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

558 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
Figure 10.25
MPSK signals.
S3
.,.---
//
E
I
I I
--
+
q2
(a)
qi ....
SM- I
(b)
Also,
P(Clmi) = P(q lies in Ri)
This is simply the volume under the conical region of the joint PDF of q1 and q2. Because
n1 and n2 are independent Gaussian RVs with variance N /2, q1 and q2 are independent
Gaussian variables with means ../E and 0, respectively, and each with variance N /2.
Hence,
and
(10.105a)
(10.105b)
To integrate over R1, we first integrate over the solid vertical strip in Fig. 10.25b. Along
the border of R1,
q2 = ±(tan ; ) q1