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

Additionally, substituting q(t) = 0 into Eqs. (10.24) and (10.25) yields
10.2 General Binary Signaling 519
E q
= 0, E pq
= 0,
and
(10.34)
If both symbols m = 0 and m = 1 have equal probability 0.5, then the average bit energy is
given by
Therefore. the BER can be written as
(10.35)
A comparison of Eqs. (10.35) and (10.33) shows that on-off signaling requires exactly twice
as much energy per bit (3 dB more power) to achieve the same performance (i.e., the same P b )
as polar signaling.
Orthogonal Signaling
In orthogonal signaling, p(t) and q(t) are selected to be orthogonal over the interval (0, Tb )­
This gives
{Tb
E pq
=
J
o p(t)q(t) dt = 0 (10.36)
On-off signaling is in fact a special case of orthogonal signaling. Two additional examples of
binary orthogonal pulses are shown in Fig. 10.7. From Eq. (10.25),
(10.37)
Assuming 1 and O to be equiprobable,
Figure 10.7
Examples of
orthogonal
signals.
p(t)
sin nw ( /
"I
(a)
q(t) q(t) sin mw 0 t
Tb t-
t-
T,12
Tb
(b)
t-+-
t-
w = 0 2'1T
Tb