Example Final Examination FINAL EXAMINATION PERIOD: SESSION 2, 2020 Unit Code: TELE3021 Unit Name: Communication Systems Duration of Exam (including reading time if applicable): Two (2) hours plus ten (10) minutes reading time Total No. of Questions: Four (4) Total No. of Pages (including this cover sheet): 13 GENERAL INSTRUCTIONS TO STUDENTS: Students are required to follow directions given by the Final Examination Supervisor and must refrain from communicating in any way with another student once they have entered the final examination venue. Students may not write or mark the exam materials in any way during reading time. Students may only access authorised materials during this examination. A list of authorised material is available on this cover sheet. All watches must be removed and placed at the top of the exam desk and must remain there for the duration of the exam. All alarms, notifications and alerts must be switched off. Students are not permitted to leave the exam room during the first hour (excluding reading time) and during the last 15 minutes of the examination. If it is alleged you have breached these rules at any time during the examination, the matter may be reported to a University Discipline Committee for determination. EXAMINATION INSTRUCTIONS: Answer all Four (4) questions. Clearly label question number on each page of your answer books. Total Marks for this paper is: 100 Marks. The questions are of equal value. MATERIALS PERMITTED / NOT PERMITTED: Dictionaries: Paper-based dictionaries permitted. Calculators: Calculators or computers are permitted, Other: Open book – notes, textbooks, and internet are permitted (online examination) No communication (personal or online) with another individual or other individuals are permitted during the examination time Appendix A. Table of Mathematical Equations Appendix B. Table of Properties of Fourier Transforms Appendix C. Table of Basis Fourier Transform Pairs Appendix D. Table of Bit Error Probabilities, BP , for Common Modulations TELE3021 Final Examination – Page 2 Example Final Examination This paper indicates the format of the TELE3021 Final Examination only. The questions in the actual Final Examination may be either unrelated or related to the questions contained in this example final examination paper. Since this paper only indicates the examination format, no answers will be provided for this paper. You will download the actual Final Examination paper from iLearn during the Examination time. There will be a link on iLearn to turn-in your completed Final Examination answer paper. You will need to write your name, student number, and page number on every page of your answer paper. You will need to clearly write the Question Number and Part Number for every answer which you provide in your answer paper. If you do not clearly write the Question Number and Part Number, you will be given zero marks for the answer. You will need to upload the completed examination within ½ hour of the finish time of the final examination. If you do not upload a scanned copy of your final examination paper within the required time or if you upload the incorrect file, you will receive a mark of zero on the final examination for TELE3021. Rules against copying, collaborating, and obtaining outside help will be strictly enforced. Techniques to determine whether examination malpractice has occurred may be used. Examination malpractice includes both copying examination solutions and allowing other students to copy your examination solutions. There are strong penalties for examination malpractice. TELE3021 Final Examination – Page 3 QUESTION 1. Analog Modulation A message signal is given by,m t cos 2 , 1where, , 2 1.5 kHz, m m m m m t A f t A f (a) (5 marks) For DSB-FC AM modulation, the modulated signal, ,s t is given by, cos 2 , where, 1, 100 kHz. c c c c s t A m t f t A f Draw a diagram for the amplitude spectrum of s t for which the frequencies and amplitudes of all signal components are numerically labelled. (b) (5 marks) What is the numerical value of the AM modulation index, AMm , for 5 2cos 2 cos 2 ?m cs t f t f t QUESTION 1 IS CONTINUED ON THE NEXT PAGE TELE3021 Final Examination – Page 4 QUESTION 1 CONTINUED FROM THE PREVIOUS PAGE (b) (5 marks) For cos 2 , ˆWhat is the Hilbert Transform of , as a function of ? cm t A f t m t m t t (d) (5 Marks) What is the power spectral density of 2 as a function of and .oj kf tk k o k x t c e c f (e) (5 Marks) An FM signal is is given by,z t 0 cos 2 2 where, cos 2 , What is the instantaneous frequency of as a function of , , and ? t c o m c o m z t A f t k m t dt m t f t z t f k f [END of QUESTION 1.] TELE3021 Final Examination – Page 5 QUESTION 2. Random Processes and Random Sequences (a) (5 Marks) A second-order stationary random process x t has autocorrelation function XR given by, 1 , ‐ , 0, elswhere. x A T T R T What is the power spectral density of and the average power in ?xS f x t x t (b) (5 Marks) A second-order stationary random process y t has power spectral density yS f given by, + . 2 o Y k o k NS f A f kf What is the autocorrelation of and the average power in ?yR y t y t What is the average power of y t if 2 oN =0 ? Express your answer as a function of , , and .k o oA f N (c) (5 Marks) 0 is a random variable with probability density function . Prove that, Pr min and then verify this inequality for the case of 1, 0 u 1. 0, U x u U U U f u U x e f u e du f u elsewhere. (d) (5 Marks) A digital communications system is characterized by a bit error rate of .BP For this system, what is the probability that N bits are transmitted such that exactly k bit errors are detected in the N bits, where and are integers fork N 0 .k N Express your answer as a function of , , and Bk N P . Hint: The probability of B kN P is relatively large, but other values of N are possible. QUESTION 2 IS CONTINUED ON THE NEXT PAGE TELE3021 Final Examination – Page 6 QUESTION 2 CONTINUED FROM THE PREVIOUS PAGE (e) (5 Marks) A sequence of independent, uniformly distributed random variables is generated. The sequence is 1 2, 3{ , ,...}U U U where the probability density function of is given by, 1, 0 u 1, 0, elsewhere.k k U U f u It is required to generate a sequence of statistically independent random variables 1 2 3, , ,...V V V such that has the probability density function given by, , 0 1, 2 , 1 2, 0, elsewhere. k k k V V V f v v v f v v v What is the function g such that ?k kV g U [END of QUESTION 2.] TELE3021 Final Examination – Page 7 QUESTION 3. Digital Detection 1 Two possible signals are transmitted over an additive, zero‐mean, white Gaussian noise channel. : + , 0 , : o tH r t A n t t T T H 1 1 + , 0 . 1The a priori probabilities are: = = . 2 is zero‐mean, white, Gaussian noise with power spectral o tr t A n t t T T n t density, = Watts/Hz. 2 o n NS t (a) (5 Marks) Draw the block diagram of the maximum likelihood detector which uses correlator and include the numerical value for the decision threshold. (b) (5 Marks) Draw the block diagram of the maximum likelihood detector which uses matched filters and include the numerical value of the decision threshold voltage and the impulse responses of the matched filters. (c) (5 Marks) Derive a mathematical equation for the probability of bit error, .BP This equation is a function of , where is the energy per received bit in Watts.b b o E E N (d) (5 Marks) For b o E N =8.46 dB, what is the numerical value of ?BP QUESTION 3 IS CONTINUED ON THE NEXT PAGE TELE3021 Final Examination – Page 8 QUESTION 3 CONTINUED FROM THE PREVIOUS PAGE (e) (5 Marks) A communications system uses coherently demodulated, maximum likelihood detected BPSK and uses a one-bit parity-check code for error detection. The demodulator input is operating at a normalized signal-to-noise ratio of b o E N . What is the probability of one or more undetected errors in a N bit block of demodulated data which contains 1 bits of data and 1 parity bitN ? Express your answer as a function of b o E N and .N [END of QUESTION 3.] TELE3021 Final Examination – Page 9 QUESTION 4. Link Calculations (a) (9 Marks) A wristwatch radio is used to transmit and receive 1 Mbits/s data with a bit-error probability of 71 10 . The transmission must operate over a distance of 10 km at a carrier frequency of 3 GHz. The modulation is DPSK (differential PSK) and the receiver in the watch is characterized by 30 dB/K.r s G T A radio transmitter at a cellular base-station transmits to the wristwatch radio. What is the minimum transmitter in dBWEIRP such that the bit error probability requirement is achieved for this link? (Assume that there is free-space loss for signal transmission over the channel). (b) (8 Marks) For the system in part A, a (15,11) Hamming Code is used for error correction by a decoder in the wristwatch radio. The Hamming Code can correct any single error in the 15-bit block but is not capable of correcting two or more binary errors in the 15- bit block. Using the error correcting code, what is the minimum transmit in dBWEIRP such that the bit error probability of 71 10 is achieved? (c) (4 Marks) How does a link budget change when error correction coding is introduced into the link design relative to a link design which does not include error correcting coding? Clearly explain the advantages of the use of error correction coding in the design of a communications link. When error correction coding is introduced into the link design, what is the effect upon the cost of the communications system and associated communications services in terms of resources and characteristics (including bandwidth, transmission latency, equipment cost and complexity, and bit error probability performance in a deep signal fade situation)? Clearly explain the negative factors and system costs associated with the use of error correction coding in a communication link design. (d) (4 Marks) Explain the role of adaptive coding and modulation (ACM) in digital communication systems, including their function, control signal overhead, signal-to-noise ratio estimation requirements, and implementation complexity. [END of QUESTION 4.] [END of EXAMINATION QUESTIONS] TELE3021 Final Examination – Page 10 _________________________________________________________________________ Appendix A. Table of Mathematical Equations 1 0 1 00 )2sin()2cos()( n n n n tnfbtnfaatw v u n v u n v u dttnftw T b dttnftw T a dttw T a )2sin()(2 )2cos()(2 )(1 0 0 0 0 0 0 n tnfj nectw 0 2)( v u tnfj n dtetwT c 02 0 )(1 dtetwfW ftj 2)()( dfefWtw ftj 2)()( TELE3021 Final Examination – Page 11 Appendix B. Table of Properties of Fourier Transforms TELE3021 Final Examination – Page 12 Appendix C. Table of Basic Fourier Transform Pairs TELE3021 Final Examination – Page 13 Appendix D Table of Bit Error Probabilities, PB, for Common Digital Modulations Modulation Type PB BPSK and QPSK (Coherently Demodulated) b o EQ N 2 M-ary PSK (Coherently Demodulated) 2 2 2 log2 sin log b o E M Q M N M BPSK (Coherently Demodulated, Differentially Encoded) b b o o E E Q Q N N 2 2 2 1 BPSK (Differentially Demodulated) b o E Ne 1 2 Binary FSK (Orthogonal Spacing, Coherently Demodulated) b o EQ N Binary FSK (Orthogonal Spacing, Non-coherently demodulated) b o E Ne 21 2 M-ary FSK (Coherently Demodulated) 2log2 b o EM Q M N M-ary FSK 2 2 2 log log1 1 exp ( 1) exp 2 1 M b bj jo o E M E MM jM N jN (Non-coherently Demodulated)
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