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

586 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
Observe that the integrand is a Ricean density, and, hence, its integral is unity. Therefore,
Note that for a matched filter,
2
A 2E p
Pmax = a 2 = N
n
For FSK, E b = E p , and Eq. (10.144a) becomes
Similarly,
and
(10.144a)
(10.144b)
(10.144c)
(10.145)
This behavior is similar to that of noncoherent ASK [Eq. (10.142c)]. Again we observe that
for E b / N » l, the performance of coherent and noncoherent FSK are essentially similar.
From the practical point of view, FSK is to be preferred over ASK because FSK has a
fixed optimum threshold, whereas the optimum threshold of ASK depends on E b / N (the signal
level). Hence, ASK is particularly susceptible to signal fading. Because the decision of FSK
involves a comparison between ro and r1 , both variables will be affected equally by signal
fading. Hence, channel fading does not degrade the noncoherent FSK performance as it does
the noncoherentASK. This is the outstanding advantage of noncoherent FSK over noncoherent
ASK. In addition, unlike noncoherent ASK, probabilities P(E lm = 1) and P(E lm = 0) are
equal in noncoherent FSK. The price paid by FSK for such an advantage is its larger bandwidth
requirement.
Noncoherent MFSK
From the practical point of view, phase coherence of M frequencies is difficult to maintain.
Hence in practice, coherent MFSK is rarely used. Noncoherent MFSK is much more common.
The receiver for noncoherent MFSK is similar to that for binary noncoherent FSK (Fig. 10.39),
but with M banks corresponding to M frequencies, in which filter H i (f) is matched to the RF
pulse p(t) cos wit- The analysis is straightforward. If m = 1 is transmitted, then r1 is the envelope
of a sinusoid of amplitude A p
plus bandpass Gaussian noise, and r1 U = 2, 3, ... , M ) is
the envelope of the bandpass Gaussian noise. Hence, r1 has Ricean density, and r2, r3 , ... , r M
have Rayleigh density. From the same arguments used in the coherent case, we have
1 00 r1 (T]A p ) -(r2+A2)/2u2 (1'1 X -x2/2a2 d )M- 1 d
PcM = P(Clm = 1) = P(O :S r1 < oo, n2 < r1 , n3 < r1 , . .. , n M < r1)
1 00
= 2 Io - 2
- e 1 p n
2 e n X ri
0 0
r1 (T]Ap ) - (
r2
+A2)/2<T 2 ( -r2/2a2 ) M -l
= - Io -- e 1 P " l - e 1 n dri
o a; a;