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ELE00131M

Page 1 of 9

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

marked)

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

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 Ruwan Gajaweera who if necessary can

be contacted by email at ruwan.gajaweera@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.

ELE00131M

© 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

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.

ELE00131M

Page 3 of 9

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

have submitted.

ELE00131M

© University of York Page 4 of 9

1

(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)

ELE00131M

Page 5 of 9

(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

marks)

(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

marks)

(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)

ELE00131M

© University of York Page 6 of 9

2

(a) [10 Marks in total]

A well-know expression for the bit error rate for the polar

signalling is: = (√

2

0

).

(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)

ELE00131M

Page 7 of 9

(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)

ELE00131M

© University of York Page 8 of 9

3

Figure 2

(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:

(

)

=

0

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.

ELE00131M

Page 9 of 9

(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.

(4 marks)

(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)

End of Paper

学霸联盟

Page 1 of 9

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

marked)

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

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 Ruwan Gajaweera who if necessary can

be contacted by email at ruwan.gajaweera@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.

ELE00131M

© 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

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.

ELE00131M

Page 3 of 9

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

have submitted.

ELE00131M

© University of York Page 4 of 9

1

(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)

ELE00131M

Page 5 of 9

(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

marks)

(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

marks)

(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)

ELE00131M

© University of York Page 6 of 9

2

(a) [10 Marks in total]

A well-know expression for the bit error rate for the polar

signalling is: = (√

2

0

).

(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)

ELE00131M

Page 7 of 9

(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)

ELE00131M

© University of York Page 8 of 9

3

Figure 2

(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:

(

)

=

0

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.

ELE00131M

Page 9 of 9

(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.

(4 marks)

(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)

End of Paper

学霸联盟