Exam 2017 EE470 (MAY) PDF

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DEPARTMENT OF ELECTRONIC & ELECTRICAL ENGINEERING

/970 INFORMATION TRANSMISSION AND SECURITY

Date: 12th May 2017

Time: 9.30 – 11.30 (2 hours)

Attempt THREE Questions

 Do not turn over the question paper until instructed to do so by the invigilator.  The use, by candidates, of mobile phones (for any purpose) is not permitted within the Examination Hall during the course of the examination. Mobile phones should be switched off during the course of the examination.  Electronic devices capable of storing, retrieving text, data or formula are not permitted to be used in the examination. Invigilators may require particular calculators to be reset.  The use, by candidates, of electronic devices capable of any form of communication to others within or outside the examination hall (for any purpose) is explicitly forbidden during the course of the examination. 

Use of paper-based dictionaries is permitted only with the explicit permission of an invigilator; all dictionaries will be checked by the invigilators at the start of the examination.

EE470/970

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Q1.

(a)

Sketch the input-output characteristic of (i) a linear quantizer and (ii) a non-linear quantizer? Explain the function of a non-linear quantizer in terms of Signal to Quantization noise ratio. What would the companding strategy be for speech signals for a telephony application? 20%

(b)

Telecommunications systems usually sample speech signals at 8 kHz. Explain how this sampling rate ensures good speech quality if the speech signal is filtered with a 0.3 kHz to 3.4 kHz bandpass filter, and which measure would be used to quantify the distortion introduced by sampling. 10%

(c)

(i) Show the relationship of the Signal to Noise ratio (SNR) at the PCM decoder output with the Signal to Quantization Noise ratio (SNqR), and write the expression for the SNR at the PCM decoder output as a function of M, where M is the number of quantization levels. (ii) If a digital communications system is to carry a single voice stream using linearly quantized PCM, what PCM bit rate will be required if an ideal anti-aliasing filter with a cut-off frequency of 3.4kHz is used at the transmitter and the SNqR is to be kept above 73dB. (iii) Find the overall SNR of the reconstructed analogue voice signal if the receiver noise introduces and error rate, on average, of one in every 106 PCM bits. (iv) What is the minimum transmission bandwidth required to transmit the above voice signal over a raised cosine channel with a roll-off factor of 40%? 45%

(d)

Find the Bit Error Rate of a 150 kbaud, equiprobable, binary, polar, rectangular pulse signalling system assuming ideal centre point detection, if the measured Signal to Noise ratio (SNR) at the detector input is 32dB. Find the probability of bit error if this link is cascaded to form a 10-hop link when repeaters are implemented using digital regenerators. What is the advantage of using digital regenerators as opposed to linear amplifiers for this particular system? 25%

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Q2.

(a)

Discuss the similarities and differences between Pulse Code Modulation and Spread Spectrum. Explain, via the example of Direct Sequence Spread Spectrum (DSSS), how spreading is accomplished at the transmitter and how de-spreading is accomplished at the receiver. 20%

(b)

Briefly explain how the signal-to-noise ratio and signal-tointerference ratio is improved between the input of the de-spreader and output of the de-spreader. Where, in the communications block, is spreading accomplished, especially in relation to multiple-access? 20%

(c)

Illustrate and briefly describe the principle behind Time Division Multiplexing and Frequency Division Multiplexing. Where, in the communications block, is multiplexing accomplished? What is the difference behind multiplexing and multiple access, regardless of the how it is accomplished? 25%

(d)

In choosing between Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA), the packet delay is often a measure of performance. This delay D is the sum of the average packet waiting time and the packet transmission time. Work out expressions for the average delay times for TDMA and FDMA. Discuss the relative performance between TDMA and FDMA w.r.t the average packet delay time. 20%

(e)

Illustrate and briefly describe the principle behind Frequencyhopping Code Division Multiple Access (FH-CDMA). Give two advantages of CDMA over TDMA or FDMA. 15%

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Q3.

(a)

A 5 kHz sinusoidal signal is used to modulate a 75 MHz sinusoidal carrier, using DSB-TC-AM with a modulation index of 0.75. (i) Sketch the time-domain waveform of the modulated carrier. (ii) Could a simple envelope detector be used to demodulate this signal? Explain your answer. 20%

(b)

Explain, with the aid of a constellation diagram, what the term ‘8-PSK’ means. 15%

(c)

A stream of data is transmitted at a rate of 20 Mbit/s using 16-QAM on a 1.0 GHz RF carrier. (i) Assuming rectangular pulse shaping, sketch the resulting magnitude spectrum (i.e. magnitude vs frequency), and calculate the theoretical minimum transmission bandwidth that is required for ISI-free transmission of the signal. (ii) If the actual transmission bandwidth is 1.6 times the theoretical minimum that is required for ISI-free transmission, what is the spectral efficiency (measured in bit·s-1·Hz-1)? 30%

(d)

(i) Explain the term Eb/N0 and how it relates to the Signal-to-Noise Ratio (SNR). (ii) A particular transmission takes place in a 10 MHz channel, and transfers data at a rate of 20 Mbit/s. The noise power is known to be 40 mW, and Eb/N0 = 20 dB. Calculate the signal power. (iii) Figure Q3 shows Bit Error Rate (BER) vs Eb/N0 curves for three modulation schemes, A, B, and C. Curve B represents 8-PSK. Which curve, A or C, is likely to represent QPSK? Explain your answer. 35%

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Q4.

Q5.

(a)

If  is a primitive root of GF(16) constructed using the primitive polynomial x4 + x3 + 1, give the polynomial representation of the all field elements. 20%

(b)

List the cyclotomic cosets for this field. Since x15 – 1 = (x + 1)( x2 + x + 1)(x4 + x3 + x2 + x + 1)(x4 + x3 + 1)(x4 + x + 1), show which elements of GF(16) are roots of which irreducible polynomial. 40%

(c)

Find the generator of a single error correcting BCH code of length 15 and list its roots over GF(16). 10%

(d)

Find the generator of a double error correcting BCH code of length 15 and list its roots over GF(16) and the number of information bits, k. 15%

(e)

Find the generator of a triple error correcting BCH code of length 15 and list its roots over GF(16) and the number of information bits, k. 15%

(a)

Briefly describe the operation of a public key cryptosystem, making reference to one-way functions. What properties should a good cryptographic one way function have? 35%

(b)

Give a brief description of the terms ‘key equivocation’, ‘message equivocation’ and ‘unicity distance’. 20%

(c)

Define in terms of message equivocation the concept of a ‘perfect cryptosystem’. Name a perfect cryptosystem, and briefly discuss any disadvantages it has. 20%

(d)

Estimate the unicity distance of cryptosystem encoding English text with the following keys. (In all cases, spaces in the text are removed, so that the message alphabet has 26 symbols. Assume the entropy of each letter in the message text is 3 2 bits.) (i) The key consists of a four digit decimal number (ii) The key consists of four random letters from a 26 letter alphabet (iii) As (ii), with the constraint that no letter is repeated 25%

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ADDITIONAL REQUIREMENTS:

A B (8-PSK) C

Figure Q3: Bit Error Rate vs Eb/N0 for three modulation schemes

END OF PAPER JI/LS/DC

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