TCOM370. Solutions to Homework 99-1

Transcription

1 COM7 Solutios to Homework 99- Problem hops (poit-to-poit liks) betwee two termils odes; rsmissio rte 96 bps o ll liks; overhed bits [Heder + riler] for ech pcket; ms per-hop sigl propgtio dely. sec. Cll set-up time for circuit switched coectio cross hops. () Messge size bits pcket size bits ll other prmeters the sme. Circuit switchig bits t 96 bps. sec. messge durtio totl propgtio dely. sec. otl time for messge is sec. Pcket switchig Number of pckets ( - bits of messge dt ) Pcket durtio /96.7 sec. Etire -bit pcket received by ech ode from precedig ode i / sec. otl messge time is therefore sec. (here re hops d pckets i successio fter the first complete pcket is received t termil ode) rsmissio dely is sec. By rsmissio Dely we me the dely betwee the sedig out of bit i the messge d its receptio t the other ed. (b) Messge size bits pcket size bits other prmeters the sme. Circuit switchig he sme s i (). Pcket switchig Number of pckets ( - 88 bits of messge dt for first pckets the th pcket hs bits of messge dt d 8 dummy bits) Pcket durtio /96. sec. Etire -bit pcket received by ech ode from precedig ode i / sec.

2 otl messge time is therefore. +..7sec. (here re hops d pckets i successio fter the first complete pcket is received t termil ode) rsmissio dely is sec. Followig solutios for problems.. d. re from the solutios mul for the textbook. Problem (.) he mi fctors tht ifluece the choice of trsmissio medium to be used i dt commuictio pplictio re the required bit rte d the distce betwee the two commuictig devices. he vrious types of trsmissio medi listed i the questio ech hs defied mximum limit i terms of these fctors d it is this tht determies the pplictio domi of ech type of medium. () wo-wire ope lies re used mily for coectig dt termil equipmet(de) - computer for exmple - to locl dt circuit-termitig equipmet(dce) such s modem. Whe desiged for use with the log switched telephoe etwork the mximum bit rte is the order of bps. Also the modem is ormlly situted less th m from the DE. he ctul mximum physicl seprtio of the devices is iflueced by the type of driver/receiver electroic circuits beig used. (b) wisted pir lies hve much better immuity to spurious oise sigls owig to the two coductig wires beig twisted together. his is exploited by the use of differetil lie driver d receiver circuits sice these operte o the differece betwee the sigls o ech lie rther th their bsolute vlue. By twistig the two coductors together y oise or spurious sigl is picked up i both coductors d hece this does ot ffect the differece sigl. his effect is further reduced by itroducig protective scree or shield roud the twisted pir s show i Fig... he two types re the kow s ushielded twisted pir (UP) d shielded twisted pir (SP). UP is used extesively i the switched telephoe etwork for coectig the telephoe to the locl exchge. I dditio both types re ow used extesively for dt commuictios d with pproprite differetil lie driver d receiver circuits physicl seprtios of up to m t Mbps re chievble. Also with dditiol sigl coditioig circuits dt rtes s high s Mbps re ow possible. (c) Coxil cble is used extesively for likig computers together i the form of etwork. Both thi-wire (. ich dimeter) d thick-wire (. ich dimeter) versios re used. he opertio bit rte is ormlly Mbps d t this rte the mximum legth of cble is m for thi-wire d m for thick-wire. Lrger dimeter coxil cble - up to ich -is lso used i commuity te televisio (CAV) etworks. (d) Opticl fiber cble is the preferred choice for high bit rtes - i excess of sy Mbps - d log physicl seprtios i excess of few kilometers. It is used i computer etworks t bit rtes of Mbps d lso i the switched telephoe etwork for likig switchig exchges either loclly tiolly or itertiolly. I such

3 pplictios my voice circuits re multiplexed together d combied bit rtes i excess of 6Mbps re frequetly used. I dditio becuse of its superior immuity to electricl iterferece compred with copper coductors opticl fiber is lso used i lower bit rte pplictios with oisy eviromets. (e) Microwve trsmissio is used i two forms: terrestril microwve d stellites. errestril microwve is used to trsmit dt t rtes i excess of Mbps t distces up to km. Normlly microwve is used whe the lyig of cbles is either impossible or would be prohibitively expesive. Stellites re lso used for computer-to-computer commuictios over wide geogrphicl res. he two ltertive cofigurtios re show i Fig... I both pplictios the stellite is luched to height of 78m bove the erth sice t this height it hs the sme period of rottio s the Erth. It is the sid to be geosttiory. he Stellite simply cts s repetig or rely sttio retrsmittig the dt it receives o oe frequecy bd out o lik betwee two groud sttios while i the secod it cts s poit-to-poit multipoit (brodcs lik betwee cetrl (hub) site d multiple physiclly-distributed receivers. I the cse of the ltter ll dt is relyed vi the cetrl hub site (computer). Problem (.) Seve-cell repet ptter Becuse of its brodcst ture the use of the rdio spectrum hs to be strictly cotrolled otherwise the vrious services would iterfere with ech other. Hece for ech service specific portio of the rdio spectrum is llocted. With pplictio such s televisio or rdio this is effectively oe-to-my form of commuictio; tht is the sigl trsmitted by the trsmitter is received by ll receivers. hus sigle frequecy bd is sufficiet. I cotrst dt commuictios ormlly requires my-to-my commuictios thus ecessittig multiple frequecy bds. o optimise the use of the llocted frequecy bd the ssiged frequecy bd is ormlly divided ito umber of sub-bds kow s cells. he frequecy bdwidth ssocited with ech cell is the

4 selected to provide wireless (cordless) lik betwee umber of user termils withi the field of coverge of cetrl (bse) sttio for tht cell. he ltter is ormlly coected to the fixed-wire etwork which is the used to provide lik betwee cells. he power output from ech bse sttio - d hece its field of coverge - is cotrolled so tht it is sufficiet to meet the umber of ctive users withi tht regio. he by ssigig the frequecy bds to ech bse sttio i regulr repet ptter it is possible to obti complete rdio coverge usig oly smll umber of frequecy bds. A exmple is the -cell repet ptter show i Fig.. d ltertive is the 7-cell repet ptter i which the distce betwee cells shrig the sme frequecy chel is lrger d hece the risk of iterferece withi cell from bse sttio i other cell o the sme frequecy is reduced. his type of iterferece is kow s chel iterferece d is discussed further i Sectio 6... Problem (.) he effects o trsmitted sigl of the differet tteutio d distortio sources listed re show i Fig..6. () Atteutio As sigl propgtes log trsmissio medium its mplitude decreses but wveform shpe of the sigl does t chge. (b) Limited bdwidth As we c see from the Fourier Series of periodic sigl it is mde up of ifiite series of siusoidl frequecy compoets. But commuictios chel hs limited bdwidth so oly those frequecy compoets tht re withi the chel bdwidth will be received. (c) Dely distortio he vrious frequecy compoets of sigl my rrive t the receiver with differet mplitudes d differet phses which re clled mplitude distortio d phse distortio. A exmple of mplitude/phse distortio is give i otes 99-B. (d) Lie d system oise Becuse the mplitude of the sigl is tteuted d differet oises re dded to the sigl the SNR (sigl-to-oise rtio) might be rther smll t the receiver. his will cuse problem t the receiver i tht relible bit decisios cot be mde. he received sigl my be urecoverble. Problem (.6) he Fourier series of periodic fuctio is: where + cos( f + b si(f

5 d / dt / / / cos(f dt b / / si(f dt From the clss otes d B we hve for pulse tri of wdth-tu pulses d period : A d A si( f ) b (i) For the uipolr biry sigl show i Fig..7() / A V. herefore V / V V si( f) / V si( ) V V V 6 V Hece V k + k... d V k + k... he Fourier series for uipolr biry sigl therefore is: t cos( ) with the s give bove. (ii) he bipolr biry sigl show i Fig..7() is simply the uipolr sigl of mplitude AV from which costt level of V is subtrcted. herefore the Fourier Series for it is simply tht of the uipolr sigl with mplitude V with reduced by costt level of V. herefore

6 V si( ) V V V 6 V Hece k + k... d k + k... b for Problem 6 (.7) Assumig oe biry digit per siglig elemet d either uipolr or bipolr ecodig the lie sigl will chge most frequetly whe the biry sequece... is beig trsmitted. All other sequeces will result i the lie sigl chgig t lower rte. he sequece... which hs the shortest period will yield the highest fudmetl frequecy compoet. Hece the fudmetl d hrmoics ssocited with this sequece will be lrger th those of other sequeces d hece determie the miimum bdwidth required for the chel. Problem 7 () / sec. sec. A( + A( t ) t ) t t [ ] [ ] is eve fuctio. / A t A t / A dt ( ) dt ( t ) / / / A t cos(f dt ( )cos(f dt / / A 8 6

7 si(f f si( f f ) si( f) f (f t si(f f + si( f) + f ) f f ( cos( f ) ) cos(f ( cos( f ) ) / b ; (sice is eve fuctio) Amplitude spectrum A + b. Amplitude Spectrum A (tu/ ) f 7

8 (b) / sec. sec. (i) t (tu/ ) (ii) t (tu/ ) 8

9 (c) / sec. sec cos(f t (tu/ 6) Note tht for () d (6) the plots re re-costructios to withi the Hz bdwidth give by the rule: bdwidth /tu. (pprox.) 9