Çankaya University ECE Department ECE 376 (MT)

Transcription

1 Çankaya Univerity ECE Department ECE 376 (M) Student Name : Date : Student Number : Open Source Exam Quetion 1. (7 Point) he time waveform of the ignal et, and t t are given in Fig a. Identify the type of modulation and dimenionality in thi ignal et. Write mathematical and t t and expreion for 1t t and the correponding bai function, 1 N plot t t. Write for the ignal vector and 1 N, and plot the correponding contellation diagram. Find the ditance between ignal vector end. b. Draw the demodulator a correlator and matched filter. Auming that the ignal 1 t from contellation i tranmitted, find the output of the correlator and matched filter. c. Find the probability of error and deciion region via the evaluation of correlation t wa tranmitted and the probability of ending metric C r, m again auming 1 t or t i unequal. t 1 ( t ) = - A in ( t / ), < t < 1 ( t ) =, otherwie ( t ) = - 1 ( t ) 1 ( t ) A Fig. 1.1 he time waveform, and t t for Q1. Solution : a. From Fig. 1.1, we ee that and t t will be A in t / t A in t / t 1t, t (1.1) otherwie otherwie he energie of thee ignal can be found from ÇÜ ECE 376 M Page 1

2 A 1 1 in / (1.) t dt t dt A t dt Both ignal can be repreented by ingle orthonormal bai function. Hence, 1 and contitute binary ASK, where M, N 1. he related bai function, t appearance to that of Fig. 1.1 and can be written a t t will will have imilar t / in t / t otherwie (1.3) t and t in term of t and the correponding vectorial repreentation are given below /, / t A t t A t 1 A /, A /, 1 d A 1 / (1.4) he contellation diagram i given in Fig A / 1 A / ( t ) Fig. 1. Contellation diagram for and t t of Fig b. he demodulator a correlator and matched filter i hown in Fig he output from the demodulator, when 1 t wa tranmitted ÇÜ ECE 376 M Page

3 Fig. 1.3 Demodulator for and t t a correlator and MF. Correlator 1 A / n, n n t t dt MF r y t r t t dt t n t t dt b b r y t r d A / n (1.5) c. he evaluation correlation metric i given below We tart with (6.1) of Note on Dimenionality of Signal_Sept 1_HE, which i r m m m Max P r Max f P (1.6) Uing (5.8) and (6.1) of the ame note, we get N 1 1 Max P r Max ln N r ln P (1.7) m n mn m N n1 Converting (1.7) into correlation metric, we obtain b ÇÜ ECE 376 M Page 3

4 1 C N N P r N r, ln ln m m n mn n1 common term 1 N ln P r ln N N ln P m r m m m m (1.8) Now evaluating C r, m for m 1, r 1 1 r 1 b r r b m 1, C, N ln P N ln p A / A / n m, C, N ln P N ln 1 p A / A / n (1.9) For correct deciion, it hould be Subtituting in (1.1) from (1.9), we get C r C r,, (1.1) b b N ln p A / A / n N ln 1 p A / A / n r p N p N ln >4 n r ln (1.11) p.5.5 b.5 p Which i the ame reult a given in (6.18) of Note on Dimenionality of Signal_Sept 1_HE. N For given operating condition, will be fixed, hence (1.11) baically become N p p r ln r ln (1.1) 4 1p 1p N contant 4.5 Graphically, (1.1) i depicted in Fig Note that p P 1 and 1 p P 1. ÇÜ ECE 376 M Page 4

5 If p <.5 Correct deciion region for 1 Correct deciion region for -A / 1 A / ( t ) If p >.5 Correct deciion region for -A / Correct deciion region for 1 A / ( t ) 1 Fig. 1.4 Variation of deciion region and the boundary with p. ÇÜ ECE 376 M Page 5

6 . (3 Point) Anwer the following quetion a rue or Fale. For the Fale one give the correct anwer or the reaon. For the rue one, jutify your anwer a) In DSB(SC), we have to ue ynchronou demodulation : rue, unle a limited amount of carrier i added prior to tranmiion. b) In demodulation of FM, we firt convert FM into AM : Partially true, but an arrangement like PLL hide thi converion internally. c) Demodulation mean extracting the carrier from the modulated ignal : Fale, demodulation mean extracting, retrieving or recovering the meage ignal from modulated waveform. d) FSK can be multidimenional : rue, FSK i particularly intended to be multidimenional. e) In the determination of correct deciion region, we can ue the ditance metric : rue, we can equally ue the correlation metric. f) PSK and QAM are three dimenional modulation type : Fale, ther are both two dimenional. ÇÜ ECE 376 M Page 6