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Sec. 7–8 Output Signal-to-Noise Ratios for Analog Systems 531
practice, since the receiver cost is usually lower. This is the case for overall system cost in
applications involving one transmitter and thousands or millions of receivers, such as in FM,
AM, and analog TV broadcasting.
For systems with additive noise channels the input to the receiver is
r(t) = s(t) + n(t)
For bandpass communication systems having a transmission bandwidth of B T ,
r(t) = Re{g s (t)e j(v ct+u c ) } + Re{g n (t)e j(v ct+u c ) }
= Re{[g s (t) + g n (t)]e j(v ct+u c ) }
or
where
r(t) = ReEg T (t)e j(v ct+u c ) F
g T (t) ! g s (t) + g n (t)
= [x s (t) + x n (t)] + j[y s (t) + y n (t)]
= x T (t) + jy T (t)
= R T (t)e ju T
(t)
(7–83a)
(7–83b)
g T (t) denotes the total (i.e., composite) complex envelope at the receiver input; it consists of the
complex envelope of the signal plus the complex envelope of the noise. The properties of the total
complex envelope, as well as those of Gaussian noise, were given in Chapter 6. The complex
envelopes for a number of different types of modulated signals g s (t) were given in Table 4–1.
Comparison with Baseband Systems
The noise performance of the various types of bandpass systems is examined by evaluating
the signal-to-noise power ratio at the receiver output, (SN) out , when a modulated signal plus
noise is present at the receiver input. We would like to see if (SN) out is larger for an AM system,
a DSB-SC system, or an FM system. To compare these SNRs, the power of the modulated
signals at the inputs of these receivers is set to the same value and the PSD of the input
noise is N 0 2. (That is, the input noise is white with a spectral level set to N 0 2.)
To compare the output signal-to-noise ratio (SN) out for various bandpass systems, we
need a common measurement criterion for the receiver input. For analog systems, the criterion
is the received signal power P s divided by the amount of power in the white noise that is
contained in a bandwidth equal to the message (modulation) bandwidth. This is equivalent to
the (SN) out of a baseband transmission system, as illustrated in Fig. 7–18. That is,
a S N b baseband
= P s
N 0 B
(7–84)
We can compare the performance of different modulated systems by evaluating
(SN) out for each system as a function of (P s N 0 B) = (SN) baseband , where P s is the power of
the AM, DSB-SC, or FM signal at the receiver input. B is chosen to be the bandwidth of the