Question 1 TELE4353. Question 1, cnt d. What is CDMA? Direct Sequence Spread Spectrum System Model. What is direct sequence CDMA?

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1 TELE45 Mobie nd Steite Couniction Systes Tutori 5 week - S 4 Question A ceur obie couniction syste is using direct sequence code diision utipe ccess CDMA technique with coherent binry phse shift keying SK odution. The syste is ccoodting K users nd the spreding fctor,, for the syste is. With no other users present, the ther noise is the ony noise in the receier. If the is 7 d fter the tched fiter nd dispreding deice, cute the before the dispreding deice. Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite Question, cnt d If the syste is ccoodting users, wht is the bit error probbiity for ech user when is 7 d s before. The probbiity of bit error for coherent SK is gien by = x e = erfc x e π x Note tht the utipe ccess interference coud be pproxited s ddition dditie white ussin noise to the ther noise. Wht is CDMA? CDMA is utipe ccess technique in which ny users shre the ibe chnne resource code or power. The sign W in CDMA syste is uch greter thn the iniu required W for sign trnsission. A pseudo noise N rndo sign conerts the nrrow bnd sign to wide bnd noise ike sign. Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite 4 Wht is direct sequence CDMA? The origin sign is utipied by ery rge W spreding N sign in direct sequence CDMA syste. The N sequence hs uch rger chip rte R c thn the sign dt rte R b. t dt Direct Sequence Spred Spectru Syste Mode Trnsitter t Receier pt rt Chnne nt t Messge t Spreding Code pt Spred Sign nt AWN Noise rt Receied Sign dt Dispred Sign t rt = t t + nt d t = rt t = t + tn t Tutori 5- Week TELE45 Mobie nd Steite 5 Tutori 5- Week TELE45 Mobie nd Steite 6

2 How does DS CDMA work? Ech user hs its own N code which is orthogon ner-orthogon to other N codes. The receier needs to know the code used by the trnsitter. The power of other users t receier deterines the noise foor fter sign dispreding nd deodution. Therefore it is necessry to contro the power of ech user in order to oid excessie interference. t Messge DS CDMA in Tie nd Frequency t Spreding Code pt Spred Sign nd-iited Spred Spectru Sign Tie Doin - - Frequency Doin Tutori 5- Week TELE45 Mobie nd Steite 7 Tutori 5- Week TELE45 Mobie nd Steite 8 M = F A = F = F Tutori 5- Week Spectru of SS Sign { t } { t } { pt } TELE45 Mobie nd Steite pt = tt = M A since >> p = 9 Spred Spectru Syste M M Tutori 5- Week - sign power TELE45 Mobie nd Steite = N = = = D Hiding Sign in Noise AWN AWN = kt Soution to prt The signs tht we re deing with he iited power. Effectie noise power before spreding or fter dispreding is σ =. Effectie noise power fter spreding or before dispreding is σ =. The rtio of the noise power before nd fter dispreding is = / = T / T. Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite

3 Soution to prt, cont d The before spreding is The fter spreding is = = = = N = 7d = 7d og = 6d = = N M Two SS Signs M ~ Sign Interference M AWN Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite 4 Signs in Noise rt = t t + t t + nt d t = rt t d t = t t t + p t t + nt t d t = t + p t t + nt t Sign Interference Noise Output Sign to Noise Rtio Sign power - > Noise power - > = Effectie interference power - > Tot noise power - > + o = = = N Tutori 5- Week TELE45 Mobie nd Steite 5 Tutori 5- Week TELE45 Mobie nd Steite 6 k Signs in Noise rt = t t + t t + + t t k k + nt d t = rt t d t = t t t + pt t + + pkt t + nt t d t = t + pt t + + pk t t + nt t Sign Interference Noise Agin we wnt to find output o ; -> ER Tutori 5- Week TELE45 Mobie nd Steite 7 M ~ M Tutori 5- Week Sign K SS Signs M Interference k TELE45 Mobie nd Steite M k AWN 8

4 Output Sign to Noise Rtio Soution to prt of Q Sign power - > Noise power - > k - Effectie interference power - > k - Tot noise power - > + = Tutori 5- Week o + k- = k- + TELE45 Mobie nd Steite 9 K = = k - k = 7d = 5. K = K = 5.89 = 7.7d = e e π K = =.56* K = 5.89 Tutori 5- Week TELE45 Mobie nd Steite K 4 Question A conoution coder with rte ½ is used for coding binry input sequence =. The foowing genertor poynois re used: g = +D nd g = + D + D. Assue tht the initi encoder stte is S I = nd two triing bits T r = re ppended t the end of the essge. Drw the encoder bock digr nd its stte digr. Question, Cont d Wht is the output essge fro the encoder utipexer? Drw he encoder treis digr nd indicte the encoder output sequence fro the utipexer on the digr. Use the Viterbi gorith to find the ost ikey infortion sequence if the receied sequence possiby erroneous is gien by: r =,,,,,, Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite Input C c Conoution Encoder C - C - th th Output enertor Sequences Here n=, k= nd =.,, conoution code is specified by the foowing sequences: g g The input sequence is: c. The output sequence is: =, =. c =. = =,,,,,, = = c g, = c g. = c c = c c c Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite 4

5 Expe of possibe outputs Stte Digr = c c = c c c = c = = =, =, = c = = =, = Ech stte is of the for C -,C - There re four sttes:,,,,, nd,. / c c / / / / / / / / Tutori 5- Week TELE45 Mobie nd Steite 5 Tutori 5- Week TELE45 Mobie nd Steite 6 Treis Digr Treis Digr / / c =. =,,,,,, = = / / / / / / / / / / / / / / / / / / / / Tutori 5- Week TELE45 Mobie nd Steite 7 Tutori 5- Week TELE45 Mobie nd Steite 8 Viterbi Agorith For ech input sequence, we trerse unique pth in the coder treis nd the coder output sequence is unique. Due to the chnne noise, we receie soe bits with errors t the receier. So the receied sequence is no onger wht ws ctuy sent. For decoding, we he to find the osest sequence tht cn be outputed by the coder to the one tht we he receied. If the input sequence hs ength L bits, the input cn tke L possibiities, so there re L different pths in the treis tht cn be tken, nd we he to serch ong these L pths to find the osest to wht we he receied. Viterbi gorith is n efficient wy to find the osest pth. Its copexity grows inery with L. / / r = Decoding stge, / / / d= d= d= d= / r =, =,, d, r = 4 4 =,, d, r = =,, d, r = =,, d, r = Tutori 5- Week TELE45 Mobie nd Steite 9 Tutori 5- Week TELE45 Mobie nd Steite

6 Decoding, stge Decoding, stge 4 / / d= d= / / d= d= / / d= d= d= d= / / d= d= / / d= d= d= / / d= d= d= d= Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite Decoding, stge 5 Decoding, stge 6 d= / / d= d= / / d= d= d= / / d= d= d= d= d= / / d= d= / / d= d= d= / / d= d= d= d= Tutori 5- Week TELE45 Mobie nd Steite Tutori 5- Week TELE45 Mobie nd Steite 4 Decoding, stge 7 Decoding stge -7 / / d= / / d= / / d= d= r = Tutori 5- Week TELE45 Mobie nd Steite 5 Tutori 5- Week TELE45 Mobie nd Steite 6

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