Eeng 360 1

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Digital Signaling

• Digital Signaling
• Vector Representation
• Bandwidth Estimation
• Binary Signaling
• Multilevel Signaling

Huseyin Bilgekul Eeng360 Communication Systems
I Department of Electrical and Electronic
Engineering Eastern Mediterranean University
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Digital Signaling

• How do we mathematical represent the waveform of
  a digital signal?
• How do we estimate the bandwidth of the waveform?

• Example Message X for ASCII computer keyboard
  - code word 0001101
• What is the data rate?

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Digital Signaling

• Baud (Symbol Rate)
• D N/T0 symbols/sec N-
  number of dimensions used in T0 sec.

• Bit Rate
• R n/T0 bits/sec
  n- number of data bits sent in T0 sec.

• How to detect the data at the receiver?

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Vector Representation

• Orthogonal function space corresponds to
  orthogonal vector space

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Vector Representation of a Binary Signal

• Examine the representation in next slide for the
  waveform of a 3-bit (binary) signal. This signal
  can be directly represented by,

.

• Orthogonal function approach

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Vector Representation of a Binary Signal
A 3 bit Signal waveform
Bit shape pulse
Orthogonal Function Set
Vector Representation of the 3 bit signal
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Bandwidth Estimation

• The lower bound for the bandwidth of the
  waveform w(t) is given by the Dimensionality
  Theorem

• Binary Signaling

Example Binary signaling from a digital source
M256 distinct messages M 2n 28 256 ? Each
message 8-bit binary words T08 ms Time
taken to transmit one message Code word
01001110 w1 0, w2 1, w3 0, w4 0, w5 1,
w6 1, w7 1, w8 0

• Case 1 Rectangular Pulse Orthogonal Functions

unity-amplitude rectangular pulses
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Bandwidth Estimation (Binary Signaling)

• Receiver end How are we going to detect data?
• Orthogonal series coefficients wk are
  needed. Sample anywhere in the bit interval

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Binary Signaling
To recover the digital data at the receiver, we
sample received wavform at the right time
instants (SYNCHRONIZATION) and from the sample
values a decision is made about the value of the
transmitted bit at that time instant.
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Binary Signaling
Which wave shape gives lower bound BW?
0 1 0 0 1 1
1
Individual Pulses
Total Waveform
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Binary Signaling Using Sa Shape
1 0
0 1 0
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Binary Signaling Using Raised Cosine Shape
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Binary Signaling

• Case 2 sin(x)/x Pulse Orthogonal Functions

Minimum Bandwidth
Where TsTb for the case of Binary signaling.

• Receiver end How are we going to detect data?
• Orthogonal series coefficients wk are
  needed. Sample at MIDPOINT of each interval

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Multilevel Signaling

• B Reduces, if N Reduces So wk should take more
  than 2 values ( 2- binary signaling)
• If wks have Lgt2 values ? Resultant waveform
  Multilevel signal
• Multilevel data Encoding l-bit binary data ?
  into L-level DAC

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Multilevel Signaling (Example)
M256-message source L4 T08 ms
Encoding Scheme A 2-Bit Digital-to-Analog
Converter Binary Input Output Level
(l2 bits)
(V) 11 3
10 1 00
-1 01
-3
Binary code word - 01001110
w1 -3, w2 -1, w3 3, w4 1
Bit rate k bits/second
Different
Baud ( symbol rate)
k baud
Relation
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Multilevel Signaling - Example
B1/TsD500 Hz
BN/2T0250Hz

• How can the data be detected at the receiver?
• Sampling at midpoint of Ts2 ms interval for
  either case (T1, 3, 5, 7 ms)

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Multilevel Signaling - Example
0 1 1 0 1
1 1 0 -3
1 3 1
Total Waveform
Individual Pulses
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Binary-to-multilevel polar NRZ Signal Conversion

• Binary to multilevel conversion is used to
  reduce the bandwidth required by the binary
  signaling.
• Multiple bits (l number of bits) are converted
  into words having SYMBOL durations TslTb
  where the Symbol Rate or the BAUD Rate
  D1/Ts1/lTb.
• The symbols are converted to a L level (L2l )
  multilevel signal using a l-bit DAC.
• Note that now the Baud rate is reduced by l
  times the Bit rate R (DR/l).
• Thus the bandwidth required is reduced by l
  times.

Ts Symbol Duration L Number of M ary
levels Tb Bit Duration l Bits
per Symbol L2l D1/Ts1/lTbR/l
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Binary-to-multilevel Polar NRZ Signal Conversion
(c) L 8 23 Level Polar NRZ Waveform Out