Sample Questions
Lecture No. 22
Dr. Aoife Moloney
School of Electronics and Communications
Dublin Institute of Technology
Lecture No. 23: Sample Questions
Overview
This lecture has looked at the following:
• Sample questions on the detection of bandpass signals in
AWGN.
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Lecture No. 23: Sample Questions
Sample Questions on the Detection
of Bandpass Signals in AWGN
• Question 1:
(a) Define the following terms:
(i) Analog modulation (ii) Digital modulation (iii) Digital
baseband modulation (iv) Digital passband modulation.
(b) Explain the benefit of modulation.
(c) Describe phase shift keying (PSK), frequency shift
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Lecture No. 23: Sample Questions
keying (FSK), amplitude shift keying (ASK) and amplitude phase keying (APK), giving the defining equation
and diagram in each case.
• Question 2:
(a) Draw a block diagram of a generic optimum coherent
receiver.
(b) Consider binary PSK (BPSK), where the two signals
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Lecture No. 23: Sample Questions
are given by:
r
2E
cos (2πf t)
s1 (t) =
T
r
2E
s2 (t) =
cos (2πf t + π)
T
(i) Represent these two signals in signal space using a
single basis function:
r
2
cos (2πf t) , f or 0 ≤ t ≤ T
Φ1 (t) =
T
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Lecture No. 23: Sample Questions
(ii) Draw a signal space diagram for BPSK, showing clearly
the two signals s1 (t) and s2 (t) and the two decision regions.
(iii) Give an equation for the probability of bit error for
coherent detection of BPSK, in terms of the energy per
binary bit, Eb , and the single–sided noise power spectral
density, N0 . State clearly whether the probability of error increases or decreases as the energy of the transmitted
signal increases.
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Lecture No. 23: Sample Questions
(iv) Explain how a BPSK signal is generated and give a
block diagram of a BPSK transmitter.
(v) Explain what is meant by coherent detection and
draw a block diagram of a coherent BPSK receiver.
• Question 3:
Find the bit error probability for a BPSK system with
a bit rate of 1 Mbit/s. The received waveforms, s1 (t) =
Acosω0 t and s2 (t) = −Acosω0 t, are coherently detected.
The value of A is 10 mV. Assume that the single–sided
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Lecture No. 23: Sample Questions
noise power spectral density is N0 = 10−11 W/Hz and
that signal power and energy per bit are normalised relative to a 1 Ω load.
Solution:
Assuming that signal power and energy per bit are normalised to a 1 Ω load we have:
A2 T
E = Eb =
2
Note: The energy and the energy per bit are equal for
binary PSK!
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Lecture No. 23: Sample Questions
We are given:
A = 10mV = 0.01V
1
1
1
=
=
= 10−6 s
T =
bit rate
1M bit/s
1000000
So
(0.01)2 (10−6 )
⇒ Eb =
= 5 × 10−11 J
2
For BPSK we have:
!
r
2Eb
Pe = Q
N0
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Lecture No. 23: Sample Questions
We have been given N0 = 10−11 W/Hz, therefore:
!
r
2 × 5 × 10−11
Pe = Q
10−11
Giving:
√ Pe = Q
10 = Q (3.16)
Looking up the tables for Q(3.16) we get Pe = 0.0008.
• Question 4:
(a) Explain quadriphase shift keying (QPSK) giving the
relevant equation.
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Lecture No. 23: Sample Questions
Express the possible QPSK signals si (t) using the following two basis functions:
r
2
cos (2πf t)
Φ1 (t) =
T
r
2
Φ2 (t) =
sin (2πf t)
T
(c) Draw a signal space diagram for QPSK, showing clearly
the decision regions.
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Lecture No. 23: Sample Questions
(d) Give the equations for the probability of bit error for
coherent detection of QPSK in terms of the energy per
symbol and the energy per bit. How does the probability
or error per bit for QPSK compare with that of BPSK?
(e) Explain how a QPSK signal is generated and give a
block diagram of a QPSK transmitter.
(f) Explain the coherent detection of QPSK with particular reference to the decision blocks. Draw a block
diagram of a coherent QPSK receiver.
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Lecture No. 23: Sample Questions
(g) Compare BPSK and QPSK with reference to power
spectral density, bandwidth and probability of bit error.
• Question 5:
(a) Explain M –ary phase shift keying (MPSK) giving the
relevant equation.
(b) Draw a signal space diagram for MPSK with M = 8.
Show clearly the decision regions and decision boundaries.
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Lecture No. 23: Sample Questions
(c) For large energy to noise ratios, the average probability of symbol error, Pe , for equally likely coherently
detected M –ary PSK can be expressed as:
!
r
π
2E
Pe ≈ 2Q
sin
N0
M
Comment on this equation with particular reference to
signal to noise ratio and number of signals, M .
(d) Draw a block diagram for a coherent MPSK receiver.
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Lecture No. 23: Sample Questions
(e) Give equations for the bandwidth, B, and the bandwidth efficiency, ρ, for MPSK. Calculate the bandwidth
efficiency for M = 2, 4, 8, 16, 32, 64. Comment on the
findings in terms of error performance, signal to noise ratio and number of signals, M .
• Question 6:
(a) Explain M –ary quadrature amplitude modulation (QAM)
giving the relevant equation.
(b) Draw a signal space diagram for M –ary QAM with
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Lecture No. 23: Sample Questions
M = 16.
(c) Compare M –ary QAM and M –ary PSK.
• Question 7:
(a) Explain binary frequency shift keying (BFSK) giving
the relevant equation.
(b) Draw the signal space diagram for BPSK, indicating
clearly the two decision regions.
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Lecture No. 23: Sample Questions
(c) Give an equation for the probability of bit error for
BFSK in terms of energy per bit, Eb , and single–sided
noise power spectral density, N0 . Compare the probability of bit error for BFSK with that of BPSK.
(d) Draw a block diagram of a coherent BFSK receiver.
• Question 8:
(a) Explain M –ary frequency shift keying (MFSK) giving
the relevant equation.
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Lecture No. 23: Sample Questions
(b) Draw a block diagram of a coherent MFSK receiver.
(c) Give an equation for the channel bandwidth, B, required to transmit M –ary FSK. Give the equation for the
bandwidth efficiency of M –ary FSK, ρ.
(d) Calculate the bandwidth efficiency for MFSK for M =
2, 4, 8, 16, 32, 64. Comment on the results and compare
them with the bandwidth efficiency of MPSK.
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Lecture No. 23: Sample Questions
Conclusion
This lecture has looked at the following:
• Sample questions on the detection of bandpass signals in
AWGN.
April 2005
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18