Likelihood function for non-coherent detection Show that the likelihood function k e Ek N0 I0 2 ffiffiffiffiffiffi Ek p N0 jLkj

Likelihood function for non-coherent detection Show that the likelihood function

k ¼ e

Ek N0

 

I0 2

ffiffiffiffiffiffi Ek p

N0 jLkj



;

which is discussed in Section 5.2 for non-coherent detection, can be derived from

kðÞ ¼ ez;

where z ¼ 2 N0 Z T 0

xðtÞskðt; Þdt
1 N0 Z T 0

s2 kðt; Þdt;

and it is assumed that the phase is uniformly distributed.