563489578934

564
Performance of Communication Systems Corrupted by Noise Chap. 7
(b) Explain why Manchester-encoded data are often used when the receiver uses a PLL for
carrier recovery, as in part (a). (Hint: Look at the spectrum of the Manchester-encoded PSK
signal.)
7–28 In obtaining the P e for FSK signaling with coherent reception, the energy in the difference signal
E d was needed, as shown in Eq. (7–46). For orthogonal FSK signaling the cross-product integral
was found to be zero. Suppose that f 1 , f 2 , and T are chosen so that E d is maximized.
(a) Find the relationship as a function of f 1 , f 2 , and T for maximum E d .
(b) Find the P e as a function of E b and N 0 for signaling with this FSK signal.
(c) Sketch the P e for this type of FSK signal and compare it with a sketch of the P e for the
orthogonal FSK signal that is given by Eq. (7–47).
★ 7–29 An FSK signal with R = 110 bits/sec is transmitted over an RF channel that has white Gaussian
noise. The receiver uses a noncoherent detector and has a noise figure of 6 dB. The impedance of
the antenna input of the receiver is 50 v.
The signal level at the receiver input is 0.05 mV, and the
noise level is N 0 = kT 0 , where T 0 = 290 K and k is Boltzmann’s constant. (See Sec. 8–6.) Find
the P e for the digital signal at the output of the receiver.
7–30 Rework Prob. 7–29 for the case of DPSK signaling.
7–31 An analysis of the noise associated with the two channels of an FSK receiver precedes
Eq. (7–44). In this analysis, it is stated that n 1 (t) and n 2 (t) are independent when they arise from a
common white Gaussian noise process because n 1 (t) and n 2 (t) have nonoverlapping spectra.
Prove that this statement is correct. [Hint: n 1 (t) and n 2 (t) can be modeled as the outputs of two
linear filters that have nonoverlapping transfer functions and the same white noise process, n(t),
at their inputs.]
7–32 In most applications, communication systems are designed to have a BER of 10 -5 or less. Find
the minimum E b /N 0 decibels required to achieve an error rate of 10 -5 for the following types of
signaling.
(a) Polar baseband.
(b) OOK.
(c) BPSK.
(d) FSK.
(e) DPSK.
★ 7–33 Digital data are to be transmitted over a telephone line channel. Suppose that the telephone line is
equalized over a 300- to 2,700-Hz band and that the signal-to-Gaussian-noise (power) ratio at the
output (receive end) is 25 dB.
(a) Of all the digital signaling techniques studied in this chapter, choose the one that will provide
the largest bit rate for a P e of 10 -5 . What is the bit rate R for this system?
(b) Compare this result with the bit rate R that is possible when an ideal digital signaling scheme
is used, as given by the Shannon channel capacity stated by Eq. (1–10).
★ 7–34 An analog baseband signal has a uniform PDF and a bandwidth of 3500 Hz. This signal is sampled
at an 8 samples/s rate, uniformly quantized, and encoded into a PCM signal having 8-bit
words. This PCM signal is transmitted over a DPSK communication system that contains additive
white Gaussian channel noise. The signal-to-noise ratio at the receiver input is 8 dB.
(a) Find the P e of the recovered PCM signal.
(b) Find the peak signal/average noise ratio (decibels) out of the PCM system.
7–35 A spread spectrum (SS) signal is often used to combat narrowband interference and for communication
security. The SS signal with direct sequence spreading is (see Sec. 5–13)
s(t) = A c c(t)m(t) cos(v c t + u c )