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BEng/MEng Degree Examinations 2020-1
Department: Electronic Engineering
Title of Exam: Digital Communication Systems for MSc
Time Allowed: 24 Hours (PLEASE NOTE: papers submitted more
than 30 minutes after the deadline will not be
Time Recommended: THREE hours
Allocation of Marks: All questions carry equal marks
Instructions for Candidates: You should attempt all 3 questions.
Write all of your answers by hand (unless you have a Student Support Plan
which allows use of a PC) and submit your handwritten answers in a single
Use only black or blue pen for any handwritten answers. Clearly write your
examination number on each page submitted. Begin each question on a
new page and clearly write the question number on each page.
More detailed instructions regarding submission of your work and conduct
during the open exam is given on the next page. Please read this carefully
before you begin, including the information regarding the conduct
expected of you during the exam.
Please see the detailed instructions on the next page regarding exam queries.
The exam setter for this exam is Dr Ruwan Gajaweera who if necessary can
be contacted by email at firstname.lastname@example.org. Please copy any
email that you send to the Chair of Board of Examiners
(email@example.com) and to firstname.lastname@example.org.
© University of York Page 2 of 9
A note on Academic Integrity:
We are treating this online examination as a time-limited open assessment, and you are
therefore permitted to refer to written and online materials to aid you in your answers.
However, you must ensure that the work you submit is entirely your own, and for the whole
time the assessment is live you must not:
● communicate with departmental staff on the topic of the assessment, except for the
● communicate with other students on the topic of this assessment.
● seek assistance with the assignment from the academic and/or disability support
services, such as the Writing and Language Skills Centre, Maths Skills Centre and/or
Disability Services. (The only exception to this will be for those students who have
been recommended an exam support worker in a Student Support Plan. If this applies
to you, you are advised to contact Disability Services as soon as possible to discuss
the necessary arrangements.)
● seek advice or contribution from any third party, including proof-readers, friends, or
We expect, and trust, that all our students will seek to maintain the integrity of the assessment,
and of their award, through ensuring that these instructions are strictly followed. Failure to
adhere to these requirements will be considered a breach of the Academic Misconduct
regulations, where the offences of plagiarism, breach/cheating, collusion and commissioning
are relevant - see AM.1.2.1”
Please make sure you note the following detailed instructions:
• If you do not submit by the deadline you will score a mark of zero unless you submit in
the first 30 minutes after the deadline in which case your mark will be subject to a 5%
late penalty. The deadline is not flexible, it may take a while for your file to be
processed through the system. Make sure you submit in good time to allow for this.
• You must submit your answers as a single pdf file. Please check that all scanned
pages are clear and visible BEFORE you submit. The Adobe Scan app is a free app
that works on all phones and can be used to photograph and then connect together all
the scans into a single document - ensure all your pages are in the correct order.
• Please make sure that every page is clearly labelled with both your examination
number (NOT your name) and the question number. It would be useful if you
numbered the pages.
• The file size limit for anonymised work submitted online is 30MB per file. Please
see Compressing File Sizes (Student Guide) for details on reducing the file sizes. If
your submission remains too large or if you experience genuine technical difficulties
when trying to submit, then you should email your submission to elec-
email@example.com. If the assessment is too large to send by email, you may use
the University of York Deposit Service. If using this service as the back-up please
specify firstname.lastname@example.org as the recipient of the drop-off. Please do not use
this backup option if the VLE submission has worked properly and you have received a
• University policy is that corrections or clarifications to the questions in the exam paper
will only be issued within the first hour of the submission window. Therefore if outside
the first hour you should answer the question as best as you can and note the
assumptions that you have made to allow you to proceed.
• All submissions may be screened for collusion and plagiarism. By submitting your
assignment you agree to the University rules on Collusion and Plagiarism. The
Department will run submissions through Turnitin wherever possible. For more
information visit york.ac.uk/integrity
• You may make multiple submissions up to the assessment deadline but by default, we
will mark your last submission before the deadline.
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IT IS YOUR RESPONSIBILITY TO MAKE SURE THAT YOUR SUBMISSION IS CORRECT.
Once you have submitted your assignment via the VLE, a 'receipt' screen appears that has a
link to the submitted file, so you can click the link and check the file to make sure it is the
correct one. You can also click back into the submission point and see links to the file(s) you
© University of York Page 4 of 9
(a) [18 Marks in total]
Figure 1 Line spectrum
Figure 1 shows a line spectrum of a signal up to the fifth harmonic
for the positive frequencies. Answer the following sub-questions
with no more than two sentences per each sub-question.
(i) What is the frequency of the time domain signal? (2 marks)
(ii) Calculate the power in this signal assuming an impedance
of 50 ohms. (8 marks)
(iii) Giving reasons, comment on the shape of the time domain
signal represented by this spectrum. (8 marks)
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(b) [32 Marks in total]
A baseband modulation scheme is using a 50% polar Return-to-
Zero (RZ) modulation scheme.
(i) Sketch the waveform to send a data packet containing a bit
stream of 1110001010. (6 marks)
(ii) What may be a disadvantage of this modulation scheme? (4
(iii) Draw the impulse response for the 50% RZ transmit filter
where T is the symbol duration. Sketch the input signal to
the filter to generate the RZ waveform you drew in (i). (10
(iv) Derive the expression for the frequency response of the
transmit filter and sketch the magnitude of the spectrum if
the symbol rate is 1 kbaud. Your sketch does not have to be
to scale, but must be fully labelled. (12 marks)
© University of York Page 6 of 9
(a) [10 Marks in total]
A well-know expression for the bit error rate for the polar
signalling is: = (√
(i) The above formula expression assumes Additive White
Gaussian Noise (AWGN). State other two assumptions
under which this formula is valid. (4 marks)
(ii) If the noise at the input to the receive filter isn’t Gaussian,
but it is still white, can this formula still be used for predicting
the bit error rate? Explain your answer with no more than
two sentences. (6 marks)
(b) [20 Marks in total]
A 100mW transmitter is used for a baseband communication
system using a polar modulation scheme operating at 1 Mbaud.
The noise present in the system is Additive White Gaussian noise
with a power spectral density of 10 nW/Hz.
(i) It has been decided to use a unipolar scheme which gives
the same bit error rate performance as the polar scheme.
Determine the required power of the transmitter based on
the provided information. Explain your answer including any
assumptions that you have made. (10 marks)
(ii) It has been found that the magnitude of the noise power
spectral density for the above described unipolar system
has doubled. What is the minimum bit error rate that the
system can achieve? (10 marks)
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(c) [20 Marks in total]
One unavoidable occurrence in QPSK is that the signal
trajectories in the equivalent baseband pass through the origin of
the complex plane for certain symbol transitions.
(i) Draw the constellation diagram of QPSK with a suitable bit
allocation to each symbol. (4 marks)
(ii) According to your diagram, state which symbol transitions
give rise to signal trajectories through the origin. Explain
why this could be a problem. (10 marks)
(iii) Explain one of the known ways to deal with the problem you
stated above. (6 marks)
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(a) [20 Marks in total]
An engineer decided to use the constellation in Figure 2 for a
linear modulation scheme. The constellation points are equi-
distant from the origin.
The optimum signal to noise ratio at the output of a matched filter
for the passband communication can be expressed as:
where NE and SE are the equivalent baseband representation of
noise and signal power respectively.
You should provide sufficient explanations for the approximations
when answering (i) - (iv) below.
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(i) Carefully copy the constellation diagram to your answer
script. Mark on your diagram the amplitude of a symbol if the
power of a symbol is given as S. (4 marks)
(ii) What is the mean symbol power in the equivalent baseband
for the modulation scheme? (2 marks)
(iii) Derive an expression for the probability of an error for a
symbol at low error rates in Additive White Gaussian noise
in terms of the symbol energy Es and single-sided noise
power spectral density N0. (12 marks)
(iv) Based on your answer to (iii), what is the mean probability of
a symbol error, PS? (2 marks)
(b) [30 Marks in total]
(i) How many bits can the modulation scheme send per
symbol? (2 marks)
(ii) Assign bits to symbols to minimise the number of bit errors.
(iii) Hence derive the probability of a bit error in terms of Eb/N0
ratio. (8 marks)
(iv) Compare this modulation scheme with the Binary Phase
Shift Keying (BPSK) to recommend which modulation
scheme is better and why? Your answer should not be
longer than five sentences. (10 marks)
(v) Draw the waveform for the in-phase (I) and quadrature (Q)
components for the following bit pattern: 10011100. Your
sketch does not have to be to a scale, but should include
important details. (6 marks)
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