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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering – Award
(Bachelor of Engineering in Electronic Engineering – Award)
(NFQ – Level 8)
Autumn 2005
Communications Engineering
(Time: 3 Hours)
Answer FIVE questions. Answer THREE questions from Section A and TWO from Section B. Use Separate answer books for each section.
Examiner: Dr R.A. Guinee Dr B.V. Donovan Prof. C. Burkley Mr. J. G. Ryan
Section A
Q1. (a) Draw the block diagram of an 8-PSK modulator. Determine the baud rate and double- sided Nyquist bandwidth in terms of the incoming bit rate to the modulator. (7 marks) (b) Using the (QIC) tribit symbols “000” and “001” from the incoming modulating binary data determine the output of the 8-PSK modulator and use this information to fill in the phasor and constellation diagrams. Determine the error distance and phase margin for this PSK scheme. (6 marks)
(c) An 8-PSK modulator operating at 70MHz is fed with a 10MBPS binary data waveform. Draw the modulator o/p spectrum and determine the maximum and minimum side frequencies. Determine minimum Nyquist bandwidth and calculate the Baud rate. Compare these results with those for BPSK, QPSK and 8 QAM systems. (7 marks)
Q2. (a) Show that for a Linear Block Code the verification procedure used is CHT^ = where C is an ( n,k ) block code and H is the parity check matrix. (4 marks) (b) If a (7,4) linear block code has the following parity matrix
P
determine its generator and parity check matrices. Determine all the code vectors for this code, the generator and parity check matrices and the minimum weight. (7 marks) (c) Show that if (^) g(x) is a generator polynomial of degree ( n-k ) and is a divisor of (^) x n^ + then g(x) generates an ( n,k ) cyclic code. If a n =7 bit cyclic code has polynomial factors for x^7^ + 1 of ( x + 1 )( x^3 + x^2 + 1 )( x^3 + x + 1 )determine one of the possible generator matrices that can be used for 4 bit data block cyclic encoding. List all the code vectors associated with the chosen generator matrix. Determine the relevant parity check matrix. What is the dual code generator polynomial h ( x ) for the generator polynomial g ( x ) you have chosen and show that g ( x ) and h ( x ) are orthogonal. (9 marks)
Q3. (a) Show that a necessary condition for the existence of an instantaneous code is given by the Kraft inequality ∑ ≤ =
n − k
l (^) k 1
where l (^) k is the kth^ codeword length for a n -symbol source. (8 marks)
(b) Show for an n -symbol source X represented by an instantaneously decodable code of length L that H ( X ) ≤ L where H ( X ) is the source entropy. (6 marks) (c) Distinguish between the following code types, (i) uniquely decodable and (ii) instantaneously decodable by giving examples for the following source alphabet
X = { s 1 , s 2 , s 3 , s 4 , s 5 , s 6 }with probabilities P ( X )={ 0. 4 , 0 .35, 0. 15 , 0. 05 , 0. 04 , 0. 01 }.
(6 marks)
Q6. A small solid-state radar system for a yacht transmits 1W pulses at 8GHz.According to the specification information the receiver noise figure is 4.77dB with an IF bandwidth of 500kHz. The tx/rx Antenna is missing! I wish to install this radar on my yacht and detect targets of 5 sq. m at a range of 5k. (a) Derive any range equation used from first principles with appropriate comments. (6 marks) (b) Determine noise floor for the receiver. (4 marks)
(c) What is the smallest sized ( area of dish or gain in dB ) antenna should I use? (10 marks) Boltzmann’s constant k = 1.38 x 10 –23^ J/K A (^) p (Power gain) = 4π A 0 /λ^2 ; A 0 = (0.65 πD 2 )/
Q7. Show how Dopplar frequency shift may be used to measure the radial velocity of a moving target and draw a block diagram of such a radar system showing how the ‘beat’ frequency could be detected and measured. (6 marks)
The carrier frequency (f (^) o ) of a CW-FM radar is modulated between fo + f (^) d and f (^) o - f (^) d at a frequency of f (^) m. Draw the receiver frequency time graph for a) a stationary target @ near range, b) an approaching target @ remote range and c) a departing target @ middle range (all relative to the transmitter graph). (3 x 3 marks) Show by geometrical means or otherwise that the Range and Velocity of the target can be determined. (5 marks)
