1. ECEN5553 Telecom Systems Dr
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)

2. Outlines Received due 5 October (local) 12 October (remote)
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3. 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.

4. 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
If T = seconds, then
this signal moves 1 Mbps. +1
time -1 T

5. 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 = seconds, then
this 1 MBaud signal moves
2 Mbps.
+.45
-.45
time
-1.34 T

6. 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

7. 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

8. 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

9. Untwisted Pairs

10. Wired Physical Links Untwisted Pair Cabling Twisted 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

11. Twisted Pair Cables
RJ45
source: Wikipedia

12. Wired Physical Links Coaxial Cable Fiber Optic 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

13. Coax Cable BNC F RG-59 flexible coaxial cable composed of:
A: outer plastic sheath B: woven copper shield C: inner dielectric insulator D: copper core
source: Wikipedia

14. Fiber Optic Cable SC
1 1/4 inch

15. 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)

16. Generating a Square Wave...
5 Hz +
15 Hz +
25 Hz
35 Hz
1.5
-1.5
1.0
cos2*pi*5t - (1/3)cos2*pi*15t
+ (1/5)cos2*pi*25t - (1/7)cos2*pi*35t)

17. Effects of Dispersion... cos2*pi*5t + (1/3)cos2*pi*15t
5 Hz +
15 Hz +
25 Hz
35 Hz
1.5
-1.5
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.

18. Smearing (a.k.a. Inter-symbol Interference)
4.5
input
output z k z2 k
4.5 20 40 60 80
100
120
140 k
127
Pulse energy is no longer confined to a T second time interval.
Makes receiver symbol detector's life more difficult.

19. Examples of Amplified Noise
Radio Static (Thermal Noise)
Analog TV "snow"
2 seconds
of White Noise

20. SNR = Average Signal Power = Infinity Average Noise Power
Binary Signal
Sequence =

21. Signal a sequence +1 and -1 volt pulses
SNR = 100
Signal a sequence +1 and -1 volt pulses
For your info, SSD BER ≈ 0.0

22. SNR = 10 Signal a sequence +1 and -1 volt pulses
For your info, SSD P(BE) = = 1/1277

23. SNR = 1 Signal a sequence +1 and -1 volt pulses
For your info, SSD P(BE) = = 1/6.3

24. SNR = .1 Signal a sequence +1 and -1 volt pulses
For your info, SSD P(BE) =

25. Single Sample Detector: SNR = 1
Threshold is placed midway between nominal Logic 1 and 0 values. 20 40 60 80
100
4.5 99 k
Detected sequence = at the receiver,
but there were some near misses.

26. Fall 2002 Final
'Average' based on 1 test chosen at random out of 150
Analogous with "Single Sample" Detector
'Average' based on 10 tests chosen randomly 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 out of 150

27. Matched Filter Detector: SNR = 1
Orange Bars are average voltage over that symbol interval. 20 40 60 80
100
4.5 99 k
Averages are less likely to be way off the mark.
SSD P(BE) = , MFD P(BE) = (10 samples/bit)

28. 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

29. Channel Capacity Bandwidth affects usable symbol rate
Rapidly changing symbols need hi frequencies
Baud rate too high? Distortion!!
M-Ary allows increased bit rate
Each symbol can represent multiple bits
SNR
Affects RCVR ability to tell symbols apart
Bandwidth & SNR affect usable bit rate

30. 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.

31. Channel Capacity (a.k.a. Shannon-Hartley Theorem)
Claude Shannon
Ralph Hartley