64-QAM Communications System Design and Characterization

1
64-QAM Communications System Design and
Characterization

• Project 1
• EE283
• daeik.kim_at_duke.edu

2
What you need to do (red)

• Assignments
• 1. Data Source (0)
• Propose a data source that you will use for your
  communication system. Discuss the randomness of
  data.
• 2. 64-QAM Memoryless Channel Coder (25)
• Design a channel coder with a code rate 1. The
  designed data source feeds the channel coder. The
  coder outputs are 64-QAM in-phase and
  quadrature-phase data. For example, with 6-bits
  taken from data source, an in-phase and a
  quadrature-phase amplitudes are produced.
• 3. QAM Base Band Modulation (25)
• Design a QAM modulator. Modulator inputs are the
  output of 64-QAM channel coder and the modulation
  frequency, etc. The output is a modulated QAM
  waveform. Show unit in-phase, unit
  quadrature-phase, and random data waveforms in a
  fine time resolution (for readability).
• 4. Channel Modeling (0)
• Design a channel module that adds Gaussian noise
  to the modulated data with a given noise
  intensity. Show a 64-QAM eye diagram.
• 5. QAM Base Band Demodulation (25)
• Design a QAM demodulator. Assume that full phase
  information is given and the phase is locked. The
  demodulator outputs are in-phase and
  quadrature-phase amplitudes. Show a demodulated
  64-QAM constellation with noise.
• 6. 64-QAM Channel Decoder (25)
• Design a QAM decoder that performs the inverse of
  the designed 64-QAM channel coder.
• 7. BER Measurements (0)
• Design a module calculates bit-error-rate with
  the original data source and the decoded data
  stream. Discuss how many measurements are
  required to get 95 or 99 confidence. Make a
  plot of BER vs SNR. All the numbers, such as
  signal power and noise power, must be obtained
  from simulation.
• 8. Bandwidth Efficiency (0)
• Calculate the bandwidth efficiency with a given
  BER. All the numbers, such as bandwidth must be
  obtained from simulation. Discuss the definition
  of bandwidth of your baseband waveform.

3
Outline

• 64-QAM communications system
• Testing and measurements
• Tools, grading, etc.

4
64-QAM Communications System Design

• Signal source and source coding
• Channel coding
• Baseband modulation
• Channel modeling
• Baseband demodulation
• Channel decoding
• Source decoding and signal sink

Simplified 64-QAM communications system
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Signal source and source coding

• Ideal source coded data
• Random
• Memoryless source
• Equiprobable
• Spectrum and autocorrelation
• A randomly generated data
• What if the data is not random?

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64-QAM Channel Coding

• 2664
• Use rate 1 code
• Map a sequence of 6-bits to 64 symbols
• Symbol error
• Bit error

An example of 16-QAM mapping
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Baseband Modulation (1)
In-phase
Quadrature-phase
8
Baseband Modulation (2)
(-1,-1)
(-1,1)
(1,-1)
(1,1)
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Baseband Modulation (3)
64-QAM waveform with random data
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Baseband Modulation (4)

• Sampling of waveform
• Minimum samples per symbol
• Number of waves per symbol
• Orthogonal signals
• 1 1 vs. 1 -1
• 1 0 -1 0 vs. 0 1 0 -1

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Channel Modeling

• Noise
• Additive
• White
• Gaussian

Contaminated baseband signal
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Eye Diagram
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Baseband Demodulation

• Correlative receiver
• Matched filter receiver

64-QAM Demodulated Data
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Clock Recovery and Phase Locking

• Clock recovery from baseband signal
• Phase locking
• Maintain constant clock and locked phase
• Clock synchronization pilot signal
• Assume perfect clock recovery and phase locking

64-QAM Demodulated with perfect phase and 2.5
phase lag
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Channel Decoding and Signal Sink

• Channel Decoding
• Inverse of channel coding
• Simple hard decision
• Signal Sink
• Compare received and decoded data with signal
  source

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Testing and Measurements

• Obtain
• 64-QAM waveform
• Eye diagram
• Bit error rate
• Bandwidth efficiency

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Signal Power and SNR
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Symbol / Bit Error Rate

• S/BERSymbol or Bit Error / Tx-Rx Bits
• How many symbols/bits to test for a given BER
• How many measurements for a given BER
• 95 or 99 confidence interval
• t-test

BER
SNR(dB)
An example of 64-QAM BER plot
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Channel Bandwidth

• 3-dB bandwidth
• Or your definition and justification

Modulated 64-QAM spectrum
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Theory vs. Practice

• Given BER plot vs. experimented BER plot
• Given bandwidth efficiency vs. experimented
  bandwidth efficiency

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Tools

• Any tools supported by ECE
• MATLAB recommended
• C, C, Java, Visual Basic, Perl, PHP
• Simulink ?

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MATLAB (1)

• gtgt A0 1 2 3 4 5
• A
• 0 1 2
• 3 4 5
• gtgt A(00.21)'
• A
• 0
• 0.2000
• 0.4000
• 0.6000
• 0.8000
• 1.0000
• gtgt plot(A,cos(2piA))

• gtgt ta1-0.010
• gtgt tb(0.011)'
• gtgt tatb'
• gtgt ta'.tb
• gtgt ta.2
• gtgt ta(110)tb(1120)
• gtgt help
• gtgt help elfun
• gtgt lookfor signal
• gtgt demo

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MATLAB (2)

• Flow control
• for N110,
• ---
• end
• if lttrue/falsegt,
• ---
• else,
• ---
• end
• switch ltvargt
• case ltcond1gt
• ---
• case ltcond2gt
• ---
• otherwise
• ---
• end

• Function call
• function Y,ZName(X)
• Name.m
• Usage
• function YName(X)
• ltCommandsgt
• Y1
• Z2
• return
• gtgt YName(1)
• gtgt Y,ZName(2)

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Matlab (3)

• Useful functions
• mean
• sum
• size
• length
• zeros
• ones
• rand
• randn
• figure
• plot
• xlabel
• ylabel
• title

• semilogx
• semilogy
• loglog
• log10
• log
• i
• j
• pi
• round
• ceil
• floor
• sgn
• fft
• spectrum

25
MATLAB (4)

• Vector operation vs. scalar operation
• gtgt A11e4 MeanSquaremean(A.2)
• gtgt A11e8
• Vector preparation before usage
• gtgt Azeros(1,100) for k1100, A(k)k1 end
• gtgt for k1100, A(k)k1 end
• gtgt A for k1100, AA k1 end

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Things to submit

• Documentation
• An electronic copy in PDF of PS format
• IEEE journal format
• Scripts execution methods
• Scripts
• tared and compressed scripts
• lastname_firstname.tar.gz or .tar.Z
• All scripts should be in lastname_firstname
  directory
• Script execution must be one-step, i.e.
  filenameenter

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Deadline

• Submit to dkim_at_ee.duke.edu
• 9/24 (Fri) 1100pm
• Time marked by the recipient server (ee.duke.edu)
• Penalty for late submission without permission
  (-20 per a day)
• No virus (frown per a virus)