EE7620 Homework Set 2 Solution:
1. g(r) =m1 iff p R / M (r / m1 ) pM (m1 ) p R / M (r / m0 ) p M (m0 )
From the figure, g (r ) = m1 iff r < 2
m1
g (r ) =
m0
if r < 2
3
and
3
if 2 r 1
3
2
P( / m0 ) = p R / M (r / m1 )dr =
I1
3
p
2
R/M
(r / m1 )dr = 4
9
3
Solution for Homework 3
Problem 1: i By equal prior probability, we have MAP rule:
1 exp , x , i ;
MAP : m = argmin P ~jmi ; P~jm xjmi = p
^
r
r
2
2
where 0 = ,3a=2, 1 = ,a=2, 2 = a=2, and 3 = 3a=2. This yields:
8
m0 ; ,2a ri ,a;
m1 ; ,a ri 0;
m=
^
m2 ; 0
Solution for Homework 3
1. The signal constellation points are located at 0:5d; 1:5d; : : : ; 0:5M , 1d. The energy
levels of the various signals are 0:52 d2 ; 0:52 9d2 ; : : : ; 0:52 M , 12 d2 . For i, we have
2
,
P = MM 2 P jinner point + M P jouter poi
Homework 5
I. For noncogerent receiver in Figure 3.4.4. of Section 3.4.2, show that in the case of M =
2 X0 ; X1; Y0; Y1 are all independent, and show that in the case of M 2, all Zi's are
independent.
II. A signal must be designed to transmit binary data
Solution to Midterm I: EE7620
1. It is easy to see that we have only two independent functions among the four.
Because s t and s t are orthogonal to each other, we obtain
t = s t = s t;
0
3
0
ks k
0
0
3
0
2
2
p
st
t = ksk = 3s t:
In terms of coordinator o