ECEN5553 Telecom Systems
Dr. George Scheets
Week #2
Exam #1: Lecture 14, 16 September (Live)
No later than 23 September (Remote DL)
Outline: Lecture 22, 5 October (Live)
No later than 12 October (Remote DL)
Outlines
Received
due 5 October (local)
12 October (remote)
0%
Communications Theory:
Moving Bits (OSI Layer 1)
Digital Signal:
A finite number of symbols are transmitted.
Ex) If we define a capital letter as a symbol,
the alphabet is digital (26 symbols, A - Z).
 Analog Signal:
An infinite number of symbols are transmitted.
Example) If we define the instantaneous
pressure as a symbol, a voice pressure wave is
an analog signal.

Example: Binary Signal

Serial Bit Stream
(a.k.a. Random Binary Square Wave)
 One
of two possible symbols transmitted every T seconds.
Here the symbol is either a positive or negative going pulse.
 When two symbols are used, a symbol is known as a ‘bit’.
volts
+1
If T = .000001 seconds, then
this signal moves 1 Mbps.
0
time
-1
T
Example:M-Ary Signal

One of M possible symbols is transmitted every
T seconds.
EX) 4-Ary signaling.
Note each symbol can represent 2 bits.
volts
+1.34
If T = .000001 seconds, then
this 1 MBaud signal moves
2 Mbps.
+.45
time
-.45
-1.34
T
M-Ary versus Binary


Two Symbols: Binary Signaling
M Symbols: M-Ary Signaling
M
is usually a power of 2
 Log2M bits/symbol

Baud rates same? Symbol shapes similar?
If yes..
 Bandwidth
required is similar
 M-Ary signaling allows increased bit rate
 Symbols get closer together if Power fixed
 Noise and/or distortion?
Receiver detection errors more likely
M-Ary signaling
M-Ary signaling used when
Bandwidth is tight
SNR's & signal distortion tolerable
P(Bit Error) OK
Dial-Up Phone Modems
(3500 Hz Channel Bandwidth)
1960's: 300 bps using binary signaling
1980's: 14,400 bps using 128-Ary signaling
1996: 33,600 bps using 1664-Ary signaling
Wired Signaling
Generally uses square pulse symbols
 Symbol shape & width → system bandwidth
 Binary → 2 possible symbols
 M-ary → M possible symbols


Can increase system bps with same bandwidth

So long as symbol width & general shape unchanged
Makes receiver's life more difficult
 Bit Error Rate tends to increase with increasing M

If Power Fixed
 Can crank up power to get same BER as binary

Untwisted Pairs
Wired Physical Links

Untwisted Pair Cabling
Highly susceptible to EM interference
 Lousy choice for telecom systems



Example: Speaker Wires, Power Lines
Twisted Pair Cabling
Fairly resistant to EM interference
 Bandwidth typically in 1-2 digit MHz


Examples: LAN wiring, Home telephone cables
Twisted Pair Cables
RJ45
source: Wikipedia
Wired Physical Links

Coaxial Cable
Resistant to EM interference
 Bandwidth typically in 2-3 digit MHz



Example: Cable TV
Fiber Optic Cable
Immune to EM interference
 Bandwidth in GHz to THz

Coax Cable
BNC
F
RG-59 flexible coaxial cable composed of:
A: outer plastic sheath
B: woven copper shield
source: Wikipedia
C: inner dielectric insulator
D: copper core
Fiber Optic Cable
1 1/4 inch
SC
Physical Layer Ailments...
Attenuation
Signal power weakens with distance
 Distortion
Pulse shapes change with distance

Copper cabling
High frequencies attenuate faster
Pulses smear
 Fiber cabling
Frequencies propagate at different speeds
Dispersion (Pulses change shape)

Generating a Square Wave...
5 Hz
+
15 Hz
+
25 Hz
+
35 Hz
1.5
0
-1.5
0
1.0
cos2*pi*5t - (1/3)cos2*pi*15t
+ (1/5)cos2*pi*25t - (1/7)cos2*pi*35t)
Effects of Dispersion...
5 Hz
+
15 Hz
+
25 Hz
+
35 Hz
1.5
0
-1.5
0
1.0
cos2*pi*5t + (1/3)cos2*pi*15t
+ (1/5)cos2*pi*25t + (1/7)cos2*pi*35t)
In this example the 15 and 35 Hz signals have suffered a
phase shift (which can be caused as a result of different
propagation speeds) with respect to the 5 and 25 Hz
signals. The pulse shape changes significantly.
Smearing (a.k.a. Inter-symbol Interference)
4.5
input
output
z
k
z2
k
0
4.5
0
0
20
40
60
80
k
100
120
140
127
Pulse energy is no longer confined to a T second time interval.
Makes receiver symbol detector's life more difficult.
Examples of Amplified Noise
Radio Static (Thermal Noise)
 Analog TV "snow"
2 seconds

of White Noise
SNR = Average Signal Power = Infinity
Average Noise Power
4.5
z2 x 0
k k
4.5
0
0
20
60
40
k
Binary Signal
Sequence = 0011010111
80
100
99
SNR = 100
4.5
z2 x 0
k k
4.5
0
0
20
40
60
80
k
Signal a sequence +1 and -1 volt pulses
For your info, SSD BER ≈ 0.0
100
99
SNR = 10
4.5
z2 x 0
k k
4.5
0
0
20
40
60
80
k
Signal a sequence +1 and -1 volt pulses
For your info, SSD P(BE) = 0.000783 = 1/1277
100
99
SNR = 1
4.5
z2 x 0
k k
4.5
0
0
20
60
40
80
k
Signal a sequence +1 and -1 volt pulses
For your info, SSD P(BE) = 0.1587 = 1/6.3
100
99
SNR = .1
8.5
z2 x 0
k k
8.5
0
0
20
60
40
80
k
Signal a sequence +1 and -1 volt pulses
For your info, SSD P(BE) = 0.3759
100
99
Single Sample Detector: SNR = 1
Threshold is placed midway between nominal Logic 1 and 0 values.
4.5
0
4.5
0
0
20
40
60
k
80
100
99
Detected sequence = 0011010111 at the receiver,
but there were some near misses.
Fall 2002 Final

'Average' based on 1 test chosen at random
126.00 out of 150


Analogous with "Single Sample" Detector
'Average' based on 10 tests chosen randomly
109.44 out of 150
Analogous with "Multiple Sample" Detector
 Average based on 10 samples tends to be more
accurate than "Average" based on 1 sample


Actual Midterm Average
106.85 out of 150
Matched Filter Detector: SNR = 1
Orange Bars are average voltage over that symbol interval.
4.5
0
4.5
0
0
20
40
60
k
80
100
99
Averages are less likely to be way off the mark.
SSD P(BE) = 0.3759, MFD P(BE) = 0.000783 (10 samples/bit)
Receiver Detection
SNR tends to worsen with distance
 Digital Receiver Symbol Detectors

Examine received symbol intervals (T sec.)
 Decide which of M symbols was transmitted
 Single Sample Detectors
Sample each symbol once
Compare sampled value to a threshold
 Matched Filter Detectors (Optimal)
Sample each symbol multiple times
& generate an average
Compare the average value to a threshold

Channel Capacity

Bandwidth affects usable symbol rate
Rapidly changing symbols need hi frequencies
 Baud rate too high? Distortion!!


M-Ary allows increased bit rate


SNR


Each symbol can represent multiple bits
Affects RCVR ability to tell symbols apart
Bandwidth & SNR affect usable bit rate
Channel Capacity (C)
Bandwidth, Bit Rate, SNR, and BER related
 Channel Capacity defines relationship
C = Maximum reliable bit rate
C = W*Log2(1 + SNR) bps

Bandwidth sets the maximum Baud rate
If move too many Baud, symbols will smear.
SNR sets the maximum number of
different symbols (the "M" in M-ary)
you can reliably tell apart.
Channel Capacity
(a.k.a. Shannon-Hartley Theorem)
Claude Shannon
Ralph Hartley