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

522 PERFORMANCE ANALYSIS OF DIGITAL COMMUNICATION SYSTEMS
Fi g
ure 10.9
Coherent
detection of
digital
modulated
signals.
t = nT
p(t) = -fi_p '(t) cos we t
I r-° b
h(t) = p(Tb - t)
(a)
Threshold
device
Decision
p(t) = -fi_p '(t) COS ll) C
f
h(t) = p '(Tb - t)
(b)
Threshold
device
Fi g
ure 10. 10
Optimum
coherent
detection of
binary FSK
signals.
y(t)
.t b dt
0
Threshold
decision
device
;_Tb dt
0
the baseband pulse* p' (t) plus a baseband noise with PSD N /2 (see Example 9.13), and this is
applied to a filter matched to the baseband pulse p' (t). The two receiver schemes are equivalent.
They can also be implemented as correlation receivers.
Frequency Shift Keying
In FSK, RF binary signals are transmitted as
0: -v12p' (t) cos [w e - (w/2)]t
1 : -vf2p'(t) cos [w e + (w/2)]t
Such a waveform may be considered to be two interleaved ASK waves. Hence, the PSD will
consist of two PSDs, centered at [f e - (f /2)] and [f e + (f /2)]. For a large f /fe, the PSD
will consist of two nonoverlapping PSDs. For a small f /fe, the two spectra merge, and the
bandwidth decreases. But in no case is the bandwidth less than that of ASK or PSK.
The optimum correlation receiver for binary FSK is given in Fig. 10.10. Because the pulses
have equal energy, when the symbols are equally likely, the optimum threshold a 0 = 0.
Consider the rather common case of rectangular p' (t) = A, that is, no pulse shaping
in FSK.
q(t) = ✓ 2 A cos (w e - t}
p(t) = ✓ 2 A cos (w e + t}
* There is also a spectrum of p' (t) centered at 2w c , which is eventually eliminated by the filter matched to p' (t) .