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Main points of this past exam are: Stationarity, Communication, Simple Sketches, Signal Processes, Amplitude Modulated Process, Autocorrelation, Fixed Amplitude
Typology: Exams
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Instructions Answer `3 questions for 100%.
Examiners: Dr. R. A. Guinne Mr. P. French Dr. S. McGrath Mr. P. Quinlan
Q1 (a) Define and explain the concepts of stationarity and ergodicity as applied to communication random signal processes by giving an example with the use of simple sketches. (8.33%)
value S (^) X ( f ). The carrier Acos(ωct+θ) has fixed amplitude A and frequency fc and
X (^) c(t) is wide sensory stationary. (13%) (c) Determine the power spectral density of the random carrier process in (b). Determine the autocorrelation of the carrier process in (b) using time averaging and show that the time average and ensemble averages are the same. (12%) [33.33%]
Q2 (a) Draw the block diagram of the optimum receiver structure for binary signal detection. Explain the functionality of each section and the process of detection. (8.33%)
(b) A matched filter is designed to provide a maximum signal-to-noise power
ratio (^2) 0
2
σ
i b
a SNR (^) T = at its output, with filtered noise variance σ 0 (^2) , for a transmitted
symbol waveform si (t) of duration T (^) b in the presence of additive Gaussian white noise with a two-sided PSD N 0 /2. Show that the optimum filter characteristic h ( t ) for matched conditions is given
0 elsewhere
sTb t for 0 t Tb h t
(c) Show that the matched filter output Z(Tb ) is identical to that of a correlator at the sampling instant t = kTb. Determine the matched filter output for a sinusoidal carrier
Q4 (a) Draw the block diagrams of a QPSK transmitter and receiver and explain their operation. Determine the baud and double-sided Nyquist bandwidth in terms of the bit rate to the modulator. (14%)
(b) Using the dibit 10, determine the output of the QPSK modulator and use this to fill in the phasor and constellation diagrams. Determine the error phase margin using the phasor diagrams. Determine the error distance d of the QPSK system. (9%)
(c) A QPSK modulator operating at 70 MHz has an input bit rate of 10MBPS. Determine the minimum bandwidth required to achieve an error probability of 10-7^ , using the PSK error performance characteristics in Fig.Q4, with a CNR of 10dB. (10.33%) [33.33%]
Fig.Q4: Error rates of PSK modulation systems
P ( e )
Eb / N (^) o (dB)
