## Communication theory

Question 1a) Explain the concept of power spectral density and write its mathematical description.
[6 marks]
b) Sketch the block diagram of an FM demodulator and briefly explain the operation of each
element. Assuming the carrier channel is subject to white noise, sketch the Power
Spectral Density of the noise signal at the output of the following points in your block
diagram:
(i) IF filter
(ii) Phase detector
(iii) Discriminator.
(iv) Post detection filter.
[10 marks]
c) For an FM receiver to operate correctly and achieve optimum detected signal-to-noise
performance a post detection filter is essential. Why is this?
[4 marks]
d) Explain how pre-emphasised FM overcomes the need for an ideal post detection filter.
[5 marks]
Page 3
Turn Over
ECS701P/D/U (2015)
Question 2
a) A single, square-pulse time-signal of unit amplitude, product modulates a cosine carrier of
frequency ? c ; evaluate and plot
I. The spectra associated with this AM signal
II. The Power Spectral Density
[8 marks]
b) Show how demodulation of the AM signal in part a) of this Question is achieved by
synchronous detection
[6 marks]
c) Explain the significance of the term ‘synchronous detection’ and consequently the
phenomenon of ‘total fading’, using an appropriate mathematical description.
[6 marks]
d) Briefly outline in relation to Question 1 why AM is inappropriate for satellite communication
[5 marks]
Page 4 ECS701P/D/U (2015)
Question 3
a) Using signal-space representation, prove that the BER of M-ary PSK is given by

[8 marks]
where M = 2? is the modulation order and ? is an integer.
b) Using signal-space representation, prove that the BER of M-ary ASK is given by
[8 marks]
where M = 2? is the modulation order and ? is an integer.
c)
i) Using signal-space representation, prove that the BER of M-ary QAM is given by

[6 marks]
where M = 2? is the modulation order and ? is an integer.
ii) Sketch a comparison of BER versus Eb/N0 for 16-QAM and 64-QAM [3 marks]
? ? 0 2 1
1 6 2 N
E
M Q b
M
M
?
? ?
? ? 0 1
1 6 2 N
E
M Q b
M
M ?
? ?
? ?)/sin( 0
2 Q N M Eb ? ?
ECS701P/D/U (2015) Page 5
Question 4
a)
i) Plot block diagram of transmitter and receiver of direct sequence spread spectrum. [6 marks]
ii) Plot the autocorrelation of a maximal linear spreading code of length N = Ts/Tc, where
Ts is the symbol duration and Tc is the chip duration. [6 marks]
b) A Rake receiver is a receiver that has several branches, with each branch synchronized to a
different multipath component. Plot the block diagram of a Rake receiver.
[6 marks]
c) We assume a multipath channel with one delayed component, as follows
Where and are the amplitudes of the multipath components, and is the delay.
Show that the inter-symbol interference (ISI) in direct sequence spread spectrum is equal to
where is the autocorrelation of the spreading code and is the th symbol.
[7 marks]
End of Paper