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(ELEC214)[2007](s)final~cs_ycy^_10308.pdf
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Question 1 (25 marks)
The following 4 signals shown in i) to iv) below are to be used in various digital binary communications systems. Answer the questions that follow:
a) (2 marks) What is the energy of each of the signals i)-iv) in terms of A and T?
b) (4 marks) What is the correlation between the signals in i) and ii); the signal in i) and iii); and the signal in i) and iv) and finally the signals in i) and i)?
c) (4 marks) Write expressions for the probability of error or bit error rate (BER) for the 4 sets of signals specified in part b) in terms of energy per bit and assuming both binary symbols are equally likely.
d) (2 marks) Which binary signal set would you recommend for use in practice and why?
e) (2 marks) The 4 signal sets are now used to transmit digitized telephone voice signals over a wired channel. Given the signals are sampled at 8KS/s and quantized to 8 bits what is the required transmission bit rate and therefore the bit period T.
f) (2 marks) What is the SNR (in dB) of the quantized signal when the telephone voice signal is quantized to 8 bits?
g) (3 marks) With an Eb/No of 10dB find the BER for each of the 4 signal sets specified in part b) when transmitting the digitized telephone signals.
h) (2 marks) For transmitting these telephone signals what do you think a satisfactory BER would be? Do you think any of the BERs are good enough for a practical system?
i) (2 marks) If now the quantization is increased to 16 bits what BER would occur if the same transmission power is used?
j) (2 marks) What methods do you suggest to reduce the required transmission power to transmit the 16 bit signals?
ELEC 214 Communication Systems
Final Exam
Wednesday, 30 May, 2007
There are a total of 4 questions
Answer all questions
Total time allowed is 3 hours
Useful formula are listed at the end of the exam paper
ii)
iii)
i)
iv)
-A
A
T/2
T
-A/2
A/2
T/2
T
-A
A
T/2
T
-A
A
T/2
T
Question 2 (25 marks)
The bit error rate (BER) verses various Eb/No values for an unknown binary communications systems is given in the table below.
BER
0.079
0.023
2.3e-3
3.2e-5
Eb/No
0dB
3dB
6dB
9dB
a) (1 mark) Convert the Eb/No values now in dB to linear units. Also take their square root.
b) (1 mark) Using the Q-function table at the back of this exam determine the value of x in the Q(x) function for the various BERs in the table above.
c) (3 marks) Compare the results from parts a) and b) above to devise an approximate Q-function formula for relating the BER to Eb/No.
d) (2 marks) From this formula deduce a possible binary digital modulation system that was used to generate the values in the table above.
e) (1 mark) What is the correlation between the signals representing a digital 1 and digital 0 fo