Things You Did not Want to Know About Digital Communications

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Things You Did not Want to Know About Digital
Communications

• Curt Schurgers
• Davor McRay

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Basic Digital Communication Principles
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How Information is Communicated
0 1 0 1 1 1 0 0 1 0 1 0
Information
V, I
Electrical waveform
Electro-magnetic waveform

• The basic information can be digital (e.g.
  computer data) or analog (e.g. traditional tv or
  radio). I will only discuss digital communication
  systems.
• The actual transmission uses electro-magnetic
  waves (Maxwell).
• A communication system transforms the information
  into an analog electrical signal, which is
  converted to the EM-wave by the antenna.

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Grouping the Information

• Information can be grouped together into
  waveforms
• If M ? ? the performance goes up, but at a cost
  of complexity
• (Shannon limit)

b bits/symbol M possible waveforms
1 bit/symbol
0
1
11
10
01
00
2 bits/symbol
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Signal Space Representation

• The basic idea is that we can transmit
  information in parallel over a set of orthogonal
  waveforms with respect to the symbol interval T.
  The inverse of this interval is called the symbol
  rate Rs 1/T.

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Detection of the Symbols

• Correlation or matched filter detector (basically
  equivalent)

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Amplitude Scaling

• Instead of sending only s1, s2, s3 sL etc.
  combine these with a set of possible scaling
  factors a1, a2, a3 aK

s1(t)
Sample at t T
X
s2(t)
Y
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Information Mapping Examples
M 4
M 2
Send s1, s2, both or none of them.
Send either s1 or s2.
M 8
M 4
Send any of these combinations.
Send ?s1 or ?s2.
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Common Elementary Modulation Schemes
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Some Elementary Schemes
FSK (Frequency Shift Keying)
Baseband PAM (Pulse Amplitude Modulation)
s1
Passband PAM (Pulse Amplitude Modulation)
f1
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Sinusoidal Waveforms
Quadrature (Q)
In-phase (I)
s2
s1
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Transmitter Structure
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Frequency Domain
T
1/T
time
frequency
Baseband
BW (bandwidth)
fc
Passband
BW (bandwidth)
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Modulation and Demodulation
Modulation
Demodulation
2.cos(2?.fc.t)
a(t)
ri(t)
b(t)
-2.sin(2?.fc.t)
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Alternative Interpretation
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QAM and PSK
QAM (Quadrature Amplitude Modulation)
16-QAM
64-QAM
4-QAM
PSK (Phase Shift Keying)
8-PSK
16-PSK
4-PSK
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Bandpass Representation
Modulation

• This is just a mathematical abstraction to simply
  analysis. The waveforms can never be complex of
  course.

Demodulation
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Performance
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Transmit Power and Energy
This is the average power consumption when each
symbol is transmitted with an equal probability
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White Noise

• In an AWGN (Additive White Gaussian Noise)
  channel, random uncorrelated fluctuations are
  added to the transmitted waveform. This models
  thermal noise phenomena inside the receiver
  electronics. The noise has approximately a flat
  power spectral density.
• The final impact on the signals can be modeled as
  an addition of uncorrelated random numbers with a
  Gaussian distribution.

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White Noise (continued )
Consider the mathematical abstraction
Consider the real waveforms
Ideal filters, average signal energy normalized
to 1
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Performance Evaluation
100
101
000
001
111
011
110
010

• The demodulator chooses the symbol that is
  closest to the received one (maximum likelihood
  decoding)
• If the noise (and distortions) is such that we
  are closer to another symbol than the correct
  one, a symbol error occurs.
• Each symbol error results in a number of bit
  errors. By carefully choosing the mapping from
  bits to symbols (Gray encoding), one symbol error
  typically results in just one bit error.

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Flat Fading Channel
At receiver !!!
?1 ? d-n
Path loss
B
A
?2
A
B
Shadowing
B
Fading (amplitude and phase component)
B
A
?3
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Inter-Symbol Interference (ISI)

• The previous symbols interfere with the current
  one.
• An equalizer is needed to resolve this issue.

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Frequency Synchronization

• If the carrier frequency fc of the receiver has a
  certain offset ? compared to the one at the
  transmitter, the constellation is rotated.
• Solution Phase Locked Loop (PLL)
• Lock the frequency
• Track variations over time

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Time Synchronization

• The A/D convertor need to know the correct sample
  time, or equivalently needs to be time
  synchronized
• Solution oversample the incoming signal and
  choose the best sample times based on maximum
  likelihood of training sequence or incoming data
  (blind synchronization).

Oversampled
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Spread Spectrum (SS)
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Principle of Direct Sequence SS (DSSS)

• The input sequence is multiplied by a faster
  sequence, called the chip sequence.
• This chip sequence is PN (pseudo noise)
• The received sequence is multiplied by the same
  chip sequence and integrated over one symbol
  time.

1 1 -1 1 -1 -1 1 -1
Chip time Tc
Receiver with incorrect code
Receiver with correct code
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Benefits of DSSS
Frequency domaint
user
Despreading
Spreading
jammer
jammer
interferer
interferer
AWGN
user
user
AWGN

• The input power is spread over a large band hard
  to intercept
• The noise is reduced (compared to the noise in
  the total bandwidth used) by the spreading gain
  ?c.
• To synchronize, we multiple with all possible
  shifted versions of the PN sequence. This
  requires a good auto-correlation.

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CDMA
Spreading code 2
Spreading code 1

• CDMA (Code Division Multiple Access) uses DSSS as
  a multi-access technique. Transmissions with
  different spreading codes to not interfere.
• However, the number of correlators in the
  receiver is limited (so the number of
  simultaneous receptions).
• Spreading codes need good cross-correlation
  properties (for all different shifts).
• Graceful degradation the performance worsens
  gradually as more users are added to the system.
• Near-far problem even with good
  cross-correlation, a nearby interferer can swamp
  the reception of a far away transmitter.

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Frequency-hopped SS (FHSS)

• Jump around between frequency bands in a pseudo
  random fashion.
• Avoids being stuck in a bad frequency band.
• As a multi-access technique, transmissions can
  collide, but occurrences are infrequent.
• Fast FHSS jump multiple times during one symbol
• Slow FHSS multiple symbols per jump

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