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Additive White Gaussian Noise (AWGN) Channel and Matched Filter Detection. ELE 745 – Digital Communications Xavier Fernando. ELE 745 – AWGN Channel. Part I – Gaussian distribution. Gaussian (Normal) Distribution.

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additive white gaussian noise awgn channel and matched filter detection

Additive White Gaussian Noise (AWGN) Channel and Matched Filter Detection

ELE 745 – Digital Communications

Xavier Fernando

gaussian normal distribution
Gaussian (Normal) Distribution
  • The Normal or Gaussian distribution, is an important family of continuous probability distributions
  • The mean ("average", μ) and variance (standard deviation squared, σ2) are the defining parameters
  • The standard normal distribution is the normal distribution with zero mean (μ=0)and unity variance (σ2 =1)
  • Many measurements, from psychological to thermal noise can be approximated by the Gaussian distribution.
pdf of gaussian distribution
PDF of Gaussian Distribution

Standard Norma Distribution

the central limit theorem
The Central Limit Theorem
  • The sum of independent, identically distributed large number of random variables with finite variance is approximately normally distributed under certain conditions
  • Ex: Binomial distribution B(n, p) approaches normal for large n and p
  • The Poisson(λ) distribution is approximately normal N(λ, λ) for large values of λ.
  • The chi-squared distribution approaches normal for large k.
  • The Student’s t-distribution t(ν) approaches normal N(0, 1) when ν is large.
area under gaussian pdf
Area under Gaussian PDF

The area within +/- σ is ≈ 68% (dark blue)

The area within +/- 2σ is ≈ 95% (medium and dark blue)

The area within +/- 2σ is ≈ 99.7% (light, medium, and dark blue)

bit error rate ber
Bit Error Rate (BER)
  • BER is the ratio of erroneous bits to correct bits
  • BER is an important quality measure of digital communication link
  • BER depends on the signal and noise power (Signal to Noise Ratio)
  • BER requirement is different for different services and systems
    • Wireless link BER < 10-6 while Optical BER < 10-12
    • Voice  Low BER while Data  High BER
slide12

Digital Receiver Performance

Probability of error assuming

Equal ones and zeros

Where,

Depends on the noise variance at on/off levels and the

Threshold voltage Vththat is decided to minimize the Pe;

Often Vth = V+ + V-

the q function
The Q Function

Fx(x) = 1 – Q(X)

slide21

BER (Pe) versus Q factor in a

Typical Digital Communication Link