64-QAM Communications System Design and Characterization

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64-QAM Communications System Design and
Characterization

• Project 1
• EE283
• Results

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What you need to do

• 1. Data Source (0) provided follow link at left
• 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) provided follow link at
  left
• Design a channel module that adds Gaussian noise
  to the modulated data with a given noise
  intensity. Show a 64-QAM eye diagram.
•  
•  Eye Plot (0) provided follow link at left
•  
• 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.
•  

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1. Data Source (0)

• Propose a data source that you will use for your
  communication system. Discuss the randomness of
  data.

4
1. Data Source (0)

• Propose a data source that you will use for your
  communication system. Discuss the randomness of
  data.

5
1. Data Source (0)

• Propose a data source that you will use for your
  communication system. Discuss the randomness of
  data.

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2. 64-QAM Memoryless Channel Coder

• 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.

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2. 64-QAM Memoryless Channel Coder (25)

• Grey Code and in phase and quadrature amplitudes

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2. 64-QAM Memoryless Channel Coder

• Different Gray codes

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3. QAM Base Band Modulation

• 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).

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3. QAM Base Band Modulation
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4. Channel Modeling

• Design a channel module that adds Gaussian noise
  to the modulated data with a given noise
  intensity. Show a 64-QAM eye diagram.
• What noise to add??

energy per bit, not sample simulation
parameters fc 2000 carrier
frequency fsamp 12000 sampling
frequency wind fsamp/fc number of samples
per window sig sum(sum(s.2))/size(symbol2vecs,1
) d N0 noise power d (sig/(2wind))
10(-SNR/10)
Not sure about the 2 ???
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4. Channel Modeling

• What noise to add??

Calculate the No per bit Eav
mean(sum(SIGNAL_LIBRARY.2,2)) Eb Eav /
SAMPLES_PER_SYMBOL / BITS_PER_SYMBOL No
Eb./10.(SNR./10)
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 Eye Plot

• Most use low sampled data

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 Eye Plot

• Few use high sampled data, more like measured eyes

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5. QAM Base Band Demodulation

• 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.

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5. QAM Base Band Demodulation

• Most did this fine

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6. 64-QAM Channel Decoder

• Design a QAM decoder that performs the inverse of
  the designed 64-QAM channel coder.

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7. BER Measurements

• 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.

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7. BER Measurements

• Make a plot of BER vs SNR. (tour de force)

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7. BER Measurements

• Make a plot of BER vs SNR.

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7. BER Measurements

• Discuss how many measurements are required to get
  95 or 99 confidence.
• http//www.maxim-ic.com/an703
• Discusses number of points (np) for

p given N error measured
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

gives the probability that k events (i.e., bit
errors) occur in n trials (i.e., n bits
transmitted), where p is the probability of event
occurrence in a single trial (i.e., a bit error),
and q is the probability that the event does not
occur in a single trial (i.e., no bit error).
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

When we are interested in the probability that N
or fewer events occur in n trials, then the
cumulative binomial distribution function of
Equation 4 is useful

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

CL- (confidence that P(?) (the actual
probability of bit error) is less than p- )
P(? gtNp-)

Confidence actual prob of error in range
   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

Poisson approximation

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

Numerically find 10-5 -30 99.76 certain _at_10
million samples And 96 errors

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

Numerically find 10-5 -10 99.73 certain _at_90
million bits and 896 errors

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

This approx works great for a lt 0.1

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

It is less accurate for n when a 0.3 but n
error matters less!

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

Numerically find 10-510-.1 99.74 certain _at_17
million bits And 171 errors

   eq. 4
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7. BER Measurements

• But we really want to know is the P(e) 10-5?

Numerically find 3.16 10-6 lt P lt 3.16 10-5 95
certain _at_ 255K bits and 3 errors

   eq. 4
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8. Bandwidth Efficiency

• 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.

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8. Bandwidth Efficiency

• Bandwidth of 1-2 x fc seems to be needed

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8. Bandwidth Efficiency

• Bandwidth of 1-2 x fc seems to be needed

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9 a)

• Compare random data to non random data in your
  link.

Slight difference in SNR due to lower average
power for repeated data
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9 b)

• Experiment with the symbols length Tlt 1/(2pifc)
  (wave forms only part of a period of the sine
  wave).

Found worked OK for down to 0.5 of sin and cos
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9 c)

• Experiment with filtering the output of the
  channel module. A filter with bandwidth around
  fcmay improve SNR.

Result was worse error rate Maybe need equalizer
to make receiver work