Computer Networks – Physical Links / Encoding

Demo: On-Off Modulation (Matlab)

Shanno-Hartley

  • Shannon-Hartley Theorem gives the theoretical throughput upper bound:
    • $C=Blog_2(1+\frac{S}{N})$
    • C: Channel Capacity, 带宽理论上限 (bps)
    • B: Bandwidth, 信道带宽 (Hz), limited by ADC, DAC rate
    • S: Signal Power, limited by safety concern
    • N: Noise Power
    • S/N or SNR: 信噪比(dB), SNR = 10 × log10(S/N)

  • Bandwidth in Hz & Bandwidth in bps
    • Rate: throughput (bps)
    • Spectrum: the width of the occupied the spectrum (Hz)
  • A/D and D/A Converter
    • (1/the space of the samples) is defined as the rate of the ADC or DAC
    • The rate of the ADC or DAC must 2 times of the bandwidth of analog signal (Sampling Theorem)

Modulation

  • Baseband Transmission 基带传输
  • Passband Modulation 频带传输

Baseband Transmission (Line Coding)

  • Symbol/Baud Rate: unit is baud(Bd) i.e. symbols per second
  • Covert to bit rate
    • Rb = RBlog2M
    • M: the number of different symbols
    • RB: Baud Rate
    • Rb: Bit Rate

Clock Recovery

  • Synchronous Transmission: Manchester Encoding
    • NRZ, Non-Return to Zero, 不归零, 高电平为1, 低电平为0
    • Machester: 由低到高的跳变为0, 由高到低的跳变为1
    • Features: Transmit the clock; complex, less overhead
http://i1.fuimg.com/610050/8a2a93dbee9ff92a.png
  • Asynchronous Transmission: 4B/5B Encoding + NRZI
    • 4B/5B, 将4位编码映射到5为编码, 保证最多有1个前导0, 2个末尾0 —— 解决连续的0
    • NRZI, Non-Return to Zero Inverted, 信号跳变为1, 保持信号为0 —— 解决连续的1
    • Features: Recover the clock from signal; simple, cheap
http://i1.fuimg.com/610050/6371b4ddd9a3c6dd.png

Passband Modulation

  • Amplitude Shift Keying (ASK)
    • Demodulation:
    • non-coherent: find the envelop; thresholding
    • coherent: $Acos(2\pi ft)*{\color{Red} cos(2\pi ft)}=\frac{1}{2}A(cos(2\pi 2ft)+1)$
  • Frequency Shift Keying (FSK)
  • Phase Shift Keying (PSK)
    • Demodulation:
    • $cos(2\pi ft)*{\color{Red} cos(2\pi ft)}=\frac{1}{2}(cos(2\pi 2ft)+1)$
    • $cos(2\pi ft + \pi)*{\color{Red} cos(2\pi ft)}=\frac{1}{2}(cos(2\pi2ft)11)$
  • Quadrature Amplitude Modulation (QAM)
http://i1.fuimg.com/610050/6f4a9975cc49aefc.png

Carrier Phase Misalignment

  • Opt1: find the accurate state of received signal (猜测对准)
  • Opt2: use orthogonal carrier waves
    • Transmitter Carrier Wave: cos(2πft + ϕ)
    • Local Carrier Wave 1: cos(2πft)
    • Local Carrier Wave 2: $cos(2\pi ft + \frac{\pi}{2})$

Select Suitable Rate

  • Rb = RBlog2M
  • $C=Blog_2 (1+\frac{S}{N})$
  • If Rb > c, there will be error, though it is not 100% correct if Rb < C.
  • Bit error rate(BER): error bits/transmitted bits

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