Sample Questions Lecture No. 22 Dr. Aoife Moloney School of Electronics and Communications Dublin Institute of Technology Lecture No. 23: Sample Questions Overview This lecture has looked at the following: • Sample questions on the detection of bandpass signals in AWGN. April 2005 Slide: 1 Lecture No. 23: Sample Questions Sample Questions on the Detection of Bandpass Signals in AWGN • Question 1: (a) Define the following terms: (i) Analog modulation (ii) Digital modulation (iii) Digital baseband modulation (iv) Digital passband modulation. (b) Explain the benefit of modulation. (c) Describe phase shift keying (PSK), frequency shift April 2005 Slide: 2 Lecture No. 23: Sample Questions keying (FSK), amplitude shift keying (ASK) and amplitude phase keying (APK), giving the defining equation and diagram in each case. • Question 2: (a) Draw a block diagram of a generic optimum coherent receiver. (b) Consider binary PSK (BPSK), where the two signals April 2005 Slide: 3 Lecture No. 23: Sample Questions are given by: r 2E cos (2πf t) s1 (t) = T r 2E s2 (t) = cos (2πf t + π) T (i) Represent these two signals in signal space using a single basis function: r 2 cos (2πf t) , f or 0 ≤ t ≤ T Φ1 (t) = T April 2005 Slide: 4 Lecture No. 23: Sample Questions (ii) Draw a signal space diagram for BPSK, showing clearly the two signals s1 (t) and s2 (t) and the two decision regions. (iii) Give an equation for the probability of bit error for coherent detection of BPSK, in terms of the energy per binary bit, Eb , and the single–sided noise power spectral density, N0 . State clearly whether the probability of error increases or decreases as the energy of the transmitted signal increases. April 2005 Slide: 5 Lecture No. 23: Sample Questions (iv) Explain how a BPSK signal is generated and give a block diagram of a BPSK transmitter. (v) Explain what is meant by coherent detection and draw a block diagram of a coherent BPSK receiver. • Question 3: Find the bit error probability for a BPSK system with a bit rate of 1 Mbit/s. The received waveforms, s1 (t) = Acosω0 t and s2 (t) = −Acosω0 t, are coherently detected. The value of A is 10 mV. Assume that the single–sided April 2005 Slide: 6 Lecture No. 23: Sample Questions noise power spectral density is N0 = 10−11 W/Hz and that signal power and energy per bit are normalised relative to a 1 Ω load. Solution: Assuming that signal power and energy per bit are normalised to a 1 Ω load we have: A2 T E = Eb = 2 Note: The energy and the energy per bit are equal for binary PSK! April 2005 Slide: 7 Lecture No. 23: Sample Questions We are given: A = 10mV = 0.01V 1 1 1 = = = 10−6 s T = bit rate 1M bit/s 1000000 So (0.01)2 (10−6 ) ⇒ Eb = = 5 × 10−11 J 2 For BPSK we have: ! r 2Eb Pe = Q N0 April 2005 Slide: 8 Lecture No. 23: Sample Questions We have been given N0 = 10−11 W/Hz, therefore: ! r 2 × 5 × 10−11 Pe = Q 10−11 Giving: √ Pe = Q 10 = Q (3.16) Looking up the tables for Q(3.16) we get Pe = 0.0008. • Question 4: (a) Explain quadriphase shift keying (QPSK) giving the relevant equation. April 2005 Slide: 9 Lecture No. 23: Sample Questions Express the possible QPSK signals si (t) using the following two basis functions: r 2 cos (2πf t) Φ1 (t) = T r 2 Φ2 (t) = sin (2πf t) T (c) Draw a signal space diagram for QPSK, showing clearly the decision regions. April 2005 Slide: 10 Lecture No. 23: Sample Questions (d) Give the equations for the probability of bit error for coherent detection of QPSK in terms of the energy per symbol and the energy per bit. How does the probability or error per bit for QPSK compare with that of BPSK? (e) Explain how a QPSK signal is generated and give a block diagram of a QPSK transmitter. (f) Explain the coherent detection of QPSK with particular reference to the decision blocks. Draw a block diagram of a coherent QPSK receiver. April 2005 Slide: 11 Lecture No. 23: Sample Questions (g) Compare BPSK and QPSK with reference to power spectral density, bandwidth and probability of bit error. • Question 5: (a) Explain M –ary phase shift keying (MPSK) giving the relevant equation. (b) Draw a signal space diagram for MPSK with M = 8. Show clearly the decision regions and decision boundaries. April 2005 Slide: 12 Lecture No. 23: Sample Questions (c) For large energy to noise ratios, the average probability of symbol error, Pe , for equally likely coherently detected M –ary PSK can be expressed as: ! r π 2E Pe ≈ 2Q sin N0 M Comment on this equation with particular reference to signal to noise ratio and number of signals, M . (d) Draw a block diagram for a coherent MPSK receiver. April 2005 Slide: 13 Lecture No. 23: Sample Questions (e) Give equations for the bandwidth, B, and the bandwidth efficiency, ρ, for MPSK. Calculate the bandwidth efficiency for M = 2, 4, 8, 16, 32, 64. Comment on the findings in terms of error performance, signal to noise ratio and number of signals, M . • Question 6: (a) Explain M –ary quadrature amplitude modulation (QAM) giving the relevant equation. (b) Draw a signal space diagram for M –ary QAM with April 2005 Slide: 14 Lecture No. 23: Sample Questions M = 16. (c) Compare M –ary QAM and M –ary PSK. • Question 7: (a) Explain binary frequency shift keying (BFSK) giving the relevant equation. (b) Draw the signal space diagram for BPSK, indicating clearly the two decision regions. April 2005 Slide: 15 Lecture No. 23: Sample Questions (c) Give an equation for the probability of bit error for BFSK in terms of energy per bit, Eb , and single–sided noise power spectral density, N0 . Compare the probability of bit error for BFSK with that of BPSK. (d) Draw a block diagram of a coherent BFSK receiver. • Question 8: (a) Explain M –ary frequency shift keying (MFSK) giving the relevant equation. April 2005 Slide: 16 Lecture No. 23: Sample Questions (b) Draw a block diagram of a coherent MFSK receiver. (c) Give an equation for the channel bandwidth, B, required to transmit M –ary FSK. Give the equation for the bandwidth efficiency of M –ary FSK, ρ. (d) Calculate the bandwidth efficiency for MFSK for M = 2, 4, 8, 16, 32, 64. Comment on the results and compare them with the bandwidth efficiency of MPSK. April 2005 Slide: 17 Lecture No. 23: Sample Questions Conclusion This lecture has looked at the following: • Sample questions on the detection of bandpass signals in AWGN. April 2005 Slide: 18

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