PROBLEMS 74315.3.19By a simple time multiplexing of natural samples
over a single line, a large radar site transmits 85
analog signals, each with 200-Hz bandwidth. If
the sampling is done at twice the Nyquist rate, one
time slot is used for synchronization, and the guard
timeτg= 2 τ, find the durationτof the pulse.
15.3.20Sketch an ASK signal for the binary sequence 1 0
11001001ifωc= 3 ωb= 6 π/Tb.
15.3.21In Equation (15.3.24), for coherent ASK,Eb=
A^2 Tb/4, withA = 2 .2V,Tb = 2. 6 μs, and
N 0 = 2 × 10 −^7 V^2 /Hz, findPefor a coherent ASK
system. Also, findEbfora1-impedance.
*15.3.22In Figure 15.3.14, when the pulse of a carrier of
amplitudeAduring 0<t≤Tbarrives at point
R, show thatD∼=A^2 Tb/4 at timeTbif noise is
neglected andωcTb>>1.
15.3.23IfEb/N 0 =20 in a coherent ASK system, find the
value ofEb/N 0 that is needed in a noncoherent
ASK system to yield the same value ofPeas the
coherent system.
15.3.24To have the same value ofPe, show thatEb/N 0 in
a coherent-ASK system has to be twice that in a
coherent PSK system.
15.3.25In a DPSK system, when the received pulses are
2 V in amplitude,Pe= 3 × 10 −^4. If the pulse
amplitude increases such thatPe= 2 × 10 −^6 , find
the new amplitude.
15.3.26Consider Figure 15.3.19, in which the receiver
becomes two coherent ASK receivers in parallel.
Justify why the difference, rather than the sum,
occurs.
15.3.27Consider Figure 15.3.19, in which the input FSK
pulse at pointRis given bysR(t)=Acos(ω 2 t+
φ 2 ), 0 <t<Tb, and zero elsewhere int, when
the bit interval corresponds to a 1.
(a) Compute the outputs from the two integrators.
(b) IfsR(t) changes in frequency and phase toω 1
andφ 1 , respectively, show that the two outputs
of part (a) are reversed. (AssumeωcTb>>1,
and make suitable approximations.)
*15.3.28Apply Equation (15.3.24) for various digital com-
munication systems withEb/N 0 =12, and using
PSK as the reference, compare their performances.
15.3.29A communication system for a voice-band (3 kHz)
channel is designed for a received SNREb/N 0 at
the detector of 30 dB when the transmitter power is
Ps=−3 dBW. Find the value ofPsif it is desired
to increase the bandwidth of the system to 10 kHz,
while maintaining the same SNR at the detector.