E(s()| (2.108) 
SNR|S(w)} = —————,. 
[var. [sw)}]/° 
If we use the asymptotic normality of $(w), for large N 
§(@)-E\S@)}| _ 5} __P_ (2.109) 
E(s@)| ae 100 
So if we set 
var. [S(@ re 
6@) = cp) (2.110) 
S(@) 
and omit the bias bw) in Eq. 2.103, i.e., if bw) =0 or E[s(w)] — s(@), then 
1 
PDE aah IS DT (2.111) 
OICe) SNRS@)| 
This relation shows that SNR {sw} is a simplified version of d(w), when the bias 
of S() is ignored. 
Also SNR can be expressed by equivalent degree of freedom, defined by Eq. 2.98 
as Vv = ———, and as S(w) follows the y7—distribution with degree of freedom 
r 
Ty 
v, where the mean and variance are v and 29, 
2v 2 
or 
v = 2[SNR{5()}]*. (2.112) 
From Eqs. 2.111 and 2.112, 
6) = c(p) /2/v. (2.113) 
41 
