude Shift Keying.
• Binary Phase Shift Keying Modulation (BPSK)• Binary Frequency Shift Keying Modulation (BFSK)
3 Basic Form of Binary Modulation
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3 Basic Form of Binary Modulation
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• In Pulse Amplitude Modulation (PAM), the information is conveyed by the amplitude of the transmitted signal.
• Binary PAM is the simplest digital modulation method.• 1 is represented by a pulse of amplitude A.• 0 is represented by a pulse of amplitude –A.
Pulse Amplitude Modulation
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[1] Signal Waveforms
Pulse Amplitude Modulation
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[2] Geometric RepresentationThe basic geometric representation of digital PAM signal waveforms is as follows:
Pulse Amplitude Modulation
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[3] Signal Space Diagrams
• In M-ary PAM, binary information sequence is subdivided into blocks of k = log2 (M) bits called symbols and each block or symbol is represented by one of M=2k
pulse amplitude values.
• The mapping or assignment of k-information bits to the M=2k possible signal amplitudes is done using Gray encoding.
• In Gray code, each code word differs in only one bit from its neighboring code words.
Pulse Amplitude Modulation
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• In Gray code, each code word differs in only one bit from its neighboring code words.
Gray Codes
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[3] Signal Space Diagrams
Pulse Amplitude Modulation
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Pulse Amplitude Modulation
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Summary of Vector Formulas
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• Analyse the properties of M=4 PAM.
• Step 1: Write the equations of the baseband waveforms.
Example 01
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• Step 2: Express the baseband waveforms in terms of basis functions.
• Step 3: Draw a signal-space diagram
Example 01
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• Step 2: Express the baseband waveforms in terms of basis functions.
• Step 3: Draw a signal-space diagram
Example 01
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• Step 4: Find the minimum distance between two signal points.
• Step 5: Find the average energy of the transmitted signals
Example 01
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• Step 6: Find the correlations between two signal points.
Example 01
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• Step 7: Draw baseband and band-pass M=4 PAM signals to represent sequence 111000011100.
Example 01
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• In the analysis we assumed rectangular pulses but in practical systems, the rise and decay times are nonzero and the pulses are generally smoother.
Pulse Shape Assumption
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• The pulse shape determines the spectral (frequency domain) characteristics of the transmitted signal.
Pulse Shape Assumption
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• Comments
Pulse Amplitude Modulation
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Announcements
• Solve questions in Tutorial 03: Signal Space and Modulation.