EE:通信原理复习笔记

This is an review of SJTU course EI302 (Communication Theory) taught by Professor Xiaoyang Lai. This course covers the first 4 chapters of Leown W. Couch, II’s Digitial and Analog Communication System.

Chapter1 基本概念

  • distance to the radio horizon
    $$d=\sqrt{2h}\ miles$$
  • information measure
    $$I_j=log_2\left({1\over P_j}\right)bits$$
  • channel capacity (bps)
    $$C=Blog_2\left(1+{S\over N}\right)$$

Chapter2 信号与频谱

Properties of Signals and Noise

  • Time Average
    $$V_{DC}={1 \over T_0}\int_{-T_0/2}^{T_0/2}v(t)dt$$
  • Root Mean Square
    $$V_{RMS}^2={1 \over T_0}\int_{-T_0/2}^{T_0/2}v^2(t)dt$$
    $$V_{RMS}=\sqrt{V_{RMS}^2}$$
  • Decibel
    $$dB=10log({P_{out}\over P_{in}})$$

Fourier Transform and Spectra

FT of key important function should be remembered.

  • $\Pi(t/T) \leftrightarrow TSa(\pi Tf)$
  • $Sa(2\pi Wx) \leftrightarrow {1 \over 2W}\Pi({f \over {2W}})$
  • $\Lambda(t/T) \leftrightarrow TSa^2(\pi fT)$
  • $sin(\omega_ct) \leftrightarrow {j\over 2}[-\delta(f-f_c)+\delta(f+f_c)]$
  • $cos(\omega_ct) \leftrightarrow {1\over 2}[\delta(f-fc)+\delta(f+f_c)]$

PSD 功率密度谱

使用自相关函数计算功率谱

Bandwidth

  • Absolute bandwidth
  • 3-db bandwidth
  • Equivalent noise bandwidth
  • Null-to-Null Bandwidth
  • Bounded spectrum bandwidth
  • Power bandwidth
  • FCC bandwidth

Chapter3 基带信号

PAM

PCM

  • 采样→量化→编码
  • Bandwidth of PCM signal relates to bit rate $R$ and waveform pulse shape.
    $$B_{PCM} \geq 0.5R = 0.5nf_s=nB$$
    $$B_{PCM} = R = nf_s=2nB \ \ \ (Rectangular)$$
  • Recalling that M = $2^n$ ($\alpha=4.77$ for the peak SNR, $\alpha=0$ for the average SNR)
    $$\left({S \over N}\right)_{dB}=6.02n+\alpha$$

Digital Signaling

ISI 码间串扰

Chapter4 带通信号

AM

  • Envelope Detector
    $$B<<{1\over 2\pi RC}<<f_c$$
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