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

562 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
where the limits of integration of b1 are (-oo, oo), and for the remaining variables the limits
are (-oo, b1). Thus,
(10.114b)
Similarly, P(C lm2), ... , P(ClmM) can be computed, and
P(C) = L P(Clm1)P(m1)
j=I
and
P eM = l -P(C)
Example 10.4 Orthogonal Signal Set
In this set all M equal-energy signals s1 (t), s2 (t), ..., SM (t) are mutually orthogonal. As an
example, a signal set for M = 3 is shown in Fig. 10.27.
Figure 10.27
Orthogonal
signals.
s2 'P2_._
The orthogonal set {sk (t)) is characterized by
j -I k
j = k
(10.115)
Hence,
Pi} = <Si, Sj > = {
i -I j
i = j
(10.116)