1ELEC S338F 2021
Assignment 4 (Cutoff: 2 May 2021 23:00)
Student Name: _____________________________
X1 X2 X3 X4 X5 X6 X7 X8
Student ID
example 1 1 8 7 3 5 0 4
Instructions:
1. Write your student ID in the box (e.g. 11873504).
2. Xn = the nth digit of your student ID. X8 = 4 and X7 =0 in the example.
3. Some of the data/parameters used in this examination depend on your student ID
information. You must use your own set of data to answer this examination.
Put down your data in the following.
Q1 


0 X7 your if dB 10
0 X7 your if dB X7
L
L = dB
2Question 1
This question carries 25% of the marks.
An antenna is connected to a receiver as shown in Figure Q1. The available signal power at
the antenna is 2010-12 W and the system bandwidth is 10 MHz. The noise temperature of the
antenna is 250K, the cable attenuation is L dB and the receiver has a noise factor of 8 dB.
where



0 X7 your if dB X7
L
(a) Assume the physical temperature of the cable and the receiver are the standard
temperature of 290K.
cable
Ta = 250K
L
F = 8 dB
Figure Q1
(i) What is the overall noise temperature of the cable and the receiver?
(6 marks)
(ii) What is the output signal-to-noise ratio at the receiver (in dB)?
(3 marks)
(b) Suppose the system requires at least an output signal-to-noise ratio of 19 dB. A stand-
alone preamplifier with a gain of 13 dB and a noise factor of 3 dB is available.
(i) Where should it be put to have maximum effect?
(2 marks)
(4 marks)
(iii) What will be the new signal-to-noise ratio (in dB)? Does your design meet the
requirement?
(10 marks)
3Question 2
This question carries 45% of the marks.
Two messages m1 and m2 are to be transmitted over an AWGN channel with noise power
spectral density No/2 Watts/Hz. The transmitted signals are given by

 
otherwise
TtA
ts b
0
0
)(1






otherise
TtTA
TtA
ts bb
b
0
4/33
4/30
)(2
(a) Show that the signal set s1(t) and s2(t) is orthogonal.
(4 marks)
(b) What is the dimensionality of the signal space?
(2 marks)
(c) Sketch the impulse response functions of the filters matched to s1(t) and s2(t)
respectively.
(8 marks)
(d) Find the energies of the signals s1(t) and s2(t). Hence determine the othonormal basis
functions 1(t) and 2(t) for this signal set. You can express 1(t) and 2(t) in terms of
s1(t) and s2(t).
(4 marks)
(e) Draw the signal constellation with basis functions 1(t) and 2(t).
(4 marks)
(f) Find the distance d between the two matched filter output signal sample values.
(3 marks)
(g) Write an expression for BER in terms of A, No and Tb.
(4 marks)
(h) Sketch the waveform r(t) = 2s1(t) - s2(t).
(5 marks)
(i) Plot r(t) on your signal constellation in part (e).
(3 marks)
(j) If r(t) is the received waveform, determine which signal s1(t) or s2(t) was sent. Justify
(Hint: the signal constellation in (i) will be helpful).
(8 marks)
4Question 3
This question carries 30% of the marks.
A signal source has 7 states A … G, which have the probabilities given in Table Q3.
State Probability
A 0.23
B 0.09
C 0.18
D 0.15
E 0.20
F 0.02
G 0.13
Table Q3
(a) Construct a Huffman code for this source. You must show your work and list the
code words. You should label the top branches with 1 and bottom branches with 0
in your Huffman coding. That is:
1
0
(12 marks)
(b) Find the efficiency of your code.
(4 marks)
(c) Use your Huffman code to decode the following sequence. (Note you will get wrong
decoding if you don’t follow the convention in (a) to produce your Huffman code).
10010111000101101
(4 marks)
(d) What is the major limitation of using Huffman coding? Briefly explain your answer.
(6 marks)
(e) How can you improve the efficiency in encoding the above signal source?
(4 marks)
END