END-OF-YEAR EXAMINATIONS ELEC321 Communication Systems (D2) Friday, 19 November 2004, 9:20 a.m. Three hours plus 10 minutes reading time.

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1 END-OF-YEAR EXAMINATIONS 2004 Uni: Day and Time: Time Allowed: ELEC32 Communiaion Sysems (D2) Friday, 9 November 2004, 9:20 a.m. Three hours plus 0 minues reading ime. Toal Number of Quesions: SIX (6) Insruions: Answer any FIVE (5) quesions only. Toal marks for his paper: 00. The quesions are of equal value. Use one or more examinaion bookles. Non-programmable eleroni alulaors may be used. No diionaries permied.

2 ELEC (D2) Page 2. Misellaneous Wrie onise bu informaive noes explaining he signifiane, in he onex of ommuniaion sysems, of he following erms. (3 marks) 'onvoluion' (3 marks) 'synhronous demodulaion' () (3 marks) 'Nyquis sampling rierion' (d) (3 marks) 'ompanding' (e) (3 marks) 'predior' for 'differenial PCM' (f) (2 marks) 'limier' (g) (3 marks) 'eye paern'

3 2. Fourier Analysis; Inersymbol Inerferene ELEC (D2) Page 3 H( ) Fig. 2 Raised-osine Filer (5 marks) The raised-osine filer of Fig. 2 has he frequeny response π H( ) = ½ ½ os. 0 2 Prove ha he impulse response is given by h( ) ( 0 2 π sin 2 ) 2 0 = 2π 2 2 π sin0 os = 0 0 π π (Hins: A an early sage in your proof, use he ideniy θ θ osθ = ½ e j ½ e -j and, a a laer sage, make use of sin( x π) = sin( x π) = sin x.) (5 marks) Wha feaure of his response does his filer share wih a brik-wall filer response, and why is his feaure imporan in dealing wih inersymbol inerferene?

4 ELEC (D2) Page 4 3. Modulaion Sysems (4 marks) Figures 3A - 3G show blok diagrams of a variey of modulaion sysems. Explain wha form of modulaion eah illusraes, briefly giving reasons for your answers. Message soure 2 os m Muliplier 2 os v o Fig. 3A generaor 4 os v o2 Message soure 2 os m Muliplier 2 os v o Fig. 3B generaor 4 sin

5 ELEC (D2) Page 5 Signal soure 2 os m Muliplier 2 sin v o Fig. 3C generaor Signal 2 soure 2 os m2 2 os Muliplier v o2 Muliplier v o 2 sin m 2 sin Fig. 3D Message soure generaor 2 os m 2 os Muliplier v o2 Fig. 3E generaor Daa soure 0 2 os Low-pass filer Muliplier

6 ELEC (D2) Page 6 Fig. 3F generaor - B 2 os Low-pass filer Muliplier Daa soure 0 Fig. 3G generaor Daa soure Daa soure B - B 2 os Low-pass filer Low-pass filer 0 2 sin Muliplier Muliplier (3 marks) Give a mahemaial jusifiaion of your answer for Fig. 3A, and alulae he modulaion index. () (3 marks) Use a phasor (veor) diagram o jusify your answer for Fig. 3B, and esimae he modulaion index.

7 4. Line Coding and Waveform Shaping ELEC (D2) Page 7 (3 marks) Line oding is a ehnique o onver a sequene of binary digis ino a sequene of suiable waveforms for ransmission. Desribe he differene beween a reurn-o-zero (RZ) and a non-reurn-o-zero (NRZ) waveform forma. Given a binary sequene , desribe and explain wih diagrams wha he polar NRZ signal, he bipolar NRZ signal and he Manheser-oded signal are, and indiae heir respeive advanages and disadvanages. (7 marks) A elephone hannel allows signal ransmission in he range 600 Hz o 3300 Hz bis per seond of daa are o be ransmied over his hannel. If 20% sinusoidal roll-off shaping is used, prove ha, wih 6-poin QAM, he desired ransmission bi rae anno be ahieved.

8 5. ASK Link Error Probabiliy ELEC (D2) Page 8 (2 marks) An M-ary ampliude-shif-keying (M-ASK) signal symbol an be defined by s() = A i os( 2πf ), 0 T 0, elsewhere where A i = A[2i - (M - )] for i = 0,,..., M-. Here A is a onsan, f is he arrier frequeny, and T is he signalling inerval. The signal onsellaion for M-ASK signal symbols is shown in Fig. 5. Imaginary 2A s 0 0 s sm -2 sm - Fig. 5 Signal onsellaion for M-ASK signals Real Use he signal onsellaion diagram o derive an expression for he probabiliy of symbol error in he presene of addiive whie Gaussian noise as a funion of A and he mean square noise power, N. I is o be assumed ha he signal symbols are equally likely o be ransmied. (8 marks) A 4-ASK ommuniaion sysem has a bi rae of 20 Mbi/s. If A = 80 mv, and he symbol error probabiliy is.95 x 0-0, alulae he noise power speral densiy, N 0, in W/Hz. Assume ha power and energy per symbol are normalised o a -ohm load. [Hin: use he approximaion erf( 20 ) 2.60 x 0-0.]

9 6. Informaion Capaiy and Coding ELEC (D2) Page 9 (6 marks) The hannel apaiy of a oninuous hannel of bandwidh W Hz, perurbed by bandlimied Gaussian noise of power speral densiy n 0 /2, is given by C = W log 2 ( S N ) where S is he average ransmied signal power and N is he average noise power. Show ha he hannel apaiy of an ideal addiive whie Gaussian hannel wih infinie bandwidh is given by C = S log 2 e =.44 S. n 0 n 0 (4 marks) Wrie down he Huffman and Shannon-Fano enoding proedures for a disree memoryless soure wih symbols x i and orresponding probabiliies p i, i =, 2,..., m. () (0 marks) In a binary single-pariy-hek ode, he pariy-hek symbol v k may be wrien as v k = u 0 u... u k- where k is he number of informaion symbols, u i is he informaion symbol for 0 < i < k - and implies modulo-2 addiion. (i) For k = 3, wrie down all he odewords in he ode. (ii) Whih error paerns an he ode dee? (iii) Compue he probabiliy of an undeeed symbol error using his ode on a binary symmeri hannel, assuming ha all symbol errors are independen and ha he probabiliy of symbol error is p = 0.0.

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