The realization of low order FSM method and its application Jiai He1,a, Xiangyang Liu1,b, Chengquan Pei2,3,c

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1 3rd Inernionl Conferene on Mhinery, Meril nd Informion ehnology ppliion (ICMMI 05 he relizion of low order FSM mehod nd i ppliion Jii He,, Xingyng Liu,b, Chengqun Pei,3, Shool of Compuer nd Communiion, Lnzhou Univ. of eh, Lnzhou , Chin; Xi n Jioong Univeriy, Shni, i n, 70000, Chin; 3 Xi n Iniue of Opi nd Preiion Mehni of CS, hni, i n, 70000, Chin. hejii@lu.n, blingyng06@6.om, Pq49669@6.om Keyword: α ble diribuion; FLOS; low order FSM lgorihm br. Cyloionry iil hrerii i he min heory of udying non-ionry periodi ignl. Signl nd noie re lwy umed h obey Guin diribuion model in rdiionl ignl proeing. he environmen of non-guin pule i inreing omple, degrdion problem of yem performne n be olved by building α ble diribuion heory model. Firly, hi pper inrodue he α ble diribuion o eime FSM yli perum nd propoe yle perum nlyi under diree ignl. hen, he verifiion i given by king M ommuniion ignl on Mlb plform. he reul how h in omple environmen, he low-level FSM lgorihm whih i bed on α ble diribuion h beer performne on robune nd noie immuniy. Finlly, he lgorihm propoed in hi pper i pplied o onru hrerii prmeer, whih i imporn for blind ignl eprion nd idenifiion. Ⅰ.Inroduion he Guin umpion bed on he enrl limi heorem onform o he norml iuion, nd i deripion i imple, nlyi nd proeing re lo onvenien, mny priniple nd mehod of rdiionl reerh re re ofen umed o be Guin model, uh ignl hrerii nlyi, ignl filering, prmeer eimion nd deeion, yem idenifiion e., nd Guin diribuion model i lwy populr in he field. Bu in pril ppliion, he ignl we mee re ofen been ompnied by ome noie whih hve low probbiliy nd loud mgniude. If we ue Guin diribuion model o deribe uh proee, he ignl proeor performne will be ignifinly degrded for he noie nno mh wih he model well. herefore, we hve o onider uing non-guin ignl noie model nd deign proeing yem, o o mke hem in line wih ignl noie hrerii beer. α ble diribuion i kind of generlized Guin diribuion[-3], nd i i lo diribuion h n ify generlized enrl limi heorem. I beome he mo poenil nd rive model o deribe rndom ignl whih hve more ignifin pike pule wveform nd hiker il probbiliy deniy nion for i beer robune performne. α ble diribuion n deribe vriou degree of impule noie, whih i bed on eing differen hrerii prmeer, no mer he noie i ymmeril or ymmeril. hi rile promoe he FSM lgorihm o α ble diribuion, mke he imulion onfirmion o FSM lgorihm under he ble diribuion, nd preen he yem blok digrm. I provide new wy for ignl eprion, reogniion nd erion under impule noie environmen. Ⅱ.Frionl lower order yli perl deniy he iil momen of ignl onin welh of feure informion.frionl lower order ii heory(flos [4,5]i powerl ool for udying α ble diribuion. ( (, Hypohei, i rel SS diribued rndom proe whoe hrerii inde i α,nd poiion prmeer i 0.I rdiionl eond-order uoorrelion nion i: 05. he uhor - Publihed by lni Pre 830

2 ( If ( τ τ = E[ ( τ ( τ +τ ] R, ( i yloionry ignl h mee he following relion ( i yle R, = R +, ( he eond-order iil momen of he ignl i no ei when i i mied wih ble diribuion impule noie. herefore, frionl lower order yle ionry ignl n be defined (3: (, ; +, = (, ( +, = ( +, ; + +, R b E b R b (, ( (3 = In ddiion:, 0 < < /. ording o Fourier erie epnion: e jπe R (, b, = R (, ;, be d + (4 mong hem ε i yli frequeny. he power perum nd uoorrelion nion re Fourier rnform pir, we define he frionl lower order yli perl deniy following : j ( ;, ( τ;, = τ (5 e e π fτ S f b R b e d he moduled ignl i yloionrii. hrough nlyi he perl orrelion ruure of he ignl, we n omplee vriey of ignl proeing k, uh blind ignl deeion, modulion reogniion nd lifiion, prmeer eimion nd blind equlizion e.. Ⅲ. Low-level FSM lgorihm ( ume i eond-order yloionry proe, he yli perum bed on oninuou FSM lgorihm h he following epreion[6,7]: jπ + (, ( X f u e du = (6 α α α S (, f = X,, f X f + (7 We obin he orreponding diree FSM lgorihm following [8] : ( M / α α α SX (, f = X,, f f vf X f vf (8 M v= M / Where X (, f mong hem ( k moohing, F = N ( h he following form: N (, = ( ( j k= 0 X f k k e π f ( k i window for he enuion d, f = MF i he widh of he perum i he frequeny domin mpling widh, i he ime domin mpling widh,, N = +. he eond-order iil momen of nd N i he ol number of mple in he he ignl i no ei when i i mied wih ble diribuion impule noie. herefore, he low-level iil feure under ble diribuion i inrodued in(4 (5, he reul following: X, f + u e j π = du p, = (9 Diree e [9] : ( α α α SX, (,,, p f = X f + X f (0 83

3 mong hem ( ( M / α ( α ( α X (, =,,, p f M v= ( M / S f X f vf X f vf ( ( X, f h following form: N ( (, = ( ( j k= 0 X f k k e ll of he prmeer re onien wih he Guin model. Ⅳ. Emple nlyi o( We ke modulion ignl f = π f perum: ( If i omple ignl, +/ ( jπ (, = ( o( π f / F v e du π f ( k for emple o nlyze low-level irulion + + ( jπ ( jπ F, v = o π f e du = o π f e du f + f p ( ( Sf, p f = lim lim F, f F, f + df f 0 f f f herefore: (4 If ( i rel ignl, ( + ( + jπ jπ, = o π = ( gn ( o( π (5 F v f f e du f f e du 0< p, = P, 0<,Mke he following hnge: f g f ( ( = ( g( = We n obin he me perl nion wih he plurl form by urning he rel form ino plurl form. o( In he diree e, f = π f (,ume i omple ignl, i he mpling ' ' ume: f ( = f ( + j f (, herefore f ( Re f ( N j, ( ( F f = k f k e inervl, k = 0 herefore: π f ( k = π ( M N j p f ( k, p(, (. ( ( S f M ( M k = 0 v= S f = k f k f k e N j p f + ( k ( k f ( k f ( ks e k = 0 he yem blok digrm i hown in figure : ( (3 (6 (7 83

4 S X α (, f - k= - + Figure low-level FSM lgorihm yem relizion digrm Ⅴ. Feure erion bed on low-level yle perum I i no diffiul o ge oher moduled ignl' yli perum epreion under ble diribuion hrough he bove mhemil nlyi. we n ele he following hrerii prmeer bed on low-level yli perum : = he mpliude of yle perum f+ / S ( f = 0 : S ( f = 0 = k Q(/ Q*( / /4 = + / BPSK p S S / ( f = 0 = k Q(/ Q*( / / = + / OQPSK MSK p S = he mpliude of yle perum / S ( f = f : S / ( f = f = k Q(/ Q*( / /4 = / BPSK MPSK p S = 3he mpliude of yle perum / S ( f = f : S = f+ / BPSK ( f = 0 = 0 = / S OQPSK / MSK ( f = f = 0 = / = / SBPSK / MPSK ( f = f = kp Q(/ Q*( / /4S S / ( f = f = k Q(/ Q*( / / OQPSK MSK p S k p From he bove heoreil nlyi, we know h i onn reled o p, nd build up following hrerii prmeer bed on low-level yli perl: = = = S ( f = f S ( f = f = = = f + S S ( f = f ( f = 0 hrough nlyi, ignl' hrerii prmeer hown in ble : ble he hrerii prmeer of differen modulion ignl BPSK QPSK/8PSK MSK/OQPSK Q(/ Q*( / Q(/ Q*( / Q(/ Q*( / Q(/ Q*( / 0 0 he reul howing in he ble, he hrerii prmeer of BPSK nd MPSK i me, nd i lwy more hn, while he hrerii prmeer of MSK nd OQPSK i 0. We n epre he BPSK/MPSK nd MSK/OQPSK by eing he hrehold h =. Similrly, for he hrerii prmeer, he BPSK nd QPSK/8PSK lo n be epred by eing he hrehold h =. We n idenify differen moduled ignl by deigning he bove lifiion, whih ruure i imple, bu h good performne in omple environmen. herefore, he low order yli perum nlyi of he modulion ignl in hi pper offer new pproh o modulion reogniion under α ble diribuion. Ⅵ. Compuer imulion We mke imulion for M modulion ignl, he rrier frequeny f = 00kHz, he mpling frequeny i 600KHz, he ymbol re i 56, nd he bebnd ignl i ingle inuoidl nion. We hooe onvenionl eond-order orrelion nlyi mehod when miing impule noie nd Guin noie (SNR = 5dB. he imulion reul figure nd figure3.mking imulion for M modulion ignl by uing he lgorihm propoed in hi pper, he imulion reul figure 833

4 nd figure 5(p=.Under Guin umpion, he yloionry of M ignl bed on eond-order yli perl heory figure 6. ording o heoreil nlyi we n obin h he mimum orrelion pek pper α = 0, α = ± f 0.

nd we ompre Figure 3 o Figure5, he lgorihm bed on he umpion of α ble diribuion h beer ni-noie performne hn Guin umpion.

5 4 nd figure 5(p=.Under Guin umpion, he yloionry of M ignl bed on eond-order yli perl heory figure 6. ording o heoreil nlyi we n obin h he mimum orrelion pek pper α = 0, α = ± f 0. Figure 5( nd Figure5(b how h wo pek pper he α = 0,nd he oher pek pper α = ± 30KHz.Figure3(, Figure3(b how he yle perum bed on he rdiionl mehod ffe perl ruure under edy noie diribuion. nd we ompre Figure 3 o Figure5, he lgorihm bed on he umpion of α ble diribuion h beer ni-noie performne hn Guin umpion. he reul how h he lgorihm bed on he umpion of ble diribuion i effeivene nd relibiliy. ( ξ = 0 (b f = 0 Figure M ignl yle perum wih mied noie Figure 3 Seionl view of he yli perum ( ξ = 0 (b f = 0 Figure 4 M ignl 3D yle perum Figure 5 Seionl view of he yli perum Ⅶ.Summry ording o he nlyi bove, i i ler h he ruure of yli perum on he lph ble diribuion i he me he ruure on he umpion of he Guin. Bu he mgniude i differen, whih minly depend on he hnge of p. If p =, he frionl yli perum i rnformed ino he eond-order yli perum. In ddiion, he nlyi of yloionriy feure bed on he umpion of non-guin h good ni-noie biliy.he yli frequeny or perl ruure n be regrded e of prmeer o idenify differen modulion ignl, whih i bed on he onluion h differen ommuniion ignl hve differen yli ruure. Beide, he heory n be pplied o he blind oure eprion, whih i of he hrer of pule noie. he yli frequeny or new vrible bed on yloionriy n be een hrerii prmeer o epre. In onluion, i i very meningl for enrihing he heory of ignl proeing o udy he hrer of yloionriy ignl under ble diribuion. knowledgemen hi work w uppored by he Nionl Nurl Siene Foundion of Chin (No.65603,nd he Nurl Siene Foundion of Gnu Provine(No.48RJZ08. For more informion on low order FSM mehod, end he emil o lingyng06@6.om. Referene [] Grdner W. Cyloionriy in Communiion nd Signl proeing[r]. New York. IEEE pre,994,pp:

6 [] Chen H L, Wng J, Zhng Y, e l. Reerh on prmeerizion of ble diribuion[c]//eleroni Engineering nd Informion Siene: Proeeding of he Inernionl Conferene of Eleroni Engineering nd Informion Siene 05 (ICEEIS 05, Jnury 7-8, 05, Hrbin, Chin. CRC Pre, 05: 405. [3] Niki C L, Sho M. Signl proeing wih lph-ble diribuion nd ppliion[m]. Wiley-Ineriene, 995. [4] Ling Y, Chen W. urvey on ompuing Lévy ble diribuion nd new MLB oolbo[j]. Signl Proeing, 03, 93(,pp: 4-5. [5] Cek M E. Cover ommuniion uing kewed α-ble diribuion[j]. Eleroni Leer, 04, 5(,pp: 6-8. [6] Grdner W. Meuremen of perl orrelion [J]. IEEE rn.ou Speeh, Signl Proeing. 986, 34(5,pp:-3. [7] him M,Cngrjh C N,Bull D R. Comple wvele domin imge ion bed on frionl lower order momen[c].ieee Inernionl Conferene on Informion Fuion 005, pp:55-5. [8] Willim.Grdner. Meuremen of Sperl Correlion [J].IEEE rnion on oui, Speeh nd Signl Proeing, O 986, Vo.34, No.5, pp:-3. [9] Grdner W. he perl orrelion heory of yloionry ime-erie [J]. Signl Proeing, 986,(, pp:

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