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ELE00092M
Page 1 of 7
MSc Degree Examinations 2020-1
Department: Electronic Engineering
Title of Exam: Introduction to Signal Processing
Time Allowed: 24 Hours (PLEASE NOTE: papers submitted more than
30 minutes after the deadline will not be marked)
Time Recommended: THREE hours
Allocation of Marks: All questions carry equal marks
Instructions for Candidates: You should attempt all 3 questions.
You may write all of your answers by hand, use a mix of handwritten and typed
answers, or type all of your answers. Whatever method you use, you must submit
your answers in a single pdf document.
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.
Paper Queries:
Please see the detailed instructions on the next page regarding exam queries. The
exam setter for this exam is Dr Yuriy Zakharov who if necessary can be contacted
by email at yury.zakharov@york.ac.uk. Please copy any email that you send to the
Chair of Board of Examiners (eugene.avrutin@york.ac.uk) and to elec-
genoffice@york.ac.uk.
© University of York Page 2 of 7
ELE00092M
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 exam
setter.
● 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 family
members.
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-genoffice@york.ac.uk. 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 elec-
genoffice@york.ac.uk 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 receipt.
• 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.
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
ELE00092M
Page 3 of 7
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 have submitted.
© University of York Page 4 of 7
ELE00092M
1
(a) [28 Marks]
Show that, in the two-user case, the Minimum Mean Squared Error
(MMSE) multiuser detector can be implemented by the scheme in
Figure 1, where )(1 ts and )(2 ts are the user signature waveforms
of a unit energy, 1A and 2A are the user signal amplitudes, and
2 is the noise variance. Note that in the MMSE multiuser
detector, the decision for the k -th user is found as
2,1),sign(ˆ == kzb kk , where kz are elements of the vector
( ) yARz 122 −−+= , y is the vector of the matched filter outputs,
R is the cross-correlation matrix of the user signature waveforms,
and A is a diagonal matrix with diagonal elements equal to the
user signal amplitudes.
(b) [10 Marks]
Explain the difference between frequency-flat and frequency-
selective fading channels.
(c) [12 Marks]
In a communication system, the propagation channel is modelled
as a time-invariant fading channel whose impulse response is a
wide-sense stationary random process. What is the coherence
bandwidth of the channel? The multipath spread of the channel is
2 μs; what is the minimum frequency shift between two frequency-
diversity channels that guarantees uncorrelated fading in the
diversity channels?
ELE00092M
Page 5 of 7
Figure 1: The MMSE multiuser receiver (two-user case)
© University of York Page 6 of 7
ELE00092M
2
(a) [10 Marks]
What is the impulse response of the filter matched to a signal )(ts ?
How does the impulse response depend on the sampling instant of
the filter output? At what time instant is the maximum signal-to-
noise ratio (SNR) at the output of the matched filter achieved?
(b) [6 Marks]
State the maximum SNR at the output of the matched filter in an
AWGN channel if the noise power spectral density is 0N and the
signal energy is sE ?
(c) [6 Marks]
Sketch the output signal of a matched filter for the case when the
signal of interest is a sinusoid with a rectangular envelope of
duration T .
(d) [10 Marks]
Give an example of a transmit filter that satisfies the Nyquist
criterion. Prove that the Nyquist criterion is satisfied for this filter.
(e) [18 Marks]
Describe the Least Mean Squares (LMS) adaptive algorithm for
Finite Impulse Response (FIR) filtering. Explain the main steps of
the algorithm. Discuss the complexity of each step.
ELE00092M
Page 7 of 7
3
(a) [20 Marks]
The block diagram of the uplink LTE (Long-Term Evolution)
transmission is shown in Figure 3. Describe how the transmission
scheme operates and explain the purpose of every block in this
diagram.
(b) [12 Marks]
Describe the selection combining (SC) technique. Find the
combining coefficients of the SC for the case when the received
signal copies in L diversity branches are modelled as
,,...,1),()()( Litntstx iii =+= where i are complex-valued
channel gains, )(tni are complex-valued zero mean random noise
components with variance
2
i , respectively, the noise components
are independent on different diversity branches, and )(ts is a
signal transmitted in the time interval ]2/,2/[ TT− .
(c) [6 Marks]
Consider a communication system with three diversity branches.
The SNR on the branches are 0 dB, 3 dB, and 0 dB, respectively.
What is the SNR at the output of the maximal-ratio combiner?
(d) [12 Marks]
What is diversity in communications systems? Explain benefits of
using the diversity. Name three diversity types that you know and
describe them. Name linear diversity combining techniques.
Figure 3: The block diagram of the uplink LTE transmission
End of Paper
Page 1 of 7
MSc Degree Examinations 2020-1
Department: Electronic Engineering
Title of Exam: Introduction to Signal Processing
Time Allowed: 24 Hours (PLEASE NOTE: papers submitted more than
30 minutes after the deadline will not be marked)
Time Recommended: THREE hours
Allocation of Marks: All questions carry equal marks
Instructions for Candidates: You should attempt all 3 questions.
You may write all of your answers by hand, use a mix of handwritten and typed
answers, or type all of your answers. Whatever method you use, you must submit
your answers in a single pdf document.
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.
Paper Queries:
Please see the detailed instructions on the next page regarding exam queries. The
exam setter for this exam is Dr Yuriy Zakharov who if necessary can be contacted
by email at yury.zakharov@york.ac.uk. Please copy any email that you send to the
Chair of Board of Examiners (eugene.avrutin@york.ac.uk) and to elec-
genoffice@york.ac.uk.
© University of York Page 2 of 7
ELE00092M
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 exam
setter.
● 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 family
members.
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-genoffice@york.ac.uk. 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 elec-
genoffice@york.ac.uk 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 receipt.
• 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.
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
ELE00092M
Page 3 of 7
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 have submitted.
© University of York Page 4 of 7
ELE00092M
1
(a) [28 Marks]
Show that, in the two-user case, the Minimum Mean Squared Error
(MMSE) multiuser detector can be implemented by the scheme in
Figure 1, where )(1 ts and )(2 ts are the user signature waveforms
of a unit energy, 1A and 2A are the user signal amplitudes, and
2 is the noise variance. Note that in the MMSE multiuser
detector, the decision for the k -th user is found as
2,1),sign(ˆ == kzb kk , where kz are elements of the vector
( ) yARz 122 −−+= , y is the vector of the matched filter outputs,
R is the cross-correlation matrix of the user signature waveforms,
and A is a diagonal matrix with diagonal elements equal to the
user signal amplitudes.
(b) [10 Marks]
Explain the difference between frequency-flat and frequency-
selective fading channels.
(c) [12 Marks]
In a communication system, the propagation channel is modelled
as a time-invariant fading channel whose impulse response is a
wide-sense stationary random process. What is the coherence
bandwidth of the channel? The multipath spread of the channel is
2 μs; what is the minimum frequency shift between two frequency-
diversity channels that guarantees uncorrelated fading in the
diversity channels?
ELE00092M
Page 5 of 7
Figure 1: The MMSE multiuser receiver (two-user case)
© University of York Page 6 of 7
ELE00092M
2
(a) [10 Marks]
What is the impulse response of the filter matched to a signal )(ts ?
How does the impulse response depend on the sampling instant of
the filter output? At what time instant is the maximum signal-to-
noise ratio (SNR) at the output of the matched filter achieved?
(b) [6 Marks]
State the maximum SNR at the output of the matched filter in an
AWGN channel if the noise power spectral density is 0N and the
signal energy is sE ?
(c) [6 Marks]
Sketch the output signal of a matched filter for the case when the
signal of interest is a sinusoid with a rectangular envelope of
duration T .
(d) [10 Marks]
Give an example of a transmit filter that satisfies the Nyquist
criterion. Prove that the Nyquist criterion is satisfied for this filter.
(e) [18 Marks]
Describe the Least Mean Squares (LMS) adaptive algorithm for
Finite Impulse Response (FIR) filtering. Explain the main steps of
the algorithm. Discuss the complexity of each step.
ELE00092M
Page 7 of 7
3
(a) [20 Marks]
The block diagram of the uplink LTE (Long-Term Evolution)
transmission is shown in Figure 3. Describe how the transmission
scheme operates and explain the purpose of every block in this
diagram.
(b) [12 Marks]
Describe the selection combining (SC) technique. Find the
combining coefficients of the SC for the case when the received
signal copies in L diversity branches are modelled as
,,...,1),()()( Litntstx iii =+= where i are complex-valued
channel gains, )(tni are complex-valued zero mean random noise
components with variance
2
i , respectively, the noise components
are independent on different diversity branches, and )(ts is a
signal transmitted in the time interval ]2/,2/[ TT− .
(c) [6 Marks]
Consider a communication system with three diversity branches.
The SNR on the branches are 0 dB, 3 dB, and 0 dB, respectively.
What is the SNR at the output of the maximal-ratio combiner?
(d) [12 Marks]
What is diversity in communications systems? Explain benefits of
using the diversity. Name three diversity types that you know and
describe them. Name linear diversity combining techniques.
Figure 3: The block diagram of the uplink LTE transmission
End of Paper
