2FSK-LFM Compound Signal Parameter Estimation Based on Joint FRFT-ML Method

Transcription

1 International Conerence on et eaureent Coputational ethod (C 5 FS-F Copound Signal Paraeter Etiation Baed on Joint FF- ethod Zhaoyang Qiu Bin ang School o Electronic Engineering Univerity o Electronic Science echnology o China Chengdu China Abtract hi paper propoe a novel ethod to etiate FSF copound ignal baed on joint FF- he repreentation o the copound ignal in FF doain i derived the chirp rate the code length o the copound ignal are etiated Joint with ethod a high accurate local earch approach i propoed the carrier requencie o the copound ignal are etiated Siulation reult how when SN>5dB our algorith can achieve a high accurate perorance ditinguih the dierent carrier requencie o the copound ignal requency i odulated by each carrier requency o FS alternately which ean the carrier requencie o FS ignal are odulated alternately he noied ignal odel can be expreed a eyword-fs-f copound ignal; paraeter etiation; ractional ourier tranor; axiu likelihood x(t = (t + n(t ( = (t = A e jπμ [t + ( ] + jπ [t + ( ]+ jθ od( = = t [ od( = I INODUCION FS (requency hit keying ignal F (linear requency odulation ignal are two kind o requency odulation ignal which have been ued in counication radar detection area their etiation ethod have been dicued by any reearcher [-] In ( n(t i Gauian white noie i the ignal (t = total length i the ignal part it can be regarded a a u o F ignal which have alternative carrier A θ are aplitude initial phae A = Ae jθ μ denote chirp repectively hen aue rate i tie oet i code length which equal the requencie In order to iprove the anti-interception capability or the detection perorance any kind o FS-F copound ignal which are PI (low probability interception ignal have been eployed in counication radar ield [3-5] Aong the FS-F ignal can overcoe the range or velocity eaureent law o FS FCW (F continuou wave ignal can achieve high accurate range velocity eaureent [5] For FS-F ignal the coon FCW ignal etiation ethod [6] cannot hle it weep length o FCW ignal i odd i carrier requency = while when equal even = In order to achieve high accurate range velocity eaureent iultaneouly the requency hit between hereore thi paper propoe a joint FF- (ractional Fourier tranor-axiu likelihood approach to etiate the ain paraeter o thi type o ignal he repreentation o the copound ignal in FF doain uing Ozakta algorith i derived a high accurate local earch approach which can ditinguih all requency hit i propoed Siulation reult how that the propoed algorith work well when SN>5 Frequency hi paper i organized a ollow In ection II the odel o FS-F ignal i given In ection III the chirp rate the code length etiation are propoed In ection IV the carrier requency etiation i dicued In ection V the iulation analyi i given ection VI i the concluion i all [5] II SIGNA ODE ie FS-F copound ignal cobine FS ignal FCW ignal together For each F ignal it carrier 5 he author - Publihed by Atlanti Pre FIGUE I FS-F SIGNA IE-FEQUENCY EPESENAION 44

2 Figure how the tie-requency repreentation o FS-F ignal without noie he gap o adjacent F ignal carrier requencie i narrow Our objective i to etiate the chirp rate code length two carrier requencie o the ignal III CHIP AE AND CODE ENGH ESIAION Becaue o Heienberg uncertainty principle windowed tie-requency analyi cannot give accurate etiation o the requencie with all gap code length iultaneouly However FF can overcoe thi law ince it i an overall tie-requency analyi it ulti-reolution property i uitable or the ignal with F part he deinition o FF i jπ( u cotα utccα+ t cot α Bα e ( t dt α nπ Sα ( u = ( t α = nπ ( t α = ( n+ π α i the rotation angle B α = jcotα n i an integer Ozakta algorith i widely ued to realize FF [7] However it require that the ignal length hould equal to the obervation tie length the obervation tie hould be yetric around the tie Unortunately our ignal cannot atiy thee requireent the repreentation o FS- F ignal in FF doain uing Ozakta algorith hould be derived irt Conider one F ignal in ( we have ( [ + ( ] + [ ( ]{ [ ] [ ] } + ε ε t [ ] (3 jπμ t jπ t ( ( t = Ae t+ t+ ake (3 be yetric around the tie yield [ ] + ( + [ + ( ] [ ε ε ] [ / / ] jπμ t t jπ t t ( t t = Ae ( t+ / ( t / t = +μ / t = + / + / Subtitute (4 into ( conider the tie doain tranlation property o FF [8] we can obtain the FF o (3 (4 { π[ μ μ α ]} S ( u = C Sa ( + ucc u = [ + ] μ μ( /ccα (6 will achieve it axiu Conider dienional noralization aue the apling requency i the coordinate o FF doain u correponding to the peak o (6 i we have u = / ( μ μ ( + + μ //ccα Fro (6 (7 the copound ignal will generate everal peak in FF doain whoe nuber equal to the nuber o F ignal in the copound ignal he coordinate o th peak in FF doain i greater than the th one thee coordinate will be aected by the code length the carrier requency according to (7 Fro the above FS-F ignal paraeter etiation baed on Ozakta algorith can be written a μ = cotα cc = u α μ + μ( μ = u cc α μ + μ( μ (8 u < u Fro (6 the peak aplitude will be aected by the correponding F ignal tie length hu to guarantee accuracy the irt the lat peak which oetie ean the aller peak hould not be ued when we calculate (8 Baed on the carrier requency property = (8 we can obtain the code length etiation = cc α / ( u u / μ (6 (7 (9 ( = jπ( μ+ cot α t + jπ[ μ μ t μ ( + ( u+ t co αccα] S u C e dt (5 Subtitute (9 into (8 the unknown paraeter in (8 becoe i known [3] other paraeter can be etiated by (8 However or the non- cooperative ituation i alway unknown (8 becoe an underdeterined yte o equation o deal thi proble next ection will give an approach j ( u+ t co cot + j [ t ( ] + j [ t ( ] C = AB e π α α πμ π α when μ =cotα (5 can be written a IV CAIE FEQUENCY ESIAION For the non-cooperative ituation Section III ha already μ etiated the chirp rate code length o copound ignal uing (8 (9 Norally the requency hit o 45

3 adjacent carrier requency i all For the purpoe o iproving etiation perorance de-chirp ethod i eployed ignal data within two code length i elected Structure F ignal a j ( t = e πμ rec t t [ ( Conider the copound ignal data in the irt etiated > code length I thee data exit two F ignal For the irt econd F ignal aue their carrier requencie a repectively j πμ ( t + + j π ( t + x Ori ( t = Ae + nt ( j πμ ( t + + j π ( t + x ( t = Ae + n( t Ori t [ ( t [ ( Ue ( the ae length data o ( to do de-chirp proce Here we conider the data in irt code length when μ μ we have x x A n = = + x A n (6 jπ ( N jπ ( N e e j ( N = = e π n = [ n ( n ( ] n = [ n ( + n ( N ] i n the apling interval In (6 n are Gauian white noie he likelihood unction o (6 i x A ( A = e σ ( πσ ( A A ( e σ x + x = πσ (7 o etiate the paraeter in (7 i equivalent to x A + x A iniizing the objective unction ( A = x A Aue ( A = x A For ( A we have x ( t = x ( t ( t = Ae + n ( t jπt + jπ Ori rec t [ (3 jπ t jπμ ( jπ ( x ( t = xori( t rec( t = Ae n ( t t [ (4 j = + μ = + μ μ A = Ae πμ j ( A = Ae πμ At thi tie the requency hit between i increaed a copared with the original requency hit Aue the noied ignal contructed by (3 (4 i x ( t = [ x ( t x ( t] (5 whoe data point nuber i N ewrite x ( t a x = ( ( ( x x x N aue the requency hopping point a hu the irt F ignal data length i the etiation ha been tranored to the etiation Cobine (3 (4 we have H H / =j ( D D/ (8 D = diag( N N (8 equal to it H x /( = can be written a hu the etiation o i arg ax( H / = x Siilarly the etiation o i H { x } arg ax / ( = N (9 ( iniizing objective unction i equivalent to axiizing ( = ( + ( ( = H x / ( = H x /( N hereore etiation i { } = arg ax ( ( 46

4 According to (9 ( ( an iterative approach can etiate the carrier requencie requency hopping tranition point Norally global earch will be ued in the greedy ethod it coputational load i heavy Furtherore when i cloed to the edge o elected data window (the elected data with one code length ethod cannot etiate the two carrier requencie [9] o overcoe the above law we give a new earch ethod Calculate Fourier tranor o (5 yield [ π ] X ( A ( Sa ( e jπ( ( = + jπ ( ( [ π( ] + ( A Sa e N ( j A Ae π j ( j ( = A = Ae πμ + π X ( A( X ( A which ean X ( will bring two peak Becaue the dechirp proce the two peak will not be overlapped he aplitude o the two peak will be aected by i at the iddle o the data window etiation will eet it optial reult According to the aplitude o the two peak in Fourier doain we can hit the data window let be cloe to the iddle o the window = X ( / X ( = X ( / X ( Set / Otherwie when < > > / Conider the noie the hit principle coare requency etiation are a ollow (a the data window hould be hited backward N / point etiate the two carrier < requencie in Fourier doain < 5 the data window hould be hited backward N /4 point etiate the two carrier requencie (b 5 the irt F ignal data in the data window i all Shit the data window backward 3 N /4 point the window will cover the econd the third F ignal hi i the reaon ( cover two code length Ater hit proce the etiated requencie becoe + μ μ + μ μ (c I are not atiied the above condition there will be no hit proce Ater hit proce coare etiation the etiated ( ( carrier requencie can be written a ( ( Subtitute the into ( yield Now i not at the edge o data window the iterative convergence rate i enhanced Furtherore intead o global earch the requency earch can be done near the coare etiated carrier requencie which reduce the coputational load ( ( arg H = ax( / ( Fix = x we have ( ( arg H = ax( / N x ro (9 ( { } ( = arg ax ( ( ( hen according to ( ( ( epeat the above proce i i = terinate the ( iterative proce the inal etiation reult are i ( i ( i Finally the = / hit etiation i hit i the hit length in tie doain < etiation i < etiation i the copound ignal carrier requencie = μ + μ = μ + μ the copound ignal carrier requencie = μ = μ + μ V SIUAION ANAYSIS Conider FS-F ignal he apling requency i et to 5Hz the aplitude i et to he chirp rate i 5Hz/u the code length i u the two carrier requencie are 7Hz 7Hz otal tie length tie oet are et to 78u 8u repectively he noie i Gauian white noie Chooe SN ro -5 to db 5 tie onte-carol iulation are conducted or each SN Figure II III how the NSE o code length/chirp rate etiation carrier requencie etiation repectively NSE - - NSE o code length NSE o chirp rate SN/(dB FIGUE IINSE OF CODE ENGH /CHIP AE 47

5 - NSE o NSE o [7] H Ozakta Orhan Arikan et al Digital Coputation o the Fractional Fourier ranor [J] IEEE ranaction Signal Proceing 44(9996 pp 4-5 [8] ao an Deng Bing Wang Yue Fractional Fourier ranor It Application [] inghua Pre 9 pp 4-7 [in Chinee] [9] uo-ching Fu Yung-Fang Chen obut Blind Frequency ranition ie Etiation or Frequency Hopping Syte [J] EUASIP Journal on Advance in Signal Proceing pp - NSE SN/(dB FIGUE IIINSE OF CAIE FEQUENCIES Fro Fig II becaue FF ha a better anti-noie property code length etiation chirp rate etiation can achieve a high accurate perorance (NSE< when SN>dB In addition ro Fig III when SN>5dB the carrier requencie etiation i accurate enough (NSE< it can ditinguih the carrier requencie with all requency hit VI CONCUSION hi paper propoe a novel ethod to etiate the ain paraeter o FS-F copound ignal baed on joint FF- he copound ignal repreentation in FF doain i derived the iproved etiation proce i elaborated Siulation reult how that our algorith can achieve a high accuracy when SN>5 ACNOWEDGEN hi tudy wa upported by the National Natural Science Foundation o China (676 EFEENCES [] S Barbaroa A Scaglione Paraeter etiation o pread pectru requency-hopping ignal uing tie-requency ditribution 997 Firt IEEE Signal Proceing Workhop on [] Signal Proceing Advance in Wirele Counication 997 pp 3-6 [3] Wei Zhang an ao A ie-fractional Fourier Joint epreentationbaed Paraeter Etiation ethod or Chirp/Frequency Hopping Spread Spectru Signal Firt International Conerence on Pervaive Coputing Signal Proceing Application pp 6-63 [4] Y oike S Ihii ohno DS/chirp hybrid indutrial UWB yte or ranging high reliability counication 4th Aia-Paciic Conerence on 8 pp -5 [5] atthia ronauge Herann ohling New Chirp Sequence adar Waveor IEEE ANSACIONS ON AEOSPACE AND EECONIC SYSES 5(4 4 pp [6] Van Nguyen A ow Coplexity Paraeter Etiation echnique or FCW Signal [J] IEEE ANSACIONS ON AEOSPACE AND EECONIC SYSES 5(4 4 pp