# Symbol Error Probability for AWGN channels

1. May 17, 2013

### MathsDude69

Hey folks,

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

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

Whereby:

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