CS144 7-1 Shannon Capacity and Modulation

Introduction to Computer Networking, Stanford University
https://lagunita.stanford.edu/courses/Engineering/Networking-SP/SelfPaced/about

Unit 7: Lower Layers 중 Shannon Capacity and Modulation 파트 수업 필기 정리

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Physical Layer

Capacity

• bits per second that a given physical layer can support

Modulation

• representation of the capacity on the medium(like channel)

Symbols vs. Bits

• Symbol: the unit of transfer at the physical layer
• can have more than one bit
  • BPSK: 1 bit per symbol (0,1
  • QPSK: 2 bits per symbol (00,01,10,11)
  • e.g. wired 100BASE-T Ethernet (100Bbps), 1Gigabit → Cat-5 cable → 5 voltage levels of PAM-5, -2 ~ +2
• Link Layer pass downs a sequence of bits to Physical Layer, bits turned into a sequence of symbols in Physical Layer.

 

Shannon Capacity

Shannon Limit

• a theoretical limit on amount of information a channel can carry
• Cannel capacity
  the number of bits per second you can send over a given channel
  

  

  • channel: the medium in which information is communicated → could be a wire, wireless, sound waves, ...
  • Bandwidth: the range of frequencies you can use
    the amount we can send is proportional to
  • the amount of bandwidth(how large a chunk of frequencies we can use)
    • building HW for very high B is difficult
  • the signal to noise ratio
    • higher S/N = lower noise (expensive HW) or stronger signal(higher voltage, louder)

 

 

Analog Signals

take a look on sinusoids
below are used to represent bits in terms of analog signals(physical medium)
→ convert bits into voltages, phases, frequencies, ...

1. Amplitude
   • Loudness, signal strength
2. Wavelength
   • length of the wave
   • the speed of light = 1ft / ns → 1,000,000,000(billion) ft/s
3. Frequency
   • number of waves per second
   • e.g.
     1 billion ft per second = 1 billion waves per second = 1GHz (light) ⇒ 1 wave is length of 1 ft
     WiFi = 2.4 GHz ⇒ 5.1 inch, 5 GHz ⇒ 2.4 inch
4. Bandwidth
   • size of frequency range
   • e.g. WiFi standard is 802.11b, select one channel 1~11 (often 1,6,11) each channel is 20 MHz wide, 20 ranges between channels
5. Phase
   • Timing of the waves within a wavelength
   • Same wave, but different starting point of the wave
   • 0~360 degree

 

 

Modulation

how to modulate the signal to represent data

Overview

• most technologies today use phase (PSK) or phase&amplitude(QAM)
• represent QAM symbol as a linear combination of the In-phase component (I) and the Quadrature component (Q): I/Q modulation
  • the way the actual circuits do it
  • visualizable in a 2D plot → representation of what the signal looks like, how it's controlled, how it's modulated, and how those map to bits

ASK

• Amplitude Shift Keying
• varying the amplitudes of the waves
• used in wired networks (most common wired Ethernet systems)
  • simple, most common wired Ethernet systems use this
    • PAM-5: 5 level pulse amplitude modulation (int -2 ~ +2)
      • 100Mbps(100BASE-T) and gigabit(1000BASE-T) Ethernet
    • PAM-16: 16 level pulse amplitude modulation
      • 10 gigabit(10GBASE-T) Ethernet
  • signal strength doesn't decrease much with distance
  • wires don't have a lot of resistance (that's why we use them to carry power)

FSK

• Frequency Shift Keying
• varying the frequencies of the waves

PSK

• Phase Shift Keying
• varying the phase(starting degrees) of the waves
• used in when there can be significant variations in signal strength
  • e.g. wireless situations, DSL(Digital Subscriber Lines), cable modems → where there could be weather damage, wire shaking, bad connections, long lines, etc ...
  • BPSK: Binary Phase Shift Keying
    • 2 Phases: 0 or 𝜋 (0, 180°) (정방향, 역방향)
    • 1Mbps and 2Mbps 802.11b (WiFi)
  • QPSK: Quadrature Phase Shift Keying
    • 4 Phases: 0, 𝜋/2, 𝜋, 3𝜋/2 (0, 90°, 180°, 270°)
    • 5.5Mbps and 11Mbps 802.11b (WiFi)

QAM [kuaem]

• Quadrature Amplitude Modulation(QAM)
  when encoding symbols,
• ASK, OOK(on-off) use only amplitude
• PSK uses only phase
• QAM uses both amplitude and phase
  • 16-QAM: 16 symbols, 4bits/symbol
    
  • a constellation used in HSPDA, 3G data standard
  • maps data into symbols → determines the wave being sent
  • 256-QAM: 256 symbols, 8bits/symbol

I/Q Modulation

• I: in-phase component (0°)
• Q: quadrature component (-90°)
  

  

• when I, Q values come in, two carriers, and add them up, come out in RF (antenna)
• A symbol is a linear combination of I and Q
  • BPSK → (I,Q) = (1,0), (-1,0)
    

    

• QPSK → (I,Q) = (1,0) (0,1) (-1,0) (0,-1)

I/Q constellation(배치)

• a 2D plot of the IQ values
  • Angle of vector: phase of signal
  • Length of vector: amplitude of signal
    

    

    
    ** vector: 방향을 지닌 선. 방향이 있는 선분, 즉 화살표를 써서 표현

 

Examples Today

- ASK/OOK (amplitude): all Wired Ethernet
- FSK (frequency): NWS(National Weather System) "Weatheradio", Bluetooth very rare to use on communication system
- BPSK: 802.11abgn, WiMAX basically all of the WiFi standards(abgn)
- QPSK: 802.11abgn, 802.15.4(low power wireless), HSPDA(3G), LTE, WiMAX
- 16-QAM: 802.11abgn, HSPDA, LTE, WiMAX data standards for mobile phones
- 64-QAM: 802.11abgn, LTE, WiMAX