Synchronization Techniques for Burst-Mode Continuous Phase Modulation

Transcription

1 Sychozao chqu fo Bu-Mo Couou Pha Moulao Ph.D. Dao Df Eha Ho Dpam of Elccal Egg & Compu Scc Uvy of Kaa E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38

2 Oul Chap : Iouco Chap : h Camé-Rao Bou fo ag Squc Dg fo Bu-Mo CPM Chap 3: mg Ca a Fam Sychozao fo Bu-Mo CPM Chap 4: Applcao o SOQPSK Chap 5: Cocluo E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38

3 Exal Cobuo Chap : Iouco Chap : h Camé-Rao Squc Dg fo Bu-Mo Bou CPM" IEEE fo aaco ag o Commucao vol. 6 o. 6 pp Ju 3. Squc Dg fo Bu-Mo CPM Chap 3: mg Bu-Mo Ca CPM" o appa a Pocg Fam of h Sychozao IEEE Global Commucao Cofc GLOBECOM'3 Dcmb fo Bu-Mo CPM Chap 4: Applcao o SOQPSK Chap 5: Cocluo E. Ho a E. P "h Camè-Rao Bou fo ag E. Ho a E. P "ag Squc Dg fo Daa-A Sychozao of Bu-Mo CPM" Pocg of h IEEE Global Commucao Cofc GLOBECOM'.. E. Ho a E. P "Maxmum Lklhoo Sychozao of E. Ho a E. P mg Ca a Fam Sychozao of Bu-Mo CPM IEEE aaco o Commucao U Rvw. E. Ho a E. P "h Camé-Rao Bou fo Daa-A Sychozao of SOQPSK" Pocg of h IEEE Mlay Commucao Cofc MILCOM'. E. Ho a E. P "O Bu-Mo Sychozao of SOQPSK" o appa Pocg of h IEEE Mlay Commucao Cofc MILCOM'3 3. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 338

4 Movao: Aoaucal lmy ga wok Ehac lmy E poc Pack-ba lmy coa o amg lmy. Bf: pcum covao mul-hop hac mobly.. A mao challg h RF lk co a ychozao of pack.. bu Phycal lay wavfom: SOQPSK a ub of CPM I h wok:. Sychozao fo gal CPM bu-mo X. Apply h ul o SOQPSK.. E aa A A GS A3 GS GS: Gou Sao A: Acl E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 438

5 Wha CPM? Couou pha moulao: E ; α xph q : M-ay aa ymbol h: moulao x q: pha po Fqucy pul: g q Duao of L Pop: Coa vlop Bawh ffc Dawback: complx a Rx q g L=: full-po L>: paal-po L E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 538

6 Sgal amo Mol Bu-Mo amo: Gua Ival L L UW L pay Pambl UW Payloa Gua Ival Bu Sucu: Pambl ag quc: quc of L kow ymbol Uqu Wo UW: bu fcao Payloa: fomao b Rcv baba gal: f w o mol: AWG f : Fqucy off θ : Ca pha τ : m lay Sychozao Paam Ukow E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 638

7 Sychozao Poblm Challg: Acquo m mu b kp mmum bu-mo commucao o av bawh hu:. Ffowa appoach fo ho acquo m. Daa-a DA algohm o a ychozao Kow Pambl Payloa DA Emao Sychoz Poblm:. Pambl g: Wha h b pambl?. mg & ca covy: Emao of 3. Fam ychozao: Dco of pambl boua E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 738

8 Compao wh Rla Wok h Wok CPM -Fqucy -Pha -Symbol mg B Pambl Rla Wok ava 7 & Shaw -PSK Dboa -MSK -Oly Symbol mg CPM -Fqucy -Pha -Symbol mg -CPM -Bu-Mo amo mg & Ca Rcovy Fam Sychozao Zhao 6 -CPM -Pha & mg o Fq. Moll 7 -PSK Cho -PSK -Couou amo E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 838

9 h Camé-Rao Bou fo ag Squc Dg fo Bu-Mo CPM E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 938

10 Opmum ag Squc Dg: Camé-Rao Bou Mho wo appoach ca b ak o o v h opmum b ag quc fo mao of u f. Mmz h mao o vaac: α ag m ˆ α E u u MSE. Mmz h CRB.. a hocal low bou o mao o vaac of ay uba mao: E CRB compu va uˆ u α CRBu α α ag mcrbu α CRB u op α α I p uu u wh Iu E l ; u α Cooal CRB Fh Ifo. Ma. FIM Lklhoo Fuco op α E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38

11 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38 Ovvw of CRB Calculao Clo-fom FIM fo CPM a o mao I how h opmum ag quc mu afy h wo coo a h am m.. Maxmz C C h hb ha hb ha E u I ' ' L L B A u u g u g R a R R C g L L g g wh

12 Popo Opmum ag Squc Popo quc ba o ou aaly M- L 4 L -M- L I af A =B =. Opmum quc fo full-po CPM.. Oly ao => a-opmum quc fo paal-po CPM A' L 3 Maxmz C R L B' g L R W ca uc h appoxmao fo paal-po by ug ah ha L o uc h g-ffc EF g L a = fo full-po CPM E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38

13 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 338 Fg a Pop of h Opmum Squc. h am quc opmum fo fqucy pha a mg whch oppo o la moulao.. I follow h am pa fo all CPM. 3. h mmz fqucy a pha CRB a p of ulyg CPM paam. 4. h mmz ymbol mg CRB o p o CPM paam uch a fqucy pul. 5. I coupl ymbol mg mao fom pha a fqucy off ma C h E u I mg : pha : fqucy : 3 u u u

14 Mo Fg 6. h popo quc aympocally opmum fo paalpo CPM ~ CRBα ~ C 8Rg 8Rg α ~ ~ CRB L α C L R L R α g 7. Compu ach cofm h popo quc a mall L 8. W alo compu CRB fo aom quc a compa wh h opmum o: h opmum quc lv gfca ga fo ymbol mg mao of paal-po ao M-ay CPM. h fqucy a pha mao a l v o h lco of ag quc pcally fo log quc. g : Hypohcal quc : Popoquc E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 438

15 mg Ca a Fam Sychozao of Bu-Mo CPM E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 538

16 mg a Ca Rcovy Famwok Rcv Sgal: Dcompo mg lay: f w wh :g lay : facoal lay Fo mg a ca covy w aum g lay kow Jo maxmum lklhoo ML mao: ˆ ˆ ag max f f ; f R fˆ f a ε a mb h abov gal I qu a - moal g ach Obcv: coupl mg a fqucy h LLF E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 638

17 h ck: Pcw La Appoxmao Pha po of h opmum quc GMSK B =.3 M=h= Uwapp Pha - Ogal pha Appox. pha Smla a coqu ymbol cau h pha o caca ufomly W u la appoxmao of h pha ach gm h a lag fo paal-po CPM l E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 738

18 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 838 ν: omalz fq. off ε: facoal lay :baba gal hf by ε Appoxma Log-Lklhoo Fuco LLF Dc-m LLF: Appoxma baba gal: l l l l l l l l l h M h M h M α L q h α xp xp xp L L L L L L h M L h M h M R ; L La pha appoxmao Ogal pha wll b u h abov LLF m hf + amplg + moulao

19 Maxmzao of h LLF Ou appoxmao coupl mg a fqucy off: ; R h maxmzao of h LLF bcom aghfowa: Sp : Fqucy off mao: Sp : ymbol mg mao: Sp 3: ca pha mao: ag max M h M h ~ ˆ ~ ˆ ˆ ag{ ~ ag ˆ M h M h ˆ ˆ ˆ M h ˆ ˆ} Fuco of G ach E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 938

20 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38 Implmao of Fqucy Emao h cv p-poc λ ν a λ ν a compu ug FF opao: h pco ca b ca va:. Zo pag po h FF K f. Ipolao of FF ul ν u maxmum FF ohw xp L L L hl M ohw xp L L hl M L h M L h M

21 Jo ML Emao Block Dagam E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38

22 -6 Emao Pfomac: Fqucy a Pha Off - omalz Fqucy Eo Vaac -7 MSK RC M=h= GMSK RC M=4h=4 CRB E B Pha Eo Vaac - -3 MSK RC M=h= GMSK RC M=4h=4 CRB E B Smla pfomac fo ff CPM chm wh L =64 Wh.5 B of CRB a low o mum SR E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 38

23 Emao Pfomac: mg Off - L =64 omalz mg Eo Vaac -3 MSK CRB MSK RC M=h= CRB RC GMSK CRB GMSK RC M=4h=4 CRB RC E B h o vaac aa h CRB fo vaou CPM. Excpo: RC u o lag vao fom ou mpla gal. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 338

24 Fam Sychozao: Ovvw Po o mg a Ca covy w mu m pambl boua.. a-of-gal SoS p:. SoS co algohm: Dc h aval of a w bu a av locao of h SoS Icomg Sampl Pambl. SoS mao algohm: Ema h xac locao of SoS wh a obvao wow o Oly Pambl Raom Daa δ w p w : Obvao wow lgh p : Pambl lgh δ : Emao paam E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 438

25 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 538 SoS Emao Algohm Apply ML mao ul o h obvao wow Uwa paam νθα a avag ou F δ fo whch h lklhoo fuco maxmz xp xp ; w w p α ; w p w p p R C p ag max ˆ w w p p D R C : opmz va mulao q C q w faco Complxy : p D

26 SoS Dco Algohm W apply a mpl lklhoo ao LR ; ; p H H : vco of p : o pambl : Fully- alg pambl : hhol ampl Ug h am chqu a SoS mao h LR bcom D' p : m complxy D' : hhol; lc fo a gv pobably of fal alam yma- Pao co. ROC: PFA PL D ' p D ' H v. PD PL D ' p D ' H h LR pfom ug a lg wow. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 638

27 Fam Sychozao Pfomac SoS Dco Rcv Opag Chaacc ROC SoS Emao Pobably of Dco P D SR = B Impovm D'= L =3 D'=3 L =3 D'=4 L =3 D'= L = Pobably of Fal Alam P x -4 FA Pobabl a compu va mulao Pobably of fal lock: P Pobably of Fal Lock P FL L=64 D=63 q= L=64 D=8 q=.5 L=64 D=4 q=.4 L=64 D= q=.3 L=3 D=3 q= L=3 D=8 q=.5 L=3 D=4 q=.4 L=3 D= q= E B E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 738

28 Pug Evyhg ogh: Smulag a Bu-Mo CPM Rcv am bu of opmum pambl L fomao b Apply AWG + aom fqucy pha a mg off Rcv ucu: SoS Dco SoS Emao Jo ML Emao MF Vb Algohm â Fam Sychozao Dg paam: = K f = Gaua polao mg & Ca Rcovy CPM Dmoulao+ PLL D=D =4 w =L opmz fo ach cao ug mulao E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 838

29 B Eo Ra BER Pfomac GMSK h= M= RC h=4 M=4 - - B Eo Ra BER - -3 B Eo Ra BER L =3 L =64 Pfc Sychozao E b B -3-4 L =3 L =64 Pfc Sychozao E b B A pambl of 64 b pfom wh. B of h al ychozao E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 938

30 Applcao o SOQPSK E E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 338

31 Wha SOQPSK? A OQSPK-lk moulao whch ha a CPM pao a Pco CPM Moulao h pco ca pcal ffccy of SOQPSK compa o a bay CPM by mpog: cao b follow by a vc va Paal-po SOQPSK-G aop by h E aa.6.5 Pha Rpo SOQPSK-MIL SOQPSK-G omalz m E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 338

32 E Sychozao Pambl Lgh of L =8 b Poc a co of pag a quc of 6 b 8 m a a a k k fo k 7 O po m of ay ymbol ay Symbol m Ix E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 338

33 Bu-Mo Sychozao of SOQSPK-G: E Pambl W apply ou CPM chqu o SOQPSK by cog ay ymbol E pambl pha po Uwapp Pha a 4 3 l SOQPSK-G SOQPSK-MIL E Appoxmao omalz m SOQPSK-G po appoxma by SOQPSK-MIL Dvao of o ML mao algohm mla o h CPM wh h= a M= E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3338

34 Emao Eo Vaac fo SOQPSK: Opmum v. E pambl -7 - omalz Fqucy Eo Vaac -8-9 SOQPSK-MIL Opmum CRB SOQPSK-MIL Opmum SOQPSK-G Opmum CRB SOQPSK-G Opmum SOQPSK-G E CRB SOQPSK-G CRB E E B omalz mg Eo Vaac -3-4 SOQPSK-MIL Opmum CRB SOQPSK-MIL Opmum SOQPSK-G Opmum CRB SOQPSK-G Opmum SOQPSK-G E CRB SOQPSK-G E E B Pfomac gaao u o ao h E pambl Pha o vaac ha h am bhavo a h fqucy E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3438

35 Ovall Pfomac of SOQPSK: Opmum v. E pambl B Eo Ra BER Pambl B BER= -4 E.4 L =8.3 L = 64.6 L = 3-4 Opmum L =3 Opmum L =64 Opmum L =8 E L =8 Pfc Sychozao E B E pambl pfom vy clo o h opmum o wh L =8 h opmum pambl wh L =64 wh. B of h E Fal lock fo L =3 a low SR E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3538

36 Cocluo Gav a ovvw of ffowa ychozao mho fo CPM Dv h opmum ag quc fo CPM AWG Mmz h CRB fo all h ychozao paam Applcabl o h CPM famly clug M-ay a paal po Dvlop a o ML DA mao algohm fo mg a ca covy Dg ba o h opmz ag quc Pfom wh.5 B of h CRB a SR a low a B fo L = 64 Smula a bu-mo CPM cv: oly. B SR lo wh h opmum pambl of L =64 Appl CPM ul o SOQSPK fo E aa Fal ul: vlop a compl ffowa DA ychozao chm fo gal CPM clug: b ag quc mg a ca covy a fam ychozao E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3638

37 Aa of Fuu Suy Applcao o fqucy-lcv chal: ag quc g mg a ca covy Fam ychozao Jo ychozao a chal mao Aaly of fam ychozao algohm a ca b appl o oh moulao Pobably of fal lock SoS mao Pobabl of fal alam a co SoS co Hawa mplmao a a-off bw complxy a pfomac E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3738

38 hak You! Quo? Pla l b OVER I wo f h chqu woul wok fo my poblm Ig Duo I m playg Fu a Wha o ha l ay? E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3838

39 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 3938

40 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 438 Dvao of CRB FIM fo CPM a AWG compu va Clo-fom FIM fo CPM a o mao: u u R α u α u u I Rcv Pambl wo o ; α α u f E Pambl Duao L C h hb ha hb ha E u I :CPM Fqucy Pul g g g C g B g A L L L L

41 ag Squc fo Symbol mg Symbol mg CRB houl b mmz CRB α 8 h C 8 ha hb I I I I 8 ha hb h CRB omao houl b maxmz o mulaouly. Maxmz C. Mmz h quaac fom: J pov-f v Jv I mmz fo v A B Aumg C p of AB: I pacc C R. Full-po CPM: g L R R g g Quaac fom : L a α op v Jv ag maxc C co. A B uffc. α ubc o A B. Paal-po CPM: R maxmz g L AD A B. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 438

42 Popog h ag quc A=B= af wh: A' L L AD B' L C maxmz wh maxmz o g ao a mmz h quc. W popo h followg bay quc: L 4 L L 4 - I af A =B =. Opmum quc fo full-po CPM.. Oly ao => a-opmum quc fo paal-po CPM. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 438

43 Galzao of h Popo Squc W ca uc h appoxmao fo paal-po by ug ah ha L o uc h g-ffc EF M-ay CPM: Fqucy a Pha CRB: Equal hol f λ =λ = o A=B= Popo quc fo ymbol mg. Appoxmao: C S ' o maxmum valu h colao CRB 3 CL B 4 3 f α 3 L CL L B BL A 4L CRB α L CL 3 3 CL 3A 3A BL 3A Fqucy Pha mg Full-po Exac Exac Exac Paal-po EF EF C a EF L E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4338

44 Popo ag Squc a Appoxmao W popo h followg quc fo gal CPM a all ychozao paam: M- L 4 L -M- L EF uc a h quc lgh ca Appoxmao o C fo paal-po CPM a ymbol mg: ~ CRBα ~ C 8Rg ~ CRB L α C L R g 8Rg L R g α ~ : Hypohcal quc α : Popoquc h popo quc aympocally opmum E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4438

45 PSD of h Opmum Squc E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4538

46 Compu Sach fo h Opmum Squc: Gc Algohm GA h ao of h mmum CRB fou va GA o h popo quc CRB:..8 REC h= M= GMSK B =.3 RC h=4 M=4 CRB Rao Squc Lgh h GA uabl o f a b quc ha h popo o v a ho o moa lgh E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4638

47 Raom v. Opmum Squc: Symbol mg Emao - u CRB REC Op. CRB REC u CRB RC Op. CRB RC 6 5 RC M=4 h=4 GMSK B =.3 REC M= h= RC M= h= CRB - UCRBCRB m B E B L u CRB v. Op. CRB fo L=3 Compao of mao pfomac fo ukow a aom wh kow a opmum ag quc. UCRB v. Op. CRB Compao of mao pfomac fo kow bu aomly lc wh kow a opmum ag quc. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4738

48 Raom v. Opmum Squc: Fqucy a Pha Emao UCRB v. Opmum CRB.8.7 GMSK B=.3 RC M=4h=4 REC M=h= RC M=h=.8.7 GMSK B=.3 RC M=4h=4 REC M=h= RC M=h= UCRBf CRB m f B UCRBCRB m B L L Fqucy a pha mao a l v o h lco of ag quc E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4838

49 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 4938 Dvao of CRB Aumpo: Jo mao of u = f θ τ AWG h FIM lm: Obvao val: = L o L ymbol Compuao of h paal vav: o fo CPM: Fqucy pul: w E f α R u u u u u I u α u u u u u ; f u u Pul Fqucy wh ; q g g L α

50 Dvao of CRB Mo Smplfcao A B a C la CRB o fqucy pul a aa ymbol. hy a appoxma a A C L L L R g wh u wh R gug u u Eg-ffc: L L L fo paal-po CPM Colao fuco of g: R g L ug L g u fo C Rg Rg L B a L Pul Shap REC 3REC RC 3RC GMSK R g Rg Rg E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 538

51 Exhauv Compu Sach fo CPM Exac compu xhauv ach v. appoxma popo quc: CPM Exhauv Sach Popo Squc ΔCRB REC REC.6% 3REC RC RC.7% 3RC Lgh = 6 Bay CPM E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 538

52 CRB fo Raom Squc Compao of h opmum quc a a aom quc u CRB:. h lklhoo fuco avag ov α. Oly fabl fo MSK-yp CPM.. bay h= a full-po I u k l E 3. h abov xpcao compu va mulao Ucooal CRB UCRB: L L aˆ aˆ E E E ah aˆ ah uk ul. Cooal CRB avag ov α. aˆ E Avagg ov α ˆ CRB αe ˆ E CRB α. A clo-fom xpo wa fou fo ymbol mg UCRB α α E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 538

53 CRB fo Raom Daa Squc: u CRB DA mao wh aom ukow aa quc: Compuao of u CRB a a uac paam. Qu complx; may o b fabl fo gal CPM. Spcal ca: bay h= a full-po:. PAM pao: a c Rcv a~. a 'puo ymbol: p Gaua RV. 3. Avagg LF ov ' + paal vav FIM lm: I u k l E 4. Mo-Calo mulao CRB. R Im f c f c L L a a E ~ E E ah a ah uk ul a ~ ~ a~ v o E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5338

54 CRB fo Raom Daa Squc: Ucooal CRB UCRB Avagg h cooal CRB w.. h ag quc ul ucooal low bou o h MSE: E Avaggov α ˆ CRB α E ˆ Symbol mg CRB ca b xp a: E CRB α UCRB α α Wh: hu: UCRB umcal E E α Qα Smplfy α α E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5438

55 Compug mg UCRB Df: Z α Qα Appoxmao va aylo : UCRB Eg-compoo of Q: E Z E E Z E E Z 3 Expc valu of Z Ug h am appoach a mployg cal lm hom: E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5538

56 UCRB: Compuao of E{Z } L Rcall Z h co mom of Z w a X Wh a qu compuao of a. Appoxmao: Callm hom ~ 3 X ` a ucola a hc p. Fally X M E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5638

57 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5738 Maxmzao of LLF Dal. Dc-m LLF:. Appoxma CPM gal: 3. Appoxma LLF R ; L xp xp xp L L L L L L h M L h M h M R ; L L L h M L L L h M L h M

58 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5838 Maxmzao of LLF Dal 4. Raag LLF a 5. If h LLF maxmz wh pha 6. h LLF bcom whch maxmz by maxmzg 7. ha R ; h M h M h M h M ag ~ ~ ~ ~ ~ R ~ ~ ~ ~ ~ h M M h ~ ~ ag ~ ~ ~ ag max ˆ ~

59 La Pha Appoxmao: Oh CPM Exampl RC M=h= Uwapp Pha RC M=4h=4 Uwapp Pha E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 5938

60 FF a Ipolao Pco -4 o zo pag omalz Fqucy Eo Vaac -5-6 o Ipolao Kf= o Ipolao Kf= o Ipolao Kf=4 Paabolc Kf= Paabolc Kf= Paabolc Kf=4 Gaua Kf= Gaua Kf= Gaua Kf=4 CRB Ou choc: K f = Gaua o polao E B Fqucy MSE fo ff polao a zo pag faco. Boh polao a zo pag mu b p ba o mulao. E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 638

61 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 638 SoS Emao Algohm Dal 3. Lklhoo fuco of all ukow paam. Dop coa faco 3. Appoxma h xpoal fuco ug g aylo xp xp ; w w p α R xp xp ; w v w p α 4 4 R R R ; w w w w w m m m m m m m m C p α

62 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 638 SoS Emao Algohm Dal 3 4. Avag h lklhoo fuco w.. θ 5. Raag h abov lklhoo fuco 6. ak h xpcao w.. aa ymbol 4 R ; ; w w m m m m C p α R ; w w w C p α R ; p w p p w R C p Pambl Raom Daa

63 E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 6338 SoS Emao Algohm Dal A fqucy ma ca b v fom ach m h LLF 8. If w u ach ma copog m h LLF bcom p of fqucy off 9. Sc h LLF ow oly a fuco of δ ca b u fo mao of SoS ag ˆ w p p R ; p w p p w R C p ag max ˆ p w p p w R C q w C

64 Opmzao of Cδ GMSK p = 64 E = B Pobably of Fal Lock P FL - - C w q D= D=4 D = 8 D= q P FL compu va mulao Cδ mo mpoa fo lag valu of D E. Ho Ph.D. Df: Sychozao chqu fo Bu-Mo CPM 6438