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

where the pulse energy is simply
l 0.3 Coherent Receivers for Digital Carrier Modulations 521
= 2 fo
T b [p ' (t) )
2
cos 2 W e t dt
= fo \p 1 (t)f dt
= E p
,
This result requires a carrier frequency sufficiently high such that J c Tb > > 1.
Binary ASK
Similarly, for binary ASK, the transmission is
1 : ,/2,p' (t) COS W e t
0: 0
This coincides with the on-off signaling analyzed earlier such that the optimum threshold
should be a 0 = E p
/2 and the minimum BER for binary ASK is
(10.40)
where
Comparison of Eq. (10.39) and Eq. (10.40) shows that for the same performance, the pulse
energy in ASK must be twice that in PSK. Hence, ASK requires 3 dB more power than PSK.
Thus, in optimum (coherent) detection, PSK is always preferable to ASK. For this reason, ASK
is of no practical importance in optimum detection. But ASK can be useful in noncoherent
systems (e.g., optical communications). Envelope detection, for example, can be applied to
ASK. In PSK, the information lies in the phase, and, hence, it cannot be detected noncoherently.
The baseband pulses p(t) used in carrier systems should be shaped to minimize the ISi.
The bandwidth of the PSK or ASK signal is twice that of the cmTesponding baseband signal
because of modulation.*
Bandpass Matched Filter as a Coherent Receiver
For both PSK and ASK, the optimum matched filter receiver of Fig. 10.5a can be implemented.
As shown in Fig. 10.9a, the received RF pulse can be detected by a filter matched to the RF
pulse p(t) followed by a sampler before a threshold detector.
On the other hand, the same matched filter receiver may also be modified into Fig. 10.9b
without changing the signal samples for decision. The alternative implementation first demodulates
the incoming RF signal coherently by multiplying it with ,/2,cos w e t, The product is
* We can also use QAM (quadrature multiplexing) to double bandwidth efficiency.