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Symbol Error Probability for AWGN channels

  1. May 17, 2013 #1
    Hey folks,

    I have been given an equation to calculate the symbol error probability as:

    Pes = [itex]\frac{N}{2}[/itex]erfc([itex]\sqrt{\frac{m.d^{2}_{0}}{4γ} . \frac{Eb}{N0}}[/itex])


    N = Average number of nearest neighbours (symbols)
    m = no of bits per symbol
    d0 = euclidean distance to nearest neighbours
    Eb = energy per bit
    N0 = noise

    (Eb/No = SNR)

    I cannot however find the meaning of γ (gamma)

    I have found several definitions of it for various constellation types:

    M-ASK - γ = (M2-1) / 3
    M-PSK - γ = 1
    M-QAM - γ = 2(M-1) / 3

    Does anyone know the meaning of gamma and how, given a constellation diagram, it may be calculated?

    This isn't homework btw, it exam revision :-s
  2. jcsd
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