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

564 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
Changing the variable so that b1 / J NE /2 = y, and recognizing that E / N = (log 2 M)
Eb/N, we obtain
(10.120b)
(10.120c)
Note that this signal set is geometrically symmetrical; that is, every signal has the same
relationship with other signals in the set. As a result,
Hence,
P(C) = P(Clm1)
and
PeM = l -P(C)
= I __ l _
!
00
-[v-J(21og e 2
M)Eb!Nr /2 [l _ Q (y)] M-1 dy
$ -oo ( 10.120d)
In Fig. 10.28 the result of PeM vs. Eb/N is computed and plotted. This plot shows an
interesting behavior for the case of M = oo. As M increases, the performance improves
but at the expense of larger bandwidth. Hence, this is a typical case of trading bandwidth
for performance.
Multitone Signaling (MFSK)
In the case of multitone signaling, M symbols are transmitted by M orthogonal pulses of
frequencies cv1 , cv2, ... , WM , each of duration TM . Thus, the M transmitted pulses are of
the form
2rr (N + k)
The receiver (Fig. 10.29) is a simple extension of the binary receiver. The incoming pulse is
multiplied by the corresponding references ,J2 cos cv;t (i = 1, 2, ... , M). The filter H (f) is
matched to the baseband pulse p'(t) such that
h(t) = p'(TM - t)
The same result is obtained if in the ith bank, instead of using a multiplier and H (f), we use
a filter matched to the RF pulse p' (t) cos wit. The M bank outputs sampled at t = TM are
b1 , b2, ... , bM .