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)

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 If T = .000001 seconds, then this signal moves 1 Mbps. +1 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 -.45 time -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 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

Twisted Pair Cables RJ45 source: Wikipedia

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

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

Fiber Optic Cable SC 1 1/4 inch

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 -1.5 1.0 cos2*pi*5t - (1/3)cos2*pi*15t + (1/5)cos2*pi*25t - (1/7)cos2*pi*35t)

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.

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.

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

SNR = Average Signal Power = Infinity Average Noise Power Binary Signal Sequence = 0011010111

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

SNR = 10 Signal a sequence +1 and -1 volt pulses For your info, SSD P(BE) = 0.000783 = 1/1277

SNR = 1 Signal a sequence +1 and -1 volt pulses For your info, SSD P(BE) = 0.1587 = 1/6.3

SNR = .1 Signal a sequence +1 and -1 volt pulses For your info, SSD P(BE) = 0.3759

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 = 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. 20 40 60 80 100 4.5 99 k 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 Each symbol can represent multiple bits SNR 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