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Communication Systems ENGR-449
Final Exam
Closed Book
Fall 2021
Time: 90 min.
1. Consider a bandpass communications link with a bandwidth of 0.5 MHz and with an available
C/N0 = 32dB Hz. The maximum bit error rate is 10?6. If the modulation is square 16-QAM using
the SRRC pulse shape with ? = 0.5,
a) What is the maximum achievable bit rate on this link?
b) Is this a power limited or bandwidth limited channel?
2. Consider a voice-grade telephone circuit with a bandwidth of 3 KHz. Assume that the
circuit can be model as an AWGN channel.
a. What is the channel capacity of such a circuit if the SNR is 20dB?
b. What is the minimum SNR required for data rate of 1200 bits/s on such a voicegrade circuit?
c. Repeat part b for data rate of 19200 bits/s.
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3. Binary data are transmitted using 8-PAM over a bandlimited channel, using the raised cosine
roll-off characteristic shown in the figure below
X(f)
T
T/2
-3.75
-2.5
-1.25
1.25
2.5
3.75
F (MHz)
Figure 1. Raised-cosine spectrum of a digital communication system.
(a) Determine the roll-off factor ? and the bit rate, in bits/s, of this system.
(b) Signals are transmitted over a bandlimited AWGN channel. Determine the minimum
probability of a bit error if the bit energy-to-noise ratio (Eb/N0) is limited to a maximum of 20 dB.
4. A voice signal (frequency range: 300-3300Hz) is digitized such that the quantization distortion
? 1% of the peak-to-peak signal voltage. Assume a sampling rate of 8000 samples/s and a
multilevel baseband PAM waveform with M=32 levels. Find the theoretical minimum system
bandwidth that avoids ISI.
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5. In a digital transmission system, a source contains 8 different symbols that occur with the
probabilities shown below:
Symbol
S0
S1
S2
S3
S4
S5
Probability
1/2
1/4
1/8
1/16
1/32
1/64 1/128 1/128
S6
S7
(a) Calculate the average bits of information per symbol (entropy) of the source.
(b) If source emits symbols every 10-6 second and a fixed length code is used, what is the
information bit-rate for this communication system.
(c) What should be bandwidth of the communication channel to guarantee the possibility of
error free transmission of these information (very low probability of error) if the signalto-noise ratio, SNR, of received signal is 10dB.

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