1. 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

2. Digital Signaling
Mathematical Representation of the waveform: Voltage (or current) waveform for digital signals:
Example: Message ‘X’ from a digital source - code word “ ”

3. 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.
Binary (2) Values
More than 2 Values
Binary signal
Multilevel signal
How to detect the data at the receiver?

4. Vector Representation
Orthogonal function space corresponds to orthogonal vector space :

5. 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

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

7. wk takes only BINARY values
Bandwidth Estimation
The lower bound for the bandwidth of the waveform w(t) is given by the Dimensionality Theorem
Binary Signaling:
wk takes only BINARY values
Waveform:
Example: Binary signaling from a digital source: M=256 distinct messages
M = 2n = 28 = 256  Each message ~ 8-bit binary words
T0=8 ms – Time taken to transmit one message; Code word:
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;

8. 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
The Lower Bound :
The actual Null Bandwidth:
Bandwidth:
 Null BW > lower bound BW

9. Which wave shape gives lower bound BW?
Binary Signaling
Which wave shape gives lower bound BW?

10. Binary Signaling Case 2: sin(x)/x Pulse Orthogonal Functions
Minimum Bandwidth
Where Ts=Tb 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

11. Multilevel Signaling Lower bound BW:
For N=8 pulses, T0=8 ms => B=500Hz.
B Reduces, if N Reduces: So wk should take more than 2 values ( 2- binary signaling)
If wk’s have L>2 values  Resultant waveform – Multilevel signal
Multilevel data : Encoding l-bit binary data  into L-level : DAC

12. Multilevel Signaling (Example)
M=256-message source ; L=4; T0=8 ms
Encoding Scheme: A 2-Bit Digital-to-Analog Converter
Binary Input Output Level
(l=2 bits) (V)
Binary code word
w1= -3, w2= -1, w3= +3, w4= +1
Bit rate : k bits/second
Different
Baud ( symbol rate): k baud
Relation :

13. Multilevel Signaling - Example
B=1/Ts=D=500 Hz
B=N/2T0=250Hz
How can the data be detected at the receiver?
Sampling at midpoint of Ts=2 ms interval for either case (T=1, 3, 5, 7 ms)

14. 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 Ts=lTb where the Symbol Rate or the BAUD Rate D=1/Ts=1/lTb.
The symbols are converted to a L level (L=2l ) multilevel signal using a l-bit DAC.
Note that now the Baud rate is reduced by l times the Bit rate R (D=R/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
L=2l D=1/Ts=1/lTb=R/l

15. Binary-to-multilevel Polar NRZ Signal Conversion
(c) L = 8 = 23 Level Polar NRZ Waveform Out