M PHNG CC H THNGTHNG TIN V TUYN SDNG MATLABSimulation of Radio Communication Systems using MatlabTrn Xun NamB mn Thng tin, Khoa V tuyn in ti hc K thut L Qu n100 Hong Quc Vit, Cu Giy , H Ni, Vit NamPhone: (069)-515392 E-mail: namtx@lqdtu.edu.vn2Mc lc1 Gii thiu Matlab 11.1 Matlab l g?. . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Khi ng v Thot khi MATLAB . . . . . . . . . . . . . . 21.3 Lm vic vi MATLAB Desktop . . . . . . . . . . . . . . . . 31.4 Cc lnh MATLAB c bn . . . . . . . . . . . . . . . . . . . 41.5 Cc k hiu c bit. . . . . . . . . . . . . . . . . . . . . . . 5Ti liu tham kho. . . . . . . . . . . . . . . . . . . . . . . . . . . 6Ti liu tham kho 62 Tnh ton v Lp trnh s dng Matlab 72.1 Cc php tnh s hc . . . . . . . . . . . . . . . . . . . . . . 72.2 Cc ton t so snh . . . . . . . . . . . . . . . . . . . . . . . 82.3 Cc ton t logic . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Vector v Ma trn . . . . . . . . . . . . . . . . . . . . . . . . 112.4.1 To vector v ma trn . . . . . . . . . . . . . . . . 112.4.2 Cc php ton i vi vector v ma trn . . . . . . 122.5 Lp trnh vi Matlab . . . . . . . . . . . . . . . . . . . . . . 192.5.1 iu khin lung (flow control) . . . . . . . . . . . 192.5.2 To chng trnh MATLAB bng tp.m . . . . . . 222.6 S dng ho trong MATLAB . . . . . . . . . . . . . . . . 242.6.1 V th . . . . . . . . . . . . . . . . . . . . . . . . 24Ti liu tham kho. . . . . . . . . . . . . . . . . . . . . . . . . . . 29Ti liu tham kho 293 L thuyt m phng 313.1 Vai tr ca m phng . . . . . . . . . . . . . . . . . . . . . . 313.2 M phng vs. Phn tch. . . . . . . . . . . . . . . . . . . . . 323.2.1 S truyn dn s qua knh AWGN. . . . . . . . 323.2.2 S truyn dn s qua knh AWGN s dng ccb lc v KCS phi tuyn . . . . . . . . . . . . . . 333.2.3 H thng truyn dn qua knh thng tin v tinh. . 353.3 Xy dng m hnh m phng. . . . . . . . . . . . . . . . . . 353.4 Cc phng php m phng . . . . . . . . . . . . . . . . . . 37iii Mc lc3.5 BER vs Xc sut li bit . . . . . . . . . . . . . . . . . . . . . 383.6 Vai tr ca m phng . . . . . . . . . . . . . . . . . . . . . . 393.7 Tnh ton qu tuyn v m phng . . . . . . . . . . . . . . . 393.8 Cc tham s nh gi phm cht h thng . . . . . . . . . . 403.9 Kim nh m hnh M phng . . . . . . . . . . . . . . . . . 413.10 Nng lng v Cng sut tn hiu . . . . . . . . . . . . . . . 413.11 M phng Monte-Carlo trong Truyn dn S . . . . . . . . . 424 Knh thng tin v tuyn 454.1 Knh tp m AWGN . . . . . . . . . . . . . . . . . . . . . . 454.1.1 Tp m AWGN. . . . . . . . . . . . . . . . . . . . 454.1.2 M phng tp m AWGN . . . . . . . . . . . . . . 474.1.3 M phng truyn dn qua knh AWGN. . . . . . . 484.2 Knh pha-inh. . . . . . . . . . . . . . . . . . . . . . . . . . 504.2.1 M hnh ton hc ca pha-inh . . . . . . . . . . . 514.2.2 nh hng ca chuyn ng ca MS . . . . . . . . 524.2.3 Hu qu ca truyn sng pha-inh a ng. . . . 534.3 Knh pha-inh Rayleigh . . . . . . . . . . . . . . . . . . . . . 544.4 M phng pha-inh Rayleigh . . . . . . . . . . . . . . . . . . 564.4.1 c tnh thng k . . . . . . . . . . . . . . . . . . . 56Ti liu tham kho. . . . . . . . . . . . . . . . . . . . . . . . . . . 58Ti liu tham kho 585 iu ch s 595.1 iu ch pha sng mang . . . . . . . . . . . . . . . . . . . . . 596 K THUT THU PHT PHN TP KHNG GIAN-THIGIAN 616.1 Cc phng php phn tp . . . . . . . . . . . . . . . . . . . 616.1.1 Phn tp thi gian . . . . . . . . . . . . . . . . . . 616.1.2 Phn tp tn s. . . . . . . . . . . . . . . . . . . . 626.1.3 Phn tp phn cc . . . . . . . . . . . . . . . . . . 626.1.4 Phn tp khng gian . . . . . . . . . . . . . . . . . 636.2 K thut kt hp phn tp khng gian thu . . . . . . . . . . 636.2.1 M hnh tn hiu . . . . . . . . . . . . . . . . . . . 636.2.2 Kt hp chn lc (Selection Combining) . . . . . . 646.2.3 Kt hp t l ti a (Maximal Ratio Combining) . 676.2.4 Kt hp ng li (Equal Gain Combining) . . . 706.2.5 Kt hp phn tp thu v tch sng MLD. . . . . . 716.3 K thut kt hp phn tp khng gian pht . . . . . . . . . . 746.3.1 Phn tp pht t l ti a (MRT) . . . . . . . . . . 746.3.2 Phn tp pht gi chm . . . . . . . . . . . . . . . 746.3.3 Phn tp pht khng gian-thi gian. . . . . . . . . 756.4 Kt lun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Mc lc iiiTi liu tham kho. . . . . . . . . . . . . . . . . . . . . . . . . . . 79Ti liu tham kho 797 CC H THNG MIMO 857.1 M hnh knh MIMO . . . . . . . . . . . . . . . . . . . . . . 857.2 Dung lng knh truyn MIMO . . . . . . . . . . . . . . . . 867.2.1 Dung lng knh truyn c nh. . . . . . . . . . . 867.2.2 Dung lng knh truyn Rayleigh pha-inh . . . . . 907.3 Cc phng php truyn dn trn knh truyn MIMO. . . . 907.4 Ghp knh theo khng gian. . . . . . . . . . . . . . . . . . . 927.5 Cc b tch tn hiu tuyn tnh . . . . . . . . . . . . . . . . . 937.5.1 B tch tn hiu ZF . . . . . . . . . . . . . . . . . . 947.5.2 B tch tn hiu MMSE . . . . . . . . . . . . . . . 967.5.3 Cc tham s phm cht b tch tn hiu tuyn tnh 987.6 Cc b tch tn hiu phi tuyn . . . . . . . . . . . . . . . . . 997.6.1 B tch tn hiu QRD . . . . . . . . . . . . . . . . 997.6.2 B tch tn hiu V-BLAST . . . . . . . . . . . . . . 1017.6.3 B tch tn hiu c tr gip ca phng php rtgn c s dn . . . . . . . . . . . . . . . . . . . . . 1047.6.4 B tch tn hiu MLD . . . . . . . . . . . . . . . . 1107.6.5 B tch tn hiu hnh cu (sphere detector) . . . . . 1117.7 Tm tt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Ti liu tham kho. . . . . . . . . . . . . . . . . . . . . . . . . . . 122Ti liu tham kho 1228 M KHNG GIAN-THI GIAN 1258.1 Gii thiu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1258.2 M khi khng gian-thi gian. . . . . . . . . . . . . . . . . . 1258.2.1 M STBC cho tp tn hiu thc . . . . . . . . . . . 1278.2.2 M STBC cho tp tn hiu phc. . . . . . . . . . . 1308.3 M li khng gian-thi gian . . . . . . . . . . . . . . . . . . 1338.4 M khng gian-thi gian cho cc h thng a ngi dng . . 133Ti liu tham kho. . . . . . . . . . . . . . . . . . . . . . . . . . . 133Ti liu tham kho 133iv Mc lcDanh sch hnh v1.1 Mi trng lm vic ca MATLAB. . . . . . . . . . . . . . . 32.1 thsin(x) vcos(x). . . . . . . . . . . . . . . . . . . . . . 262.2 M t BER ca h thng BPSK trn knh pha-inh Rayleigh. 273.1 H thng d dng thc hin phn tch gii tch. . . . . . . . . 323.2 H thng kh thc hin phn tch gii tch. . . . . . . . . . . 343.3 H thng kh thc hin phn tch gii tch. . . . . . . . . . . 363.4 Lc xy dng m hnh m phng. . . . . . . . . . . . . . 363.5 Mi quan h gia sai s, thi gian chy m phng so vi phc tp ca m hnh. . . . . . . . . . . . . . . . . . . . . . . 374.1 Mt v d v tp m Gauss vi gi tr trung bnh 0 v phngsai2= 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2 Hm mt xc sut Gauss vi2= 1. . . . . . . . . . . . . 464.3 Mt ph cng sut v hm t tng quan ca tp m trng. 474.4 S m phng truyn dn BPSK trn knh AWGN. . . . . . 484.5 Phm cht BPSK trn knh AWGN. . . . . . . . . . . . . . . 504.6 M hnh truyn sng a ng. . . . . . . . . . . . . . . . . . 514.7 p ng xung ca mt b lc FIR. . . . . . . . . . . . . . . . 544.8 Hm phn b Rayleigh vi2= 1. . . . . . . . . . . . . . . . 556.1 Phng php kt hp chn lc. . . . . . . . . . . . . . . . . . 646.2 Phnphi xcxut(CDF)caSNRchophngphpkthp phn tp la chn. . . . . . . . . . . . . . . . . . . . . . 666.3 li phn tp ca cc phng php kt hp phn tp. . . . 666.4 Phng php kt hp t l ti a. . . . . . . . . . . . . . . . . 676.5 Phnphi xcxut(CDF)caSNRchophngphpkthp t l i a. . . . . . . . . . . . . . . . . . . . . . . . . . . 696.6 S my thuvi2 nhnhphn tpMRC v mt b tchtn hiu ti u. . . . . . . . . . . . . . . . . . . . . . . . . . . 816.7 Phm cht BER trung bnh ca my thu MRC vi Mnhnhphn tp s dng iu ch BPSK. . . . . . . . . . . . . . . . 816.8 SphntpMRTcNnhnhphntpvi ccngphn hi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826.9 S phn tp pht gi chm viNnhnh phn tp. . . . . 82vvi Danh sch hnh v6.10 SmyphtmkhiSTBCAlamoutivi 2antenphtv 1 anten thu. . . . . . . . . . . . . . . . . . . . . . . . . . . 826.11 S Alamouti STBC vi 2 anten pht v 2 anten thu. . . . 836.12 PhmchtBER cacc h thngAlamoutiSTBC sosnhvi cc h thng MRC. . . . . . . . . . . . . . . . . . . . . . . 837.1 M hnh knh MIMO v tuyn. . . . . . . . . . . . . . . . . . 857.2 M hnh tng ng ca knh truyn SISO. . . . . . . . . . 867.3 M hnh tng ng ca knh truyn MISO. . . . . . . . . . 877.4 M hnh tng ng ca knh truyn SIMO. . . . . . . . . . 887.5 Dung lng knh truyn MIMO pha-inh Rayleigh. . . . . . . 917.6 Phng php phn knh theo khng gian. . . . . . . . . . . . 927.7 Phn loi cc b tch tn hiu MIMO-SVD. . . . . . . . . . . 927.8 S b tch tn hiu tuyn tnh cho MIMO-SDM. . . . . . . 947.9 M t nguyn l hot ng ca b tch tn hiu V-BLAST. . 1027.10 Phm cht ca cc b tch tn hiu cho h thng 44 MIMO-SDM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.11 Biu din mt dn 2 chiu. . . . . . . . . . . . . . . . . . . . 1057.12 V d biu din thao tc ca thut ton LLL trn mt li 2chiu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.13 Min (vng )quyt nh ca cc b tch tn hiu [16]. . . . . . 1087.14 Mhnhtngngcabtchtnhiuctrgiprtgn c s li. . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.15 Thut ton tch tn hiu cu [28]. . . . . . . . . . . . . . . . . 1158.1 Configuration of a STBC system. . . . . . . . . . . . . . . . . 126Chng 1Gii thiu Matlab1.1 Matlab l g?MATLAB[1][2]ltvittt caMatrixLaboratoryvi nghaphnmmng dng cho tnh ton ma trn. MATLAB c m t nh l mt gi phnmm dng cho tnh ton k thut tch hp cc cng c tnh ton, trc quanha(visualization), vlptrnh. Mi trnglmviccaMATLABdsdng v gn gi vi biu din ton hc ca cc php ton. Cc ng dng inhnh ca MATLAB bao gm:Tnh ton ton hcPht trin thut tonThu kt d liu (data acquisition)M hnh, m phng v to muPhn tch, khai thc v trc gic ha d liu, ha khoa hc v k thutPht trin ng dng bao gm c vic pht trin giao din ngi s dngMATLABlmt h thngtng tc trong phnt dliucs lmtmngkhngcnnhkchthc. iunychophpgii quytcnhiu vn tnh ton, c bit l cc vn gn vi cc php ton ma trnhay vector, m ch tiu tn mt phn thi gian cn thit vit cc chngtrnhsdngccngnngkhngtngtcvhng(scalar)nhChayFORTRAN.H thng MATLAB bao gm nm phn chnh:Mi trng pht trin (Development Environment). y l mttphpcccngcvphngtinhtrngi dngsdngcchmvtpMATLAB. Nhiucngclccgiaodinhangidng(GUI: Graphical UserInterface). TphpcngcnybaogmMnhnhMATLAB(MATLABDesktop)vCasLnh(Command12 Chng 1. Gii thiu MatlabWindow), Lch s Lnh (Command History), Chng trnh Son tho vG ri (Editor and Debugger), v mt Trnh duyt (Browser) xem trgip, KhnggianLmvic(Workspace), ccTp, vngdnTmkim (Search Path).Th vin Hm Ton hc (Mathematical Function Library). yl mt tp hp cc thut ton tnh ton tri rng t cc hm c c nhcng, tr, sin, cos, cc php tnh s hc phc, ti cc hm phc tp hnnho ma trn, tnh gi tr ring(eigenvalue)ca ma trn, cc hmBessel, v cc php bin i nhanh.Ngn ng MATLAB (MATLAB Language). y l ngn ng matrn/mng bc cao vi cc khai bo lung iukhin,cc hm s, cccu trc d liu, vo/ra, cc c im lp trnh hng i tng. N chophpvitc cc chngtrnh gn nh hay cc chngtrnh ng dngphc tp.ha(Graphics.)MATLABcnhiuphngtinhinthvectorv ma trn dng th, cng nh sa i v in cc th ny. N baogm cc hm bc cao trc gic ha cc d liu hai v ba chiu, x lnh, hot hnh, v biu din ha. N cng bao gm c cc hm bcthp cho php ty bin ha ha cng nh xy dng cc giao din ha hon chnh cho cc ng dng MATLAB ca ngi s dng.GiaodinChngtrnhngdngMATLAB (MATLAB Ap-plication Program Interface [API]). y l mt th vin cho phpvitccchngtrnhCvFortrantngtcviMATLAB. Nccccphngtingiccthngtrnh(routine)tMATLAB, dngMATLAB nh l ng c tnh ton, v dng c v vit MAT-files.MATLAB cung cp mt h cc gii php theo tng ng dng, c gila hp cng c (toolbox). Hp cng c MATLAB bao gm mt tp hp y cc hm MATLAB dng tp "m" (m-file) dng m rng mi trngMATLAB cho vic gii quyt cc loi vn c th. Cc v d v phm vi ngdngcacchpcng cMATLABlxltnhiu,hthng iukhin,mng n-ron, fuzzy logic, wavelet, m phng, v nhiu ng dng khc.1.2 Khi ng v Thot khi MATLAB khi ng MATLAB t Windows, nhp p (double-click) vo biu tngMATLABtrn mn hnh desktop ca windows. Sau khi khi ng xong mn hnh s hinra ca s Mi trng Lm vic ca MATLAB gm 3 phn chnh l: Th mcHinthi (CurrentDirectory),ca s Lchs Cu lnh(CommandHistory)v Ca s Cu lnh (Command Windows) nh Hnh 1.1.1.3. Lm vic vi MATLAB Desktop 3Hnh1.1:Mi trng lm vic ca MATLAB kt thc MATLAB c th thc hin bng cch nhp phm chut trivo ng ca s hnh du sao ( ) pha trn v bn tay tri ca s MAT-LAB. Ngoi ra cng c th kt thc MATLAB bng cch nhp vo cu lnhquit ca s Command Windows ri bmEnter.1.3 Lm vic vi MATLAB DesktopMATLABDesktopbaogmmtThanhCngc(Tool Bar)vi ccmenuFile, Edit, Debug, Desktop, Windows v Help. Bn cnh Thanh Cng cl mt menu ko xung (Pull-down Menu) cho php xem v thay i th mclmvichinthi. Ni dungcathmclmvichinthi chinthcasCurrent Menu. Phadi casCurrent MenulcasCommandHistoryhinthccculnhMATLABcnhptrc.Tiptheoca s Command History xung pha di c phm , cho php truy nhpnhanh n cc th vin ca MATLAB, Simulink v cc ci t Desktop Toolshay l cc la chnPreferences.Castonht trongMATLABDesktoplcasculnhCommandWindow dng nhp cc cu lnh MATLAB hay chy cc chng trnh chotrc.4 Chng 1. Gii thiu Matlab1.4 Cc lnh MATLAB c bnCc cu lnh ca MATLAB gn ging vi cc cu lnh Unix. Mt s cu lnhc bn ca MATLAB c tm tt li di y: lsLit k ni dung ca th mc lm vic hin thi. Cng c th dng culnhdir thay cho cu lnhls. V d: ls. ..templitkthmccontempbntrongthmclmvichinthi caMATLAB. pwdHin th ng dn ca th mc hin ti. V d: pwdans =C:\MATLAB701\workch ra ng dn ca th mc lm vic hin ti lC:\MATLAB701\work whoch ra cc bin ang c lu b nh. V d: a=1a =1 b=2b =2 whoYour variables are:a blit k hai bina vb ang c lu tr b nh chng trnh.1.5. Cc k hiu c bit 5 clear [tn bin]xa bin c tn c khai bo khi b nh. V d: clear a whoYour variables are:b xa ht tt c cc bin ang c lu ti b nh, s dng lnhclear allclclnh xa ton b thng tin trn Command Windows v a con tr trv v tr ban u.1.5 Cc k hiu c bit( ) du ngoc trn c s dng ch ra th t u tin trong cc biu thcs hc hoc bao quanh i s ca mt hm s. Du ngoc n cng cdng bao quanh ch s phn t trong mt vector hay ma trn. Ngoira, du ngoc n ny cn c s dng bao quanh cc ch s di(subscript) logic.V d:A(2) ch ra phn t th 2 caA.A([1 23]) lit k cc phn t th nht, hai v ba caA.A(A>0.5) lit k cc phn t caA ln hn0.5.[ ] du ngoc vung c s dng to cc vector v ma trnV d:A=[2 6 3]A =2 6 3to mt vector hng vi ba phn tA=[2 6 3; 12 3]6 Chng 1. Gii thiu MatlabA =2 6 31 2 3nh ngha mt ma trn vi su phn t cho trc.{ }du ngoc mc c s dng to ra cc mng t bo (cell array). Bdu ngoc mc ny tng t nh b ngoc vung ngoi tr cc cp nesting c bo ton.biu din php ton chuyn v lin hp phc ca mt ma trn. V d, A lma trn chuyn v lin hp phc ca A cnA. l ma trn chuyn v caA.. duchmbiudinphncchgiaphnnguynvphnthpphncamt s thp phn. V d: = 3.1416.; duchmphydngngncchcchngkhi khai bomatrn, hocngn khng hin th kt qu mt php ton trn mn hnh.% duphntrm dngto chthch.Ttccc culnhvitsauduphn trm ny u b b qua.... du 3 chm dng ni hai phn ca mt cu lnh trn 2 dng vi nhau.Mt cu lnh di c th vit trn 2 dng cho tin theo di. Khi , du3 chm c s dng ni 2 dng vi nhau.Ti liu tham kho[1] GettingstartedwithMatlab. The Mathworks Inc., 2006.[2] A. Biran and M. Breiner, MatlabforEngineers. Addison Wesley, 1995.Chng 2Tnh ton v Lp trnh sdng Matlab2.1 Cc php tnh s hcBn php tnh s hc c bn gm cng, tr, nhn, chia c th hin tngng bng cc k hiu+, , ,/. V d2 +1ans=33 1ans=22 3ans=66/3ans=2Vi cc php tnh phc tp hn c du ngoc th du ngoc n (gm cm v ng) c s dng phn cch th t u tin. V d, php tnh[(2 + 3) (15 3)][7 + 5 4]2(2.1)c biu din trong Matlab nh sau78 Chng 2. Tnh ton v Lp trnh s dng Matlab((2+3)-(15-3))*(7+5-4)/2trong du ngoc n c s dng thay cho du ngoc vung c mcnh dng cho vector v ma trn trong Matlab.Trong Matlab php tnh ly m c biu din bi k hiu bi du m nh:5 2ans=252.2 Cc ton t so snhTrong Matlab cc ton t so snh c biu din nh sau: nh hn (), nhhnhocbng(=), bng(trng)nhau (==), khc nhau (=). Khi hai mng c cng kch thc c so snhvi nhau th ton t so snh s thc hin vic so snh tng phn t vi nhau.Cc ton t,= ch so snh phn thc ca cc ton hng vinhau.Cc tont== and =thc hinsosnhcphnthcv phnoca hai ton hng. Kt qu ca php ton so snh cho ta1 nu php so snhl TRUE v ngc li0 nu FALSE. Mt s v d v ton t so snh c trnhby di y1==2ans =03 >1ans =14 =Bans =0 1 10 1 110 Chng 2. Tnh ton v Lp trnh s dng Matlab1 1 0A = 5:)for i=1:nRowfor k=1:nColif H(i,k)>=5disp([Phan tu o dong num2str(i) cot num2str(k)])endendendKt qu ca vngfor ny lH =1 8 34 9 67 2 5Cac phan tusau >= 5:Phan tuo dong 1 cot 2Phan tuo dong 2 cot 2Phan tuo dong 2 cot 3Phan tuo dong 3 cot 1Phan tuo dong 3 cot 3Do hmdisp ch lm vic vi cc k t (string) nn hmnum2str cdng phn i s ca hm disp bin i cc ch s i v k v dng k t. Cu lnhwhileVnglpwhilelplimtnhmculnhmtslnnhtnhbngiukhin ca mt iu kin logic. Cu trc vng lp while c kt thc bi mtt kho end. V d sau y m t cch to ra mt chui d liu {1, 1} trong cha 10 bit1.1Sau khi quen vi Matlab c th dng hm c snfind thay cho vngfor ny.2.5. Lp trnh vi Matlab 21clear allrand(seed,0)noOne=0;k=1;while noOne0.5;s(k)=1-2*n(k);if s(k)==1noOne=noOne+1endk=k+1;endsKt qu thu c l mt chui 24 bit1, 1 trong c cha 10 bit1s=Columns 1through 151 1 -1 -1 -1 1 -1 -1 1 1 -1 -1 1 1 1Columns 16through 241 -1 -1 -1 -1 -1 1 -1 1 Cu lnhbreakCu lnhbreak cho phpthot sm khi vng lpfor hay vng lpwhile.Trong trng hp c nhiu vng lp lng vo nhau th cu lnh break ch chophp thot ra khi vng lp trong cng. V d sau y m t li phng phpto mt chui d liu {1, 1} trong cha 10 bit 1 s dng vng lp for kthpviculnhbreak. Trong trnghpc100 bitc to ranhngcha c 10 bit 1 th chng trnh cng dng li.rand(seed,0)noOne=0;for k=1:100n(k)=rand>0.5;s(k)=1-2*n(k);if s(k)==1noOne=noOne+1;endif noOne==10breakendendsKtqu chngta cngthuc mt chui24 bit ging nh vdv culnhwhile22 Chng 2. Tnh ton v Lp trnh s dng Matlabs=Columns 1through 151 1 -1 -1 -1 1 -1 -1 1 1 -1 -1 1 1 1Columns 16through 241 -1 -1 -1 -1 -1 1 -1 12.5.2 To chng trnh MATLAB bng tp.mTrongphntrcchngtathyMATLABnhlmtmi trngtnhtontngtc. Ngoi chcnngcamtmi trngtnhtontngtc,MATLABcnchophpxydngccchngtrnhlptrnhnhccngnng lp trnh thng dng vi mt kho d liu cc hm xy dng sn (built-infunctions). Cc chng trnh MATLAB c lu gi vi phn tn tp m rng.m v thng c gi l cc tpm (m-file). C hai loi tpm:Chng trnh (script): thc hin mt tp hp cc cu lnh v lm vicvi cc d liu nm khng gian cng tc (workspace). Cc chng trnh(script) khng nhn i s u vo v cng khng tr cc i s u ra.Hm (function): thc hin mt tp hp cc cu lnh cha trong n. Tuynhin, ccfunctionnhnccisuvovchoccisura.Cc bin khai bao bn trong function ch tn ti trong function.xemhngdnsdngccfunctiontCommand Windownhpvohelp functionName. V d, xem cch s dng hmor chng ta nhp vohelp orv nhn c hng dn sau| Logical OR. A | B is a matrix whose elementsare 1s where either A or Bhas a non-zeroelement,and 0s where both have zero elements. A and B musthave the same dimensionsunless one is a scalar.C = OR(A,B)is called for the syntax A | B when A or B is anobject.See also XOR. son tho cc script hay cc function ca MATLAB chng ta c thsdngbtkmtchngtrnhsonthovnbnnorilulivi tnm rng.m. Chng ta cng c th s dng ngay chng trnh son tho caMATLAB (MATLAB Editor). xem hay son tho li mtm-file c snch cn s dng cu lnhedit fileName to mt tp mi ch cn s dng cu lnh2.5. Lp trnh vi Matlab 23editkhng cn tn tp. To cc hm MATLABtomtfunctiontrongMATLABchngtacntomtscriptvi dngu tin c cu trcfunction [Output1,..., OutputM]=functionName(Input1, ...,InputN)Trong {Input1,..., InputN} l N i s vo v {Output1,..., OutputM}l M i s ra. Tn ca hm functionName nht thit phi ging vi tn tp mv khng trng vi tn cc tp c sn.V d sau y hng dn cch vit mt function tnh bit thc=a2 4ac ca phng trnh bc haiax2+ bx + c = 0function delta=discriminant(a,b,c)% Function to calculate the discriminant ofa quaratic equation% ax^2 + bx+ c= 0delta=b^2 -4*a*c;Gi s phng trnh bc hai cn tm nghim s lx2+ 4x + 3=0. Cch s phng trnh la=1, b=4 vc=3. S dng hmdiscriminant.mva to chng ta c th tnh c ngay bit thc ca phng trnh nydelta=discriminant(a,b,c)delta =4 To cc chng trnh MATLABMtchngtrnhMATLABchamttphpccculnh. Khichymtchng trnh MATLAB th MATLAB tin hnh tt c cc cu lnh cha trongn. Cc chng trnh MATLAB c th lm vic vi cc d liu ang tn ti trong workspace, hoc cng c th to ra cc d liu mi lm vic. Tuy ccchng trnh MATLAB khng tr li cc i s ra (output argument) nhngcc bin do chng trnh to ra c lu li workspace v c s dng cc cu lnh tip theo.V d chng trnh quadEqn.m sau y m t mt chng trnh MATLAB tnh nghim ca phng trnh bc haiax2+ bx + c = 0Vi d: Chng trnhquadEqn.m% Chuong trinh tinh nghiem so cua mot phuong trinh bac hai24 Chng 2. Tnh ton v Lp trnh s dng Matlab% Nhap cac hang so a, b, cdisp(Chuong trinh tinh nghiem cua phuong trinh bac 2)a=input(Nhap vao hang so a=);b=input(Nhap vao hang so b=);c=input(Nhap vao hang so c=);% Tinh biet thuc deltadelta=discriminant(a, b, c)% Xet biet thuc va tinh nghiem soif delta >0x1=(-b + sqrt(delta))/(2*a);x2=(-b - sqrt(delta))/(2*a);disp([Hai nghiem cua pt lax1= num2str(x1) va x2= num2str(x2)])elseif delta==0x1=-b/(2*a);disp([Phuong trinh co mot nghiem duy nhat x= num2str(x1)])elseif delta triangle (right)p pentagramh hexagramVdsauymtphngphpsdnghmplotvhaithsin(x) vcos(x) chung trn mt hnh v.x =0:pi/10:2*pi;y =sin(x);z= cos(x);plot(x,y,r+:, x,z, b-.o)xlabel(x)ylabel(sin(x)/cos(x))title(Do thi ham sin(x) vacos(x))legend(sin(x),cos(x))gridTrong ng thsin(x) c biu din bi ng t nt mu vicc du cng (+), cn ng th cos(x) c biudin bi ng gchv chm (.) mu xanh nc bin vi cc du trn. Cu lnhxlabel(x)v xlabel(sin(x)/cos(x)) dng nh du trc honh v trc tung ca th. Cu lnhtitle(Do thi ham sin(x) va cos(x)) dng t tncho th. Cu lnhlegend(sin(x),cos(x))dng ghi ch gii chotng th v cui cng, cu lnhgrid dng hin th cc ng li gitr th. Kt qu c th c biu din trn Hnh v 2.2S dng cu lnhhelp plot chng ta c th bit thm chi tit v cchdng hmplot.Mt cu lnh v th khc thng c s dng nhiu trong thng tins v t s li bit (BER: Bit Error Rate) l cu lnhsemilogy(x,y). Culnh tng t nh cu lnhplot nhng cho php biu din trc tung ca th thang logarith.26 Chng 2. Tnh ton v Lp trnh s dng Matlab0 1 2 3 4 5 6 710.80.60.40.200.20.40.60.81xsin(x)/cos(x)Do thi ham sin(x) va cos(x)sin(x)cos(x)Hnh2.1: thsin(x)vcos(x)V d, t sBERcahthngtruyndnBPSKquaknhpha-inhRayleigh phn tch bng l thuyt l [1]BERBPSKFading=121 11 +1Eb/N0(2.7)trong Eb/N0 l t s nng lng bit tn hiu trn ph tn s tp m (mts trng hp c hiu v gi l t s tn hiu trn tp mS/N). S dngchng trnhBERBPSKFading.m sau vi cu lnhsemilogy(BER,EbNodB) chophp v th BER theo t sEb/N0 trn thang logarith.[BERBPSKFading.m]% Chuong trinh ve do thi BER cua h/t BPSK tren kenh fading RayleighEbNodB=0:30EbNo=10.^(EbNodB./10)BER=1/2*(1-1./sqrt(1+1./EbNo))semilogy(EbNodB,BER)xlabel(Eb/No)ylabel(BER)title(Ti so BER cua hethong BPSK qua kenh pha-dinh Rayleigh )2.6. S dng ho trong MATLAB 27grid0 5 10 15 20 25 30104103102101100Eb/NoBERTi so BER cua he thong BPSK qua kenh phadinh Rayleigh Hnh2.2:M tBER ca h thngBPSK trn knh pha-inh Rayleigh.Mt s cu lnh v th thng dng khc gmbar hayhist. bitthm chi tit v cc cu lnh ny s dng lnhhelp trong MATLAB.Bi tp1. Sdnghmrandntomtchui ngunhingmN=1000gitrx = {x1, x2, ..., xk, ..., xN}. Vit chng trnh tnh gi tr trung bnh (kvng)Ex, phng sai2x v lch chunx s dng cc cng thc sauy28 Chng 2. Tnh ton v Lp trnh s dng MatlabEx=1NNk=1xk(2.8)2x=E(x2) E2x=Nk=1x2kNNk=1xkN2(2.9)x=2x(2.10)2. Vit chng trnh to mt chui 1 v+1 ngu nhinx c di104bit. To mt chuibit th 2yging nhx tuy nhincc phn t th10, 50, 100, 150, 250, 300, 350 b o du so vi cc phn t tng ngy. Tc l,y10= x10, ..., y350= x350. So snhy vx v tnh ton ts sai s gia hai chui.3. Davo v dv thBER ca h thng BPSKtrn knhpha-inhRayleigh mc 2.6.1 v hm sai s berfc c sn trong MATLAB,i. Vit chng trnh v th BER ca h thng BPSK trn knh tpm Gauss theo cng thc sau[1]BERBPSKAWGN=12erfcEb/N0(2.11)ii. V th BER ca h thng BPSK trn knh tp m Gauss kt hpvi thBER cah thng BPSKtrnknhpha-inhRayleighvo mt hnh v, nh du v t ch gii cho tng th.4. Vit mt hm MATLABy=QPSKMap(x) nhn i s l mt chui ngunhin 1 v 0 c di Nbit. Hm QPSKMap thc hin kim tra tng cp2 bit lin tipxn vxn+1 ri thc hin php bin i sauxnxn+1ym00 12+ j1201 12+ j1210 12 j1211 12 j12trong n = 1, 2, ..., Nvm = 1, 2, ..., N/25. Vit mt chng trnhQPSKMod to ra 20 bit 0, 1 ngu nhin. S dnghmMATLABQPSKMapv dtrnchuynchui bit{0,1}thnhchui cc du QPSKym.Ti liu tham kho 29Ti liu tham kho[1] H. Harada and R. Prasad, Simulation and Software Radio for Mobile Com-munications. Artech House, 2002.30 Chng 2. Tnh ton v Lp trnh s dng MatlabM PHNG CC H THNGTHNG TIN V TUYN SDNG MATLABSimulation of Radio Communication Systems using MatlabTrnXunNamB mn Thng tin, Khoa V tuyn in ti hc K thut L Qu n100 Hong Quc Vit, Cu Giy , H Ni, Vit NamPhone: (069)-515392 E-mail: namtx@lqdtu.edu.vnChng 3L thuyt m phng3.1 Vai tr ca m phng2Cc h thng thng tin hin i i hi phi p ng c nhu cu truyndn d liu tc cao. Tuy nhin, cc h thng ny thng li b hn ch vcng sut v bng tn. Cc yu cu mu thun ny dn n vic s dng ccphng thc iu ch bc cao, m sa sai v cc phng php x l tn hiuphc tp khc pha thu. nh gi phm cht ca mt h thng truyn dnngintrnknhtpmGausstrngcngtnh(AWGN: AdditiveWhiteGaussian Noise) truyn thng th phng php gii tch ton hc c th csdngrthuhiu. Tuynhin, i vi cchthngtruyndnhinilm vic trn cc knh phc tp, nh knh thng tin di ng t bo, chu nhhng ln ca pha-inh a ng v nhiu, th vic thit k v phn tch giitch tr nn ht sc phc tp. C mt iu may mn l nh s pht trin camy tnh trong vi thp k gn y, nn my tnh ngy cng c tnh nngxlcaovgithnhthp. Hqucasphttrinnylcckthutthit k v phn tch da trn my tnh ngy cng tr nn ph bin. i vithngtin,cc xl phctp camy thuv my phthay cc nhhngca knh truyn nay c th m phng bng cc my tnh thng thng.Ngoi ra, s pht trin ca my tnh cng h tr cho s pht trin cal thuyt m phng. Trong nhng nm gn y, ngy cng c nhiu cng cm phng c tnh nng cao h tr cho vic m phng c thc hin d dnghn. ng c quan trng cho m phng l do m phng l cng c qu gi chophp tm hiu su v hot ng ca h thng. Mt h thng m phng honchnh ng vai tr nh mt phng th nghim cho php kim tra ti nhiu vtr trong h thng. V v vy, cc tham s nghin cu nh rng bng tn,b lc hay t s tn hiu trn tp m (SNR: Signal to Noise Ratio) c th thayi c theo mong mun. Hiu qu ca cc thay i ny c th d dng quanst trn mn hnh my tnh. Cc tham s nh dng sng, ph tn hiu, s mu mt, chm sao tn hiu, biu histogram, hay nhiu biu khc uc th c hin th trn mn hnh my tnh, cho php ngi nghin cu c2Source:W.H.Tranteretal.,Principlesof CommunicationSystemsSimulationwithWirelessApplica-tions,Prentice-Hall,2004.3132 Chng 3. L thuyt m phngth phn tch, nh gi v so snh vi cc kt qu thc hin trn phn cng.3.2 M phng vs. Phn tch hiu r vai tr ca m phng, chng ta xt 3 s h thng sau y.3.2.1 S truyn dn s qua knh AWGNHnh3.1mtmtstruyndnthngtinscbn. Ti phapht,ngun d liu to ra mt chui cc du pht dk, trong mt du pht ctoraclpvi ccdukhc. i vi mththngthngtinnh phn,chui du pht cha hai du {1, 0}. Cc ngun d liu kiu ny thng cs dng ph bin trong m phng v c gi l ngun gin on khng nh(DMS:Discrete MemorylessSource). Cc du pht c to ra sau cnh x thnh cc dng sng ph hp. Vi h thng nh phn, tp dng sngc nh ngha {s1(t), s2(t)}. My pht (Tx), sau , s thc hin chc nngkhuch i dng sng u ra ca b iu ch pht i trn knh truyn vicng sut yu cu.NgunDliuiuchvTx+Lcphihp LymuQuytnhdkdkzkdkKnhtruynAWGN~^Hnh3.1:V d v mt h thng d dng thchin phn tch gii tch.Tn hiu pht i qua knh truyn trc khi n my thu. Trong thc tknh truyn l mt mi trng truyn dn phc tp, gy nh hng ln nchtlng truyndntnhiu.Tuynhin,trongvdnginny,chngta gi thit knh truyn ch to ra tp m trng cng tnh (AWGN). Tn hiuthu nhn c u vo my thu s c a qua b lc phi hp, cn cgi l my thu tng quan. u ra b lc phi hp c ly mu ti cui chuk du to nn thng k quyt nh (decision statistic),dk, ri so snh vingng quyt nh T to nn c lngdk ca tn hiu gc dk. Nudk> Tth quyt nh c thc hin theo mt trong hai du, cn ngc li,dk< T,quyt nh theo du cn li. My thu kiu ny thng c gi l my thu tiu do bn cht ca vic c lng tn hiu pht l lm ti gin xc sut li3.2. M phng vs. Phn tch 33PE.H thng cp n Hnh 3.1 l mt h thng c th phn tch bnggii tch mt cch d dng nh cc kin thc c bn v l thuyt thng tin vgii tch. Thc t l xc sut li PE c tnh ton mt cch d dng vtrnh by trong hu ht cc ti liu v thng tin s, v cho biPE= Q__kEsN0_(3.1)trongEslnnglngtrungbnhcaccdupht, N0lmtphcng sut n pha ca tp m,kl h s xc nh bi tng quan gia ccdng sng {s1(t), s2(t)}. Nu cc tn s c chn mt cch chnh xc, cc tnhiu khng tng quan vk= 1. Vi tn hiu iu ch kha dch pha (PSK),cc tn hiu iu ch c cng tn s v cng sut, nhng khc pha ban u.Trong trng hp pha khc nhau, sao chos2(t) = s1(t)}, th cc tn hius tng quan ngc (anticorrelated), vk= 2.S d chng ta ni rng h thng truyn dn trn Hnh 3.1 l h thng cth phn tch bng gii tch d dng l do cc l do sau:Do gi thit knh truyn AWGN v my thu tuyn tnh. Gi thit nydn n thng k quyt nhd tr thnh mt bin Gauss ngu nhin.Do cc gi thit ngun d liu khng c nhDo gi thit ng b du c thc hin l tng nn chng ta c thbitchnhxc thi im bt u v ktthc ca mt du, v vy,chophp thng k quyt nh c tch ra mt cch chnh xc.Mc d cth phn tchc d dng nhngtrong mt s trng hpxy dng chng trnh m phng cho cc h thng kiu ny vn cn thit. Ldo l do y l mt h thng c bn nn n thng c s dng lm c s m rng cho cc h thng truyn dn phc tp hn. V d, nu thay khiknhAWGN bng khi knh pha-inh Rayleigh chng ta c m hnh truyndn s qua knh pha-inh Rayleigh, hay chng ta cng c th thm vo khisan bng knh my thu c c s truyn dn s dng b san bng loi b nh hng ca pha-inh chn lc theo tn s i vi knh c tr. Trongnhng trng hp nh vy, vic xy dng thnh cng chng trnh m phngchohthngtruyndncbnckimnghimbnglthuytny, chophp m rng nhanh chng xy dng thnh cng chng trnh m phngcho cc h thng phc tp.3.2.2 S truyn dn s qua knh AWGN s dng cc b lc vKCS phi tuynTrongmc trc chngta xtmt s truyndncbn trong thngtin.Chngtacng thy rng vis truyndn cbn thnhsdng mt s gi thit chng ta c th phn tch d dng phm cht li bt ca34 Chng 3. L thuyt m phngNgunDliuiuch+Lcphihp LymuQuytnhdkdkzkdkKnhtruynAWGN~^KCSvLcPhituynHnh3.2:V d v mt h thng kh thc hin phn tch gii tch.h thng. Trong mc ny chngta s xt mt s phc tp hn, trong c s dng thm mt b khuch i cng sut (KCS) phi tuyn v b lc u ra my pht. Chngta bit rng b khuchi cng sut phituynchiusutnguncaohnbkhuchi cngsuttuyntnh, vv vy,thng c s dng cc ng dng i hi tit nghim ngun nh thng tindi ng chng hn. Tuy nhin, vic s dng b khuchi phi tuynli tonn mo hi v mo iu ch ln nhau (intermodulation), lm cho ph ca tnhiu u ra KCS rng hn rt nhiu so vi ph u ra b iu ch. B lcu ra, thng thng l mt b lc bng thng c tn s trung tm trng vitnssngmang, cnhimvlmsuygimmohi vmoiuchlnnhau do tnh phi tuyn ca b KCS gy nn. Tuy nhin, b lc ny li lmcho tn hiu b phn tn theo thi gian, do gy nn nhiu xuyn du (ISI).HuqucaISIlxcsutli camtduphthucvomthaynhiudu trc . Nu nh xc sut li ca du thi ph thuc vok du trc th chng ta cn tnh xc sutPr(Ei|di1, di2, ..., dik)i vi trng hp nh phn c2kchui khc nhau, do chng ta cn tnhcho2ktrnghp.Githitlmidudliucxcsutl0hay1nhnhau, chng ta c xc sut li ca du thi c tnh nh sauPE=12k1di1=01di2=0 1dik=0Pr(Ei|di1, di2, ..., dik) (3.2)Tc l, chng ta cn tnh2kxc sut li khc nhau, vi mi xc sut li phthucmttrong2kchui trc, sauchiatrungbnhchok. Doknhtruyn ang xt l knh AWGN nn mi xc sut trong 2kxc xut li l hmQ Gauss. Phng php tnh d hiu, vic tnh ton i s ca mi hmQ linhm chn, v v vy, m phng thng c s dng thay th cho gii tch.H thng Hnh 3.2 c mt tnh cht quan trng lm cho phn tch trnn d dng hn. l phn h thng t im c tp m n im xut hin3.3. Xy dng m hnh m phng 35thng kVkl tuyn tnh. Thng kdkc th c biu din dngdk= Sk + Ik + Nk(3.3)trong SkvIkl cc thnhphncadkdo tnhiuvnhiu,cnNklthnh phn do tp m. Do tnh cht tuyn tnh nn nu tp m l Gauss thNkcnglmtbinngu nhinGauss,don lktqucaphpbinituyn tnh ca mt bin ngu nhin Gauss. Hn na, thng k quyt nh cadkcng s l mt bin Gauss c cng phng sai nh caNk, nhng vi gitr trung bnhSk + Ik, trong c hai thnh phn ny u xc nh. Gi trtrungbnhcadkc xc nht kinthc vmt phcngsutcatp m knh v bng tn tp m tng ng ca h thng t knh n ura cadk. V vy, hm mt ph cng sut (PDF) cadkc th bit cv xc sut li d dng c xc nh. Ni tm li, l do chng ta c th ddng xc nh PDF cadk, cho d h thng c tnh phi tuyn, l do tp mkhng i qua phn phi tuyn ca h thng.Do tp m ch i qua phn tuyn tnh ca h thng nn phng php mphng c n gin ha. Cng do tp m khng i qua phn phi tuyn nngi tr trung bnh cadkc th xc nhc bng gii tch v do PDFcadk c th bit c v xc sut li c xc nh d dng. Cc khi nimny c kt hp vo trong mt k thut m phng va n gin, li nhanhchng.l phngphpbngii tch(semi-analytical),trong gii tchv m phng c kt hp vi nhau lm cho m phng c thc hin nhanhhn. M phng bn gii tch l mt cng c quan trng v c s dng rngri trong nghin cu.3.2.3 H thng truyn dn qua knh thng tin v tinhH thng m t Hnh 3.3 c bit n nh l mt h thng khng th phntch c bng gii tch. H thng ny l mt m hnh truyn dn hai chngqua knh v tinh, trong b pht p c m hnh ha bi mt b khuchi cngsutln(HPA)phi tuynvmtblcloi bmohi ngoibng tn do tnh phi tuyngy nn. So snh Hnh 3.3 v Hnh 3.2 chngtathychngccutrctngtnhau. Tuynhin, mhnhknhvtinhHnh 3.3 c b xung thm hai ngun tp m: mt cho ng ln (up-link)v mt cho ng xung (down-link).Nh vy,tn hiu my thucha haithnh phn tp m, trong tp m tuyn ln i qua mt b khuch i phituyn. Dchochngtacgithitlctpmtrnnglnvngxung u l tp m Gauss, th PDF ca tp m my thu vn rt kh xcnh, c bit l vi tp m ng ln. V vy, m phng l cng c cn thiti vi cc h thng kiu ny.3.3 Xy dng m hnh m phngBc u tin trong vic pht trin mt chng trnh m phng ca mt hthngthng tinlphttrinmhnhmphngcah thng.Mhnh36 Chng 3. L thuyt m phngNgunDliuiuch+Lcphihp LymuQuytnhdkdkDownlinknoisedkKnhtruyn~^KCSpvLchituynKCSpvLchituyn+UplinknoiseHnh3.3:V d v mt h thng kh thc hin phn tch gii tch.MhnhmphngPhncngMhnhgiitchHnh3.4:Lc xy dngm hnh m phng.thngcbiudindngtonhcmtmi quanhvo/racahthng. Ngh thut ca m hnh ha l pht trin m hnh hot ng c chay cc tnh nng cn thit nhng li khng qu phc tp c th thchin c bng cc my tnh thng dng. Yu cu ny i hi phi c s thahip gia tnh chnh xc, phc tp v yu cu tnh ton ca m hnh.i vi mt qu trnh m phng, thng thng c hai m hnh c xydng: m hnh gii tch v m hnh m phng nh Hnh 3.4. C hai m hnhny um t tnh tru tng ca h thng. M hnh gii tch thng biudin dng cng thc ton hc hay cc h phng trnh xc nh mi quanh vo/ra ca h thng. Cc cng thc ny thng l m t mt phn ca hthng, v c chnh xc trong mt gii in p, dng in, hay tn s no. M hnh m phng thng l mt tp hp ca cc thut ton thc hingii php tnh ton bng s (numerical) ca cc cng thc xc nh m hnhgii tch. Cc k thut gii tch s v x l tn hiu s l cc cng c c sdng pht trin cc thut ton ny.Mi quan h gia sai s m hnh, phc tp v thi gian m phng c3.4. Cc phng php m phng 37SaismhnhThigianmphngCaoDiNgnThp phctpMhnhCaoThpSaisvsphctpThigianmphngvsphctpVnghotngthctHnh3.5: Mi quanhgiasais,thi gianchymphngsoviphctpcamhnh.biu din Hnh 3.5. Chng ta c th thy rng mt m hnh c phc tpthp csai s m hnhha ln, nhng li yucu thi gian chy m phngngn. Ngc li, m hnh c phc tp ln c sai s nh nhng li yu cuthi gian m phng di.3.4 Cc phng php m phngC hai loi m phng c bn: m phng xc nh v m phng ngu nhin. Mphng xc nh thng gp trong trng hp m phng cc mch in cthit k s dng mt chng trnh thit k nh kiu SPICE. Chng trnh nycsdngtoramtmchinvcpdnguvo.Chngtrnhm phng to ra dng in chy cc nhnh ca mch inv in p quatng phn t. in p v dng in thng c biu din bi cc dng sng.Khong thi gian mong mun ca cc dng sng ny c xc nh trc khichy m phng. Do mch in c nh v tn hiu u vo l xc nh nn miln chy m phng s cho cng mt kt qu ging nhau. Hn na, c th sdng tnh tay tm ra cng cc dng sng nh vy. Trong trng hp ny,mphngc sdng tit kimthigian v trnhcc liton hc dophi thc hin cc php ton di v nhm chn.Nugithituvocahthnglmtdngsngngunhin. Nichnh xc l nu u vo h thng l mt hm mu ca mt qu trnh ngunhin, th mt cch tng ng c th coi tr khng ca in tr l mt binngu nhin xc nh bi mt hm mt xc sut xc nh. Kt qu ca mphng ny s khng cn l mt dng sng xc nh v cc mu ca dng sngny s to nn mt tp hp ca cc bin ngu nhin. Cc m phng trong xut hin cc gi tr ngu nhin c gi l cc m phng ngu nhin. ly v d, chng ta gi thit in p qua mt phn t mch in ckhiule(t)vmphngc sdngtorae(t)trongkhongthigian 1ms,tc le(0.01). Trong m phngxc nhth e(0.01) khng i vchng ta c kt qu nh nhau sau mi ln m phng.Mt v d khc l h thng truyn dn s trong tn hiu thu bao gm38 Chng 3. L thuyt m phngtn hiu pht cng t m ngu nhin. Gi thit rng nhim v ca chngtal tnh xc sut li du ti u ra my thu. T gio trnh truyn dn chngta bit rng i vi truyn dn tn hiu BPSK qua knh AWGN, th xc sutli du lPE= Q__2EbN0_(3.4)trong Eb l nng lng du, N0 l mt ph cng sut tp m mt pha,vQ(x) l hm Q Gauss c nh ngha biQ(x) =12_xexp_y22_(3.5) rngPEl mt s ch khng phi mt bin ngu nhin, mc d tp mngu nhin xut hin u vo my thu. SPEl mt gi tr trung bnh saumt s ln th v hn, trong mt ln th bao gm vic gi mt s du siquahthngvquanstktquura.Ttnhinlktquscthl chnh xc hoc l mt li u ra. i vi cc qu trnh Ergodic (dng),chng ta c th xc nh xc sut li bng 2 cch. Chng ta c th xem mtbitctruynvtnhPEnhltrungbnhtphp(ensembleaverage),trongchngtacmttphp(ensemble)caccdngsngtpm ccng tnh cht thng k. Mt cch khc l chng ta c th xc nhPEnhl trung bnh thi gian bng cch truyn v hn cc du nh phn v s dnghm mu n ca tp m. im mu cht laf chng ta tnhPEda trn mts v hn cc du nh phn pht i. Nuthay v xc nhPEda trn mts vhn cc du pht, chngta c lngPEda trn mt s vhn ccdu pht, chng ta c lngPEs dng mt s hu hn cc du nh phnpht, chng ta s tm c rng c lng caPEthc t l mt bin ngunhin do mi hm mu c khong hu hn s to nn mt gi tr khc nhau(mong mun l khng nhiu lm) cho xc sut li. iu ny s c trnh by phn sau khi chng ta xem xt k thut Monte Carlo3.5 BER vs Xc sut li bitXththngtruyndnsnginHnh3.1vgithitrngchngtacn tnh t s li bit. K thut m phng c bn nht xc nh i lngphm cht quan trng ny l gi mt s ln cc du s qua h thng v tnhli thucuramythu. Kthutnycgi lmphngMonteCarlo. NuNdu c h thng x l vNe li m c u ra h thngth c lng Monte Carlo ca xc sut li lPE=NeN. (3.6)ilng ny c gi l BER theoNdu. ngha ca BER l n chotaclngcaxcsutlidu,mtheonhnghatnsuttngica3.6. Vai tr ca m phng 39xc sut lPE=limNNeN. (3.7)Do mt m phng theo yu cu c th ch cn x l mt s hu hn cc du,nn xc sut li du ch c th xc nh xp x.Do thut ng t s li bt v xc sut li bit thng c dng chung, cth c lng tng trong vic phn bit hai khi nim ny. Thc cht hai khinim ny hon ton khc nhau. BER l c lng ca xc sut li bit. BERthc cht l mt t s (t l), do n mang nghaNe li trongNdu truyn.Nu xt mt th nghim truynNdu qua mt knh ngu nhin (tp m)Kln, th s li NE m c trong mi ln thng khc nhau. Xc sut li bit,tuy nhin, li l mt s ch khng phi mt bin ngu nhin. V d, xc sutli bit cho mt h thng nh phn PSK trn knh AWGN lQ(_2Eb/N0) lc nh nuEb vN0 khng i.Thc t l vi Nln, c lngPEhi t nPE, theo nh ngha tnsut tng i ca xc sut.3.6 Vai tr ca m phngM phng c s dng rng ri trong nhiu cng on ca qu trnh thit kv trin khai cc h thng truyn dn hin i. Mc nh chnh ca m phngl nh gi phm cht v ti u tham s. Ngoi ra, m phng cn c sdng thit lp cc th tc kim chun (benchmark), d on tui th, vthm nh h thng sau khi c trin khai ra hin trng. Phng phpm phng s chu chi phi hay hng dn do dng thit k tng qut s dng.Thit k ca mt h thng truyndn phc tp thng c thc hintheophngthcttrnxungdi. Tcl, khi thitkmththngchngtabtumchthngvbtubxungchi titcathitkth thngxung cc h thng con, vcui cngl nmc phnt. Khitrinkhaihthngthqutrnhlicthchintdilntrn.Tcl, cc phn t c ch to trc, sau chngc lp rp thnh cc hthng con, v cui cng ton b h thng c xy dng t cc h thng con.Tngtnhthitkhthng,phttrinmphngcngcthchintheogii php t trnxung di. Chngta btu vimt m phngmc h thng c mc tu tng cao, tip theo l cc m hnh c th hn vm phng ca cc h thng con v cc phn t. Khi bt u qu trnh trinkhai, cc c tnh o c ca cc phn t v h thng con c b xung vom hnh m phng.3.7 Tnh ton qu tuyn v m phngQu trnh thit k mt h thng truyn dn bt u t vic xc nh v phntchcc yucungidngvk vngphmchtnhh schoqua,tlli, xc sut outage, v cc iu kin rng buc v bng tn, cng sut, trng40 Chng 3. L thuyt m phnglng, phc tp/chi ph, knh cng tc, tui th mong mun ca h thng.Da trn yu cu ngi dng, k s h thng xc nh cc khi nim ban uca h thng nh s iu ch, k thut m ha v san bng nu cn thit.Mttphpcaccgitrthams, cgi lch tiumcA,nhmccngsut, bngtn,vch siuchcngcthitlptronggiaionu ny ca thit k.Mc ch chnh ca giai on ny l xc nh t-p ca h thng v ccgi tr tham s s p ng cc rng buc thit k. Nh ni trc y, phmcht h thng l hm s ca t s tn hiu trn tp m (SNR, hay tng nglEb/N0) v mo tng cng gy ra do cc phn t trn ng truyn dn. Ts SNR c xy dng thng qua qu trnh tnh ton qu tuyn, m ch yul lin quan n tnh ton cng sut v cc tham s lin quan nh cng sutpht, li anten, suy hao truyn, li cng sut, h s tp m ca cc bkhuchi vlc. Mc dtnhton qutuynkhng phil biton quantm ca m phng, n li gip thit lp mt di cc gi tr SNR hayEb/N0 tin hnh c lng phm cht trong khong .Ngi thit k bt u vi cu hnh ban u ca h thng vi cc ch tiucp A v qu tuyn. Qu tuyn ch ra Eb/N0 ti mt im quan trng (critical)cahthngsaukhi ttcccsuyhaotrinkhai ctnhn. imccny thng chnh l u vo my thu. Qu tuyn c gi l cn bngnunh tuyncEb/N0 ln, vi mt l an ton (safe margin), to raphm cht chp nhn c ca h thng.Nu qu tuyn khng cn bng, cc ch tiu cp A, suy hao trin khai, vngay c cu hnh h thng cn thay i v qu tuyn cn phi tnh li. V d,c th cn thay i li cng sut pht, kch thc anten hay cc b khuch itp m thp. Sau khi cn bng c qu tuyn, th s dng m phng kim tra li qu tuyn v iu chnh li h thng. Nu nh qu tuyn ccn bng th chuyn sang giai on tip theo l thit k cc h thng con vcc phn t.3.8 Cc tham s nh gi phm cht h thngC nhiu i lng c s dng nh gi phm cht mt h thng. ivi cc h thng truyn dn thng tin thng thng t s SNR (hay t s CNR:Carrier-to-Noise Ratio) c s dng cho h thng tng t v BER (hoc cth SER: Symbol Error Rate hay FER: Frame Error Rate) c s dng chocc h thng truyn dn s. SNR c th cng c s dng lm tham s phcho nh gi phm cht ca h thng truyn dn s.T s SNR c nh ngha l t s ca cng sut tn hiu trn cng sutca tp m, tc lSNR =PsPn=E{s2(t)}E{n2(t)}(3.8)trong E biu din php ton ly gi tr k vng.Vi h thng truyn dn s, t s li bit BER thng khng th xc nh3.9. Nng lng v Cng sut tn hiu 41c m c c lng nh m phng Monte-Carlo. Gi thit s Nbit ctruyn i v xy raNe bit li u ra, t s BER c nh ngha lBER =NeN. (3.9)Thc cht y l c lng ca xc sut li bt c nh ngha biPE=limNNeN(3.10)Vi t s li khung chng ta cng c th nh ngha tng tFER =NfeNf. (3.11)trong Nfel s khung thu li vNfl tng s khung gi i.3.9 Nng lng v Cng sut tn hiuCc thnh phn nng lngEs v cng sut tn hiuPs c nh ngha nhsauEs=_s2(t)dt (3.12)Ps=limT1T_T/2T/2s2(t)dt (3.13)Trong trng hp tn hiu ri rc ( ly mu), nng lng v cng sut tnhiu c nh ngha nh sauEs= Tsn=s2[n] (3.14)Ps=limN12N+ 1Nn=Ns2(t)dt (3.15)Nu chui tn hiu l hu hn v chui c pht lp li, thEs= TsN1n=0s2[n] (3.16)Ps=1NN1n=0s2[n] (3.17)TrongMatlabcngsutcachui tnhius[n]ctnhnhsdnghmnorm.m nh sau:Ps=norm(s) 2/length(s)3.10 M phng Monte-Carlo trong Truyn dn S nh gi phm cht ca mt h thng thng tin s, m phng Monte-Carlothng c s dng c lng t s BER. Nh tho lun phn trn,42 Chng 3. L thuyt m phng c c lng chnh xc ca BER, chng ta cn tng s lng bit gi i nv cng (). Tuy nhin, vic tng s lng bit gi i ng ngha vi thi gianchy m phng s lu hn. V vy, c c s tha hip gia chnh xcca kt qu m phng v thi gian chy m phng, chng ta mong mun tmc s lng bit cn gi i Ntng ng vi gi tr BER mong mun. Chngta s nghin cu vn ny thng qua trng hp di y.Xt bin ngu nhiny= s + z (3.18)trong s l mt hng s, zl mt bin ngu nhin Gauss vi gi tr trungbnh m v phng sai 2z= 1. R rng l y cng l mt bin ngu nhin Gaussvi gi tr trung bnhm v phng sai2y= 1.Gi thit l chng ta cn c lng xc suty< 0 cho mt gi trs chotrc, tc lP(s) = P(y< 0|s) (3.19)bng m phng Monte-Carlo. C th l chng ta s dng my tnh to ramt chui cc bin Gauss ngu nhin, c k vng bng 0 v phng sai bng1, c lp thng k v c phn b ging nhau (i.d.d.),zi, i=1, 2, ..., N. Nhcngzi vis, chng ta c mt chui cc bin ngu nhinyi = s + zi, i = 1, 2, ..., N. (3.20)T cc bin ngu nhin tao ra bng my tnh ny, chng ta mong munclngxcsutmtbinngunhinGauss, vi kvngm, m>0vphng sai n v, nh hn 0. Chng ta lm php kim tra xem yi< 0 v nhngha mt bin ngu nhin mixi nh sauxi=_0, nu yi 01, nu yi < 0(3.21)Nh vy, c lng ca xc sutP(y < 0|s) lP(s) =1NNi=1xi(3.22)Ni cchkhc, clngP(s)nginlsccbinngunhinyi, i =1, 2, ..., Nnh hn 0 chia cho tng sNbin ngu nhin.Doc lngP(s) lmt hms ca cc binngunhin xi, i =1, 2, ..., N, nnncnglmtbinngunhin. xcnhchnhxccac lngny sovigitr thtP(s), chngta tnhgi trk vngvphng sai ca c lng ny. u tin l gi tr k vng caP(s)E[ P(s)] =1NNi=1E[xi] (3.23)Nhng doE[xi] = 0 P(yi > 0) + 1 P(yi < 0) (3.24)3.10. M phng Monte-Carlo trong Truyn dn S 43nnE[ P(s)] =1NNi=1P(yi < 0) (3.25)=1NNi=1P(s) = P(s) (3.26)iu ny chng t rng gi tr k vng ca c lngP(s) ng bng gi trthtP(s).Tip theo, chng ta tnh phng sai ca c lngP(s). Phng sai caP(s) c nh ngha nh sau2P(s)=E_P(s) E[ P(s)]_2(3.27)=E_P2(s)_P2(s) (3.28)Tuy nhin,E[ P2(s)] =E_1N2Ni=1Nj=1xixj_(3.29)=1N2Ni=1E[x2i] +1N2Ni=1Ni=1,i =jE[xixj] (3.30)V chng ta cE[x2i] = 0 P(yi 0) + 1 P(yi < 0) (3.31)vE[xixj] =E[xi] E[xj] = P2(s) (3.32)Thay (3.31) v (3.32) vo (3.30), chng ta thu c phng sai ca clng nh sauE[ P2(s)] =1NP(s) +N(N 1)N2P2(s) (3.33)1NP(s)[1 P(s)] (3.34)Ni chung, khi clngP(s)davomphngchngtamongmunlch chunP(s)l nh so vi P(s). V d, gi s l chng ta c lng mtxc sut nh,P(s) =103. Chng ta cn bit s mu cn thit l bao nhiu m bo lch chunP(s) l nh so viP(s)? Tc lP(s)=_ 1NP(s)[1 P(s)]_1/2P(s) (3.35)hay, mt cch tng ng,2P(s) P2(s).44 Chng 3. L thuyt m phngV vyN 1P(s)(3.36)Vd, nuP(s)=103, th N 1000. Nu chngta chn kchthc muN= 104, th trung bnh, chng ta s c 10 gi tr ca yi, i = 1, 2, ..., 104s nhhn 0. Chng ta coi kch thc mu ny nh gi tr nh nht thu c clngtincycaP(s).Vvy, theokinhnghim(asaruleofthumb)kchthc mu cn tha mnN>10P(s)(3.37)khiP(s) 1. iu kin ny thng c lng xc sut li ca mt hthng truyn dn s chu nh hng ca tp m cng v nhiu khc.V d: Trong mt h thng thng tin s, tn hiu thu c vi mc inps, (s > 0), chu nh hng ca tp m Gauss cng tnh c k vng bng 0v phng sai n v. Xc nh s mu nh nht Ncn thit xc nh xcsutP(y 0.5hocbk = randn(1, N) > 0trongNlsmucnto.Chui d liu bksau c iu ch BPSK. Php iu ch BPSK ycthcoitngngviphpnhxsk=_ Esnubk= 0Esnubk= 1(5.1)6364 Chng5. MphngMonte-Carlomtshthngvtuyninhnhtonnchui dupht sk {+Es, Es}. TrongtrnghpiuchBPSK, Es=Eb=1nnsk {+1, 1}. Dophpnhxbk sktrongiuchBPSKccthchinbngMatlabnhsausk = 1 2 bkCcduphtsktruynquaknhtruynvchunhhngcatpmAWGN. DonhhngcaAWGN, tnhiuthuyklxpchng(cng)caccduphtskvccdutpmnk,tclyk= sk + nk(5.2)trongnklccdutpmAWGNphccdngnk= nI,k + jnQ,k(5.3)trongnI,kvnQ,ktngnglthnhphnngphavvungphacatpm. Dophngsaicacc thnhphn2nI= 2nQ= 2n= N0/2, trongN0/2 l mt ph cng sut tp m. Nh vy, phng sai ca tp m nktrthnh22n=N0.toctpmnkviphngsai22nchngtacthsdnghmrandncsntrongMatlabtorachui ccdutpmcphnbchunchnhtc,rinhnvilchchuncatpmnnhsaunk = sigma (randn(1, N) + j randn(1, Ns)) (5.4) to ra tp m cnng lng tha mn t s (Eb/N0)reqchotrc chngtatlchchunn=_(2n) =Eb2(Eb/N0)req. (5.5)Tcl,sigma = sqrt(Eb/(2 EbNo))nk = sigma (randn(1, N) + j randn(1, Ns))Timythu,dotnhiuiuchBPSKch chathnhphnngpha(phnthc), nntchtnhiuphtskttnhiuthucyk, mythuthchintchlyphnthctrc, sauthchintchtnhiusdngphng php tch sng hp l ti u (MLD: Maximum Likelihood Detection).Cth,mythuthchinphpsosnhvquytnhsau:if yk 0 sk= +1 (5.6)elseif yk< 0 sk= 1 (5.7)PhpsosnhnycthchintrongMatlabnhsdnghmsign(yk).Tnhiutchc sksaucsosnhvi tnhiuphtsktnhtonphmchtlibtBERcahthng.Mtv dmuchngtrnhmphngtruynBPSKquaknhAWGNctrnhbychngtrnhMATLABBPSKAWGN.mMatlab Program5.1.Chngtrnh thc hin mphng viN= 105du BPSK {+1, 1}. Kt quBER thu c t chng trnh m phngBPSKAWGN.m c so snh vi gi trlthuyt[1]BERBPSKAWGN=12erfc__Eb/N0_(5.8)xcnhtnhchnhxccaktqumphng(xemHnhv5.2).5.1. MphngtruyndnBPSKquaknhAWGN 650 1 2 3 4 5 6 7 8 9 10106105104103102101Eb/No [dB]BERBER cua BPSK qua kenh AWGNBy simulationBy theoryHnh 5.2:Phm cht BPSK trn knh AWGN.MatlabProgram5.1 BPSKAWGN.m% Chuongtrinhmo phongtruyendanBPSKqua kenhAWGN% DinhnghiathamsoEbNodB=0:10;EbNo=10.^(EbNodB./10);sigLen=5*10^5;% Tao tinhieuBPSK{+1,-1}s=1-2*(rand(1,sigLen)>=0.5);% TinhtoannangluongbittinhieuEbEb=norm(s)^2/sigLen;% Mat dopho AWGNNo=Eb./EbNo;% Vonglap tinhtoanBER theoEb/Nofor k=1:length(EbNo)% TaoAWGNn=sqrt(No(k)./2).*(randn(1,sigLen)+j*randn(1,sigLen));% Tinhieuthuy=s+n;% Tachtinhieushat=sign(real(y));error=s-shat;noError=length(find(error~=0));BER(k)=noError/sigLen;end66 Chng5. MphngMonte-Carlomtshthngvtuyninhnh% BER lythuyetcua truyendanBPSKquakenhAWGNBERtheory=1/2*erfc(sqrt(EbNo));% Ve do thisemilogy(EbNodB,BER,*,EbNodB,BERtheory)xlabel(Eb/No)ylabel(BER)legend(Bysimulation,Bytheory)title(BERcuaBPSKquakenhAWGN)grid5.2 MphngtruyndnM-PSKquaknhpha-inhRayleighSmphngMonte-CarlocahthngtruyndnMPSKquaknhpha-inhRayleighcbiudinHnh5.3DataSourcebk+AWGNnky gs nk k k= +kCoherentDetectorgkErrorDetectionSER/BERCalculationyk^ Modulatorsksksk^MappingqkFadinggeneratorgk *gkgk*Decisionsk=Q{ } yk^^sk^Hnh5.3: SmphngtruyndnMPSKquaknhpha-inhsdngtchtnhiung b (coherent detection).01 2345 67( -1) Mp/M2p/MIQHnh5.4: S phn b tn hiu (signal constellation) ca tn hiu 8PSK.5.2. MphngtruyndnM-PSKquaknhpha-inhRayleigh 67Da trn thut ton m phng truyn dn BPSK qua knh AWGN, chngta c th xy dng thut ton m phng h thng truyn dn MPSK qua knhpha-inhRayleighnhsau:1. Todliuviuch: iuchM-PSKthchinnhm=log2 Mbtdliunh phnthnhmtimtnhiutrnsphnbtnhiunhtrnHnh5.4. Datrnphngphpgnnhnccimtnhiut0nM 1nhhnhv, chngtathyrngimtnhiuthicthcbiudinbisi = Aexp_2M i +M_(5.9)TrongA=EslbintnhiuvMlphabanucastnhiu.Nhvy,torachuiccduiuchMPSKsk,chngtacth to ra cc snguynngu nhinbk {0, 1, 2, ..., M 1}, ri thayi = bkcngthc(5.9).Nhvy,tonqutrnhtodliu,mapping,viuchcthcthchinbngMatlabnhsaubk = randint(1, N, [0 M 1]);theta = 2 pi/M bk + pi/M;sk = A exp(j theta)2. Toknhpha-inh:knhpha-inhgkctobithuttontopha-inh Rayleigh Mc 4.5. Trong trng hp pha-inh Rayleigh c th sdngktquBitp4.1.3. TotpmAWGNnk: tpmnkctorasdngphngphpmtMc5.1vi2n=Es2Es/N0.VitnhiuMPSKmtduskcha = log2 Mbitdliunhphn,vvy,quanhnnglngbitvducbiudinbiEs= Eb= Eb log2 M4. Tchtnhiungb(coherentdetection): nguynltchcoherentde-tection l s dng lin hp phc ca c lng knh truyn gk(c lngcnhccbclngknh)nhnvitnhiuthuykquayphatnhiu,bdchidopha-inh,vvtrbanu,tcl, yk= gkyk.thun tin cho m phng chng ta c th coi gkc c lng mt cchchnh xc, tc l, gk= gk, v s dng ngay gkcho tch tn hiu coherent.Mcdbngcchnynhhngquayphadopha-inhckhcphc, nhnggcphatnhiuthuvnkhngtrngvi gcphacatnhiu pht do cn chu nh hng ca tp m. S dng phng php tchtn hiu hp l ti a (MLD), b tch tn hiu thc hin quytnh datrngcphaca yk.Tcl,k= yk(5.10)trong biu din php tnh ly gc pha. Trong Matlab php tnh lygcnycththchincnhhmcsnangle. Tgcphak68 Chng5. MphngMonte-Carlomtshthngvtuyninhnhnychuidliuphtbanubkbngthaotcnhxngcbk=_M2k_(5.11)trong biu din php tnh lm trn v s nguyn gn nht v pha0, tc l php tnh ly floor. Trong Matlab php tnh c thc hinbnghmcsnfloor.5. TnhtontsliduSERvtslibitBER: sai sdu ca gia tnhiuphtbkvtnhiuthuc bk,cxcnhnhsosnhhiusk= bk bk, mi k = 0tng ngvi mt du b sai. V vy,t s SERcthtnhctnhbiSER =NseN(5.12) tnh c t s BER chng ta c th s dng hm biterr ca Matlabnhsau:BER = biterror(bk, bk_hat, kappa) (5.13)vikappa= = log2 M.Bi tp5.1S dng thut ton m phng truyn dn M-PSK Mc 5.2, vit chngtrnh m phng tnh t s li SER v BER cho iu ch QPSK qua knhpha-inhRayleigh.Sosnht sBERcaQPSKthucvixcsutlicaBPSKcngthc(2.7),vitnhnxt.Ti liuthamkho[1] H. Harada and R. Prasad, Simulation and Software Radio for Mobile Com-munications. ArtechHouse,2002.