563489578934

– f c f c
f
566
Performance of Communication Systems Corrupted by Noise Chap. 7
7–39 Referring to Fig. P7–38, suppose that the receiver consists only of the upper portion of the figure,
so that point C is the output. Let the input be an SSB signal plus white noise with a PSD of N 0 /2.
Find (S/N) out .
7–40 Consider the receiver shown in Fig. P7–40. Let the input be a DSB-SC signal plus white noise
with a PSD of N 0 /2. The mean value of the modulation is zero.
(a) For A 0 large, show that this receiver acts like a product detector.
(b) Find the equation for (S/N) out as a function of A c , m 2 , N 0 , A 0 , and B T when A 0 is large.
Bandpass input
r(t)=s(t)+n(t)
Bandpass filter
H(f)
|H(f)|
B T
+
+
A 0 cos[ c t+¨c ]
Envelope
detector
Output
m
~
(t)
Capacitor
(allows only
AC to pass)
1
Oscillator
Figure P7–40
7–41 Compare the performance of AM, DSB-SC, and SSB systems when the modulating signal m(t) is
a Gaussian random process. Assume that the Gaussian modulation has a zero mean value and a
peak value of V p = 1, where V p ≈ 4s m . Compare the noise performance of these three systems by
plotting (S/N) out /(S/N) baseband for
(a) The AM system.
(b) The DSB-SC system.
(c) The SSB system.
7–42 If linear modulation systems are to be compared on an equal peak power basis (i.e., all have equal
peak signal values), show that
(a) SSB has a (S/N) out that is 3 dB better than DSB.
(b) SSB has a (S/N) out that is 9 dB better than AM.
(Hint: See Prob. 5–11.)
7–43 Using Eq. (7–132), plot the output SNR threshold characteristic of a discriminator for the parameters
of a conventional broadcast FM system. (∆F = 75 kHz and B = 15 kHz.) Compare plots of the
(S/N) out vs. (S/N) baseband for this system with those shown in Fig. 7–24.
★ 7–44 An FM receiver has an IF bandwidth of 25 kHz and a baseband bandwidth of 5 kHz. The noise
figure of the receiver is 12 dB, and it uses a 75-µsec deemphasis network. An FM signal plus
white noise is present at the receiver input, where the PSD of the noise is N 0 /2 = kT/2. T = 290
K. (See Sec. 8–6.) Find the minimum input signal level (in dBm) that will give a SNR of 35 dB at
the output when sine-wave test modulation is used.
7–45 Referring to Table 5–4, note that a two-way FM mobile radio system uses the parameters b f = 1
and B = 5 kHz.
(a) Find (S/N) out for the case of no deemphasis.
(b) Find (S/N) out if deemphasis is used with f 1 = 2.1 kHz. It is realized that B is not much larger
than f 1 in this application.