B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

576 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
Figure 10.33
Simplex signals. '1'2 '1'2
{E
m
{E S1 '1'1 - '1'1 -
(a)
'1'3
'-/2£13
'iE/2
s '
1 s'2 'P1---+-- '1'1 -
s'1
s'2
(c)
/ (d)
We can calculate the mean energy of the simplex set by noting that it is obtained by
translating the orthogonal set by a vector a, given in Eq. (J0.127),
For orthogonal signals,
I
M
a = M Ls;
i=l
Therefore,
./E M
a = M L<P;
i=I
where E is the energy of each signal in the orthogonal set and (f); is the unit vector along the
ith coordinate axis. The signals in the simplex set are given by
(10.128)
The energy E' of signal s is given by Is 1 2 ,
E' = <S , S > (10.129)