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/

http://users.cecs.anu.edu.au/~Salman.Durrani/


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]


Outline

3. How can we efficiently transmit digital information over AWGN communication channels ?•

Binary Modulations

•

PAM•

BPSK, QPSK

•

QAM


• 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


3 Basic Form of Binary Modulation


• 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


[1] Signal Waveforms



[2] Geometric RepresentationThe basic geometric representation of digital PAM signal waveforms is as follows:



[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.



• In Gray code, each code word differs in only one bit from its neighboring code words.

Gray Codes


[3] Signal Space Diagrams



Summary of Vector Formulas


• Analyse the properties of M=4 PAM.

• Step 1: Write the equations of the baseband waveforms.

Example 01


• Step 2: Express the baseband waveforms in terms of basis functions.

• Step 3: Draw a signal-space diagram

Example 01


• Step 4: Find the minimum distance between two signal points.

• Step 5: Find the average energy of the transmitted signals

Example 01


• Step 6: Find the correlations between two signal points.

Example 01


• Step 7: Draw baseband and band-pass M=4 PAM signals to represent sequence 111000011100.

Example 01


• 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


• The pulse shape determines the spectral (frequency domain) characteristics of the transmitted signal.

Pulse Shape Assumption


• Comments



Announcements

• Solve questions in Tutorial 03: Signal Space and Modulation.

week04 l10 pam

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