Çankaya University ECE Department ECE 376

Transcription

1 Çankaya Univerity ECE Department ECE 36 Student Name : Student Numer : Open oure exam Duration : 2 hour Quetion. (3 Point) 55 Mit/e inary meage ignal i given. We plan to hire a hannel with a andwidth MHz to pa thi inary meage ignal. Find into what Mary PSK or QAM we hould ue for thi purpoe. he MHz hannel i meaured to e flat in lie of MHz. Hene we further plan to onvert thi Mary PSK or QAM ignal into OFDM. Find the uarrier in uh an OFDM ytem. Solution : Auming the invere of the it/ymol duration i approximately equal to the required andwidth, then for a R 55 Mit/e, inary meage ignal, we would require a andwidth of B R / 55 MHz, 6.45 ne (.) It i given that B MHz, we need to et (ymol duration) / MHz ne. hu onverting to M ary PSK or QAM, we hould have k / log M M By etting the numer of uarrier to the M ary level, we alulate the ymol duration for the individual uarrier a M me (.2) For orthogonality to e atified whilt remaining within the MHz given andwidth, our uarrier mut have an integer numer of yle within 6.5 me. Hene a imple hoie i n f Hz, f Hz, fn n Hz,, f65536 MHz (.3) For the frequenie lited in (.3), it i eay to verify that p m f f, m M, p m i, i M m (.4) p m Note that in the frequeny liting of (.3), oth the given hannel andwidth i not exeeded, additionally adjaent frequeny paing i le than the MHz lie of the total hannel andwidth, namely f65536 f MHz B MHz, f p f p Hz MHz (.5) We an hek for orthogonality, oth y aigning inuoidal and exponential arrier. hi i done elow ÇÜ ECE 36 Final Exam Sayfa

2 p m e p m I o 2 f t o 2 f t dt, I exp j2 f t exp j2 f t dt (.6) (.6) an e verified in Matla quite eaily. A few omment are in order for the OFDM ytem deign of aove. One i numer of uarrier are too high, if a pratial implementation eome diffiult with uh numer of uarrier, poile olution are a) Inreae the andwidth aove MHz ) Ue a moother haping waveform, thu have a redution in Mary value ÇÜ ECE 36 Final Exam Sayfa 2

3 2. (4 Point) wo preading equene of L are given elow e, e (2.) We have two meage ignal uing the preading equene of (2.). Auming that in the time interval to.2 me the of the firt uer i a, while for the eond uer 2 a. Following the operation in Fig.2.2 of leture note entitled, "Spread petrum ytem_23_he", find the output of the orrelator, z and z. Make omment on your finding. Solution : he relevant lok diagram i reprodued elow. Fig. 2. Blok diagram of a DS ytem oniting of two uer. o evaluate z and z, we ue (2.) and (2.8) of leture note entitled, "Spread petrum ytem_23_he", whih are z a a 2 e t e2 t dt a a 2 e t e2 t dt z a a 2 2 e t e2 t dt a a e 2 t e2 t dt From the ame note, we know that (2.) ÇÜ ECE 36 Final Exam Sayfa 3

4 t e t e2t dt e e (2.2) Hene after inerting the numeri value, (2.) will eome 4 4 z 2, z 2 (2.3) 2 It i quite eay to ee that 4 4 Sign z Sign 2, Sign z2 Sign 2 (2.4) So that demodulation will e ueful. ÇÜ ECE 36 Final Exam Sayfa 4

5 3. (3 Point) Anwer the following quetion a rue or Fale. For the Fale one give the orret anwer or the reaon. For the rue one jutify your anwer. a) DS pread petrum ytem employ PN equene with large L : rue, ine we need quite maximum numer of PN equene, whih an e ahieved y uing large L. ) In ode diviion multiplexing, we have to ue PN equene, whih are orthogonal : rue, thi i the eential requirement for PN equene. ) In QAM, there i no energy differene etween the ignal vetor : Fale, ine QAM i a omination of PSK and ASK. d) OFDM ue orthogonal uarrier to improve the error performane : Inomplete, the ue of orthogonal uarrier alo onerve on andwidth, a hown in Fig. 3.6 of leture note entitled, Note on OFDM_23. e) FM i a type of pread petrum ytem : It an e onidered a uh ine after modulation infinite numer of ideand are reated. But there i no philoophy of CDM in FM. ÇÜ ECE 36 Final Exam Sayfa 5