Circular Faster Than Nyquist: Transmitter and iterative receiver design

Texte intégral

(1)Circular Faster Than Nyquist: Transmitter and iterative receiver design Romain Tajan, Charly Poulliat, Marie-Laure Boucheret. To cite this version: Romain Tajan, Charly Poulliat, Marie-Laure Boucheret. Circular Faster Than Nyquist: Transmitter and iterative receiver design. 9th International Symposium on Turbo Codes and Iterative Information Processing (ISTC 2016), Sep 2016, Brest, France. pp. 241-245. �hal-01709136�. HAL Id: hal-01709136 https://hal.archives-ouvertes.fr/hal-01709136 Submitted on 14 Feb 2018. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18832. To link to this article : DOI : 10.1109/ISTC.2016.7593113 URL : http://dx.doi.org/10.1109/ISTC.2016.7593113. To cite this version : Tajan, Romain and Poulliat, Charly and Boucheret, Marie-Laure Circular Faster Than Nyquist: Transmitter and iterative receiver design. (2016) In: 9th International Symposium on Turbo Codes and Iterative Information Processing (ISTC 2016), 5 September 2016 - 9 September 2016 (Brest, France).. Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr.

(3) # ) !" ) ) %#!") !"" ) ) " "$) $ )

(4) !) ,*'+6 (+6 &.)56 ,2))'016 .'$2.$6 ,2!&$.$016 6 6

(5) 6 ,."$246 6 +'36 ,%6 ,."$246 6 .

(6) 6 )$+!$6 .+!$6 *')6 .,*'+0(+'*/ ,."$24%.6 1+'3$./'056 ,%6 ,2),2/$6 6 ,2),2/$6 .+!$6 *')6 !&#5-,2))'0*.'$2.$ ,2!&$.$0$+/$$'&0%.6. 8a|~z`c~Ep " " " " " " !. "

(7) " " " " " " " ! " " " "

(8) " " " " " " " " " " " " " "

(9) " " " "

(10) " " ". KKR> " " "

(11) " " " " " " " " " " " " " ". ,

(12) s. #*2.+32"+*\. Ia_gWJLeLJshaseLJjILshVLs_j]HLesaMsghGhLgsG_JshasVG_J[LsVWUVLes Ia]beLggWa_sMGIhaeg

(13) sjhsWhsaMhL_sIa]LgslWhVsGsgWU_WQIG_hs[aggs W_sbLeMae]G_IL

(14) s ,_s hVWgs bGbLes lLs Ia_gWJLes G_s WhLeGhWkLs 2W_W]j]s 2LG_s <djGeLs %eeaes 22<%s [W_LGfs LdjG[WoLes Maes ]WhWUGhW_Us \<,s W_heaJjILJs Hns'=3sgWU_G[W_U

(15) sgsG_s LPIWL_hs W]b[L]L_hGhWa_s lLsbeabagLshasjgLsGsIWeIj[Gesbj[gLs gVGbW_Us lVWIVsWgsGIVWLkLJs hVeajUVs IWeIj[Ges Ia_ka[jhWa_s Ghs hVLs L]WhhLe

(16) s BLs beabagLs G_s LPIWL_hs W]b[L]L_hGhWa_s aMs hVWgs IWeIj[Gfs bj[gLs gVGbW_Us W_s hVLs MeLdjL_InsJa]GW_

(17) s,hshVL_sG[[algsjgshasbLeMae]s[alsIa]b[LmWhns LdjG[WoGhWa_s W_s hVLs MeLdjL_Ins Ja]GW_s Ghs hVLs eLILWkLe

(18) s =VLs IaeeLgba_JW_Us heG_g]WhhLesWgs HGgLJsa_s'Gghs 'ajeWLes=eG_gMae]s ''=sabLeGhWa_gshVGhsG[[algsGs[alsIa]b[LmWhnsG_JshVGhsGkaWJgs hVLs W_heaJjIhWa_s aMs Gs InI[WIs beLQms Ggs Ja_Ls W_s C#'Do G_Js C#(Do a]bGfLJs has C#'Do C#(Do hVLs beabagLJs GeIVWhLIhjeLs lW[[s Gjha]GhWIG[[ns VGkLs Gs HLhhLes gbLIheG[s LPIWL_Ins W_s bGehWIj[Ges Maes VWUVs JGhGs eGhLgs hVGhs IeLGhLs \<,s lWhVs Gs [a_Us JL[Gns gbeLGJs G_Js gas Gs [a_Us InI[WIs beLQm

(19) s =VLs beabagLJs GeIVWhLIhjeLs Wgs gheGWUVhMaelGeJ[ns LmhL_JGH[Ls has SLdjL_Ins gL[LIhWkLs IVG__L[gs HnsGJJW_UsGsInI[WIsbeLQmsGIIaj_hW_UsMaeshVLs[L_UhVsaMshVLsMeLr djL_InsgL[LIhWkLsIVG__L[sa_[n

(20) s=VLsbeabagLJs22<%sLdjG[WoLes VGbbL_gs HLMaeLs hVLs ]GhIVLJs Q[hLes VL_ILs lLs Jas _ahs VGkLs has VG_J[Ls IaeeL[GhLJs _aWgLs Ggs Whs Wgs hVLs IGgLs W_s C#'Do C#*Do C#(Do =VWgs ghejIhjeLs beLkL_hgs jgs Mea]s ]GZW_Us ghea_Us Gggj]bhWa_gs a_s hVLs _aWgLs Ggs G_s :s Gggj]bhWa_s W_s C#*Do aes lVWhLs _aWgLs Gggj]bhWa_sW_s C#'Do aes CU(Do ,_s C#+Do G_sLPIWL_hs 5'"2 582s ]j[hWIGeeWLes'=3sGeIVWr hLIhjeLs Wgs beabagLJ

(21) s gs hVWgs GeIVWhLIhjeLs Wgs 5'"2 HGgLJs Whs Wgs G[gas HGgLJs a_s Gs ''=s ghLbs ValLkLes W_s ajes IGgLs ,''=s G_Js ''=s ghLbgs GeLs jgLJs Maes G_s LMQIWL_hs Ia]bjhGhWa_s aMs Gs IWeIj[Ges Ia_ka[jhWa_s gashVGhs lLs Ia_gWJLesgW_U[LsIGeeWLes'=3

(22) s =VLseLghsaMshVWgsbGbLesWgsaeUG_WoLJsGgsMa[[alg

(23) s=VLsbeabagLJs IWeIj[Ges '=3sGeIVWhLIhjeLsWgs JLhGW[LJs W_s <LIhWa_s,,

(24) s,_s<LIhWa_s ,,,s hVLs WhLeGhWkLs 22<%s Wgs JLeWkLJ

(25) s ,_s <LIhWa_s ,@s gW]j[GhWa_s eLgj[hgs hVGhs gVals hVLs bLeMae]G_ILgs aMs ajes GbbeaGIVs GeLs beLr gL_hLJ

(26) s. 2aghslGkLMae]gsMaes]aJLe_sIa]]j_WIGhWa_sgnghL]gsgGhWgMns hVLs3ndjWghsIeWhLeWa_shaseL]akLs,_hLes<n]Ha[s,_hLeMLeL_ILs\<,s Ghs hVLs eLILWkLe

(27) s <nghL]gs hVGhs GW]s has W_IeLGgLs hVLWes hVeajUVbjhs Hns VGkW_Us Gs JGhGs eGhLs GHakLs 3ndjWghs eGhLs GeLs IG[[LJs 'GghLes =VG_s 3ndjWghs '=3s gnghL]g

(28) s ,_heaJjILJs Hns <G[os C#Do W_s hVLs LGe[ns gLkL_hWLgs Whs Wgs gVal_s hVGhs '=3s IG_s W]beakLs hVLs JGhGs eGhLsHjhshVLsUL_LeGhLJs\<,s]GnsHLsbeaVWHWhWkLsIa]bGeLJshashVLs W_IeLGgLsaMshVLs]aJj[GhWa_saeJLe

(29) s1GhLes 2Goas C'Do gValLJshVGhs j_IaJLJs '=3s Wgs baggWH[Ls lWhVajhs G[hLeW_Us hVLs Whs %eeaes :GhLs %:sbLeMae]G_ILsaMsGsHW_GensIa^]j_WIGhWa_slWhVsGsIGfJW_G[s gW_Lsbj[gLsGgs[a_UsGgshVLseGhWasaMshVLs3ndjWghseGhLsG_JshVLsGIhjG[s gn]Ha[s eGhLs Wgs GHakLs Gs hVeLgVa[Js _als IG[[LJs 2Goas Haj_J

(30) s 2aeLs eLIL_h[ns '=3s VGgs Z_al_sGs eLUGW_s aMsW_hLeLghs Ggs W_s C(Do C*Do C+Do C-Do C.Do C/Do G_Js eLMLeL_ILgs hVLeLW_

(31) s ,_s bGehWIj[Ges C.Do VGgsgVal_shVGhs'=3sGIVWLkLgshVLs]GmW]G[sW_Mae]GhWa_seGhLsMaes W_JLbL_JL_hs G_Js WJL_hWIG[[ns JWgheWHjhLJs )GjggWG_s IaJLHaaZg

(32) s ,_s MGIhs C.Do G[gas Ia_gWJLegs ]aJj[GhWa_s Ia_gheGW_LJs W_bjhg

(33) s ,_Mae]GhWa_s eGhLgs Maes ]aJj[GhWa_s Ia_gheGW_LJs G[bVGHLhgs GeLs _j]LeWIG[[ns Ia]bjhLJsjgW_UshVLs ]LhVaJs beabagLJs W_s C0D1o hVWgs ]LhVaJs eLdjWeLgs has W]b[L]L_hs hVLs MaelGeJs bGehs aMs Gs /:s GV[s aIZLs/L[W_LZs:GkWks G[UaeWhV]sa_shVLsheL[[WgsGIIaj_hW_Us Maes hVLs IVG__L[s ]L]aen

(34) s 2aghslaeZgsa_s'=3sIa_gWJLes eLILWkLegshVGhsGeLsheL[[Wgs HGgLJs JLhLIhaegs Ma[[alW_Us Gs ]GhIVLJs Q[hLeW_Us JLeWkLJs LWhVLes Sa]s hVLs 'ae_Lns eLILWkLes lVL_s _aWgLs lVWhL_W_Us Wgs baggWH[Ls WL

(35) s Maes Ia]beLggWa_s MGIhaegs GHakLs Gs UWkL_s hVeLgVa[Js aes WMs _ahs Gbb[WIGH[Ls Mea]s hVLs >_ULeHaLIZs eLILWkLes C#!Do ahVs eLILWkLes GeIVWhLIhjeLgs GeLs HGgLJs a_s heL[[WgLgs lVagLs _j]HLes aMs ghGhLgs ,,

(36) s ".3( .\ ,3(0\ 0 ,"*\ Wgs Lmba_L_hWG[s W_s hVLs LdjWkG[L_hs \<,s IVG__L[s [L_UhV

(37) s'aes'=3s hVLs LmGIhs W]b[L]L_hGhWa_s aMs hVLgLs eLILWkLegs Wgs eLgheWIhLJs has 7 Bd[fXPggKIofPN[GTo BLs Ia_gWJLesGsMeG]Ls HGgLJsheG_g]WggWa_s lVLeLs hVLsMeG]Lgs gn]Ha[seGhLgsI[agLshashVLs3ndjWghseGhLsgW_ILshVLgLseGhLgsIeLGhLs \<,slWhVsg]G[[s[L_UhV

(38) s2aeLakLeshVLs]aJj[GhWa_saeJLesWgsaMhL_s VGkLs JjeGhWa_s "4 4 HLW_Us hVLs _j]HLes aMs gjHSG]Lgs Ia]r ZLbhs[alshasGkaWJsGsIa]b[LmWhnsW_IeLGgL

(39) s:LJjILJsIa]b[LmWhns bagW_Us Gs SG]L

(40) s BLs lW[[s Ia_gWJLes hVGhs IaJLlaeJgs G[lGngs heL[[WgsHGgLJsJLhLIhaegs gjIVsGgs /:s C##Do VGkLsHLL_sG[gas gbG_s G[[s gjHSG]Lg

(41) s =VLs heG_g]WggWa_s aMs 44 W_Mae]GhWa_s.

(42) =` \s Wgs aHhGW_LJs Ggs hVLs JWgIeLhLs hW]Ls IWeIj[Ges Ia_ka[jhWa_s HLhlLL_s C` YsjbgG]b[LJsHns GsMGIhaes 4 G_JshVLs gG]b[LJsQ[hLes N7[6ks VL_ILs j` \sIG_sHLsIa]bjhLJsjgW_UshVLsGeIVWhLIhjeLs beabagLJsW_s '-*?;&s 'o lVLeLs. ECSP>\ k EP;SH8PHW\ QD8N><\ ")\. #"p\s. HWhgs _c h] s:V s sh3)AHfsMa[[algs hVLs ghLbgs beLgL_hLJs W_s '-*?;&s#o 'Weghs _c WgsL_IaJLJsW_has 4 gn]Ha[gsjgW_UsGs9 Gens Whs,_hLe[LGkLJs aJLJs2aJj[GhWa_s , 2s _c WgsL_IaJLJsW_has F] s V s s 3+AVfsjgW_Us Gs IVG__L[s Gs HW_Gens IaJLlaeJs Vc IaJLslWhVseGhLs !4 IhVL_s Vc WgsW_hLe[LGkLJsgashVGhs #'4 #)(4 G_Js Q_G[[ns Vc Wgs ]aJj[GhLJs jgW_Us hVLs 9 Gens ]aJj[GhWa_s W_has Bs C] s sC_,VKs =VWgs ]aJj[GhLJs bGIZLhs Wgs gb[Whs W_has 4 bGehgs B`s C` ] s sC` ,A&f

(43) s LGIVs bGehs HLW_Us IWeIj[Ge[ns gVGbLJs W_JLbL_JL_h[ns aMshVLsahVLeg

(44) s =VLsgVGbW_UsQ[hLesWgsGs:aahs:GWgLJs agW_Ls:: sQ[hLes Nses lWhVsea[[aOsIaLPIWL_hssG_Js3ndjWghsHG_JlWJhVs Wc s <n]Ha[gs c C` YsGeLsgL_hslXhVsGsgn]Ha[sbLeWaJs 6cs 96Os lWhVs9s= EFs G_Js hVLsIWeIj[Gf[ns bj[gLs gVGbLJs Ggs Ma[[algs . . . . . . . -Vs. . 8II N7S6kIRT/s T2s. ,hs IG_s HLs _ahLJs hVGhs ajes ga[jhWa_s Wgs JWOLeL_hs Sa]s hVLs a_Ls beabagLJs W_s C#'Do gW_ILs hVLs IWeIj[Ges Ia_ka[jhWa_s Wgs Gs JWeLIhs Ia_gLdjL_ILs aMs hVLs ''=.,''=s ghLbgs G_Js JaLgs _ahs eLdjWeLs has heG_g]Whs G_ns InI[WIs beLQm

(45) s a_gLdjL_h[ns ajes ga[jhWa_s VGgs Gs HLhhLes gbLIheG[s LPIWL_Ins hVG_s hVLs a_Ls beabagLJs W_s C#'Do ,_s hVWgs bGbLes lLs a_[ns Ia_gWJLes Gs RGhs IVG__L[s WMs Gs MeLdjL_Ins gL[LIhWkLsIVG__L[sWgsIa_gWJLeLJsGsInI[WIsbeLQmsgVaj[JsHLsGJJLJs hasL_gjeLsGsIWeIj[GesIa_ka[jhWa_saMshVLsIVG__L[sG_JsGsgW]b[WQLJs LdjG[WoGhWa_

(46) s 'aeshVLseLghsaMshVWgsGehWI[Ls lLsIa_gWJLeshVGhs 6sWgsgjMQIWL_h[ns [GeULs gas hVGhs hVLs 6<"s 6alLes <bLIheG[s "L_gWhns aMs jesIG_s Ia_gLr HLsIa_gWJLeLJsGgsoLeasajhgWJLsGs HG_JlWJhVs Os djL_h[nshVLsgbLIheG[sLMQIWL_InsaMshVLsbeabagLJsIa^]j_WIGhWa_s #o gnghL]s Wgs . ,Vs. j`es s I C` YN7es X6cs Y2s . .o. lVLeLs N7esWgshVLsbLeWaJWIs gj^]GhWa_s aMs NesJLQ_LJs Ggs. N7es. . ". I Nes [6s. 'o. \^s. 'W_G[[nshVLsIa]b[LhLsSG]LsWgsaHhGW_LJsGgshVLsIa_IGhL_GhWa_s aMsG[[s gjHSG]Lgs. lVLeLs !4 Wgs hVLs HW_Gens IaJLs eGhLs 9s Wgs hVLs ]aJj[GhWa_s aeJLes G_Jss WgshVLsea[[aOsMGIhaesaMshVLsbj[gLsgVGbW_Us::

(47) s. 9s. . ;. >[o gOKo XGgbPlo L\bXo \Lo gOKo bKHKPjKIo fPN[GTo. a_gWJLeW_Us Gs Ia]b[Lms JJWhWkLs BVWhLs )GjggWG_s 3aWgLs B)3s IVG__L[s lWhVs kGeWG_ILs 3$I hVLs eLILWkLJs gWU_G[s Iaer (o eLgba_JW_Us has hVLs eLILbhWa_s aMs hVLsbGIZLhs asIG_s HLsLmbeLggLJs ]GheWIWG[[ns Ggs. 3Vs jes I=`e;7sesa6 s `2s . >`s #B`s l`s. lVLeLs ;7s seLbeLgL_hgs Gs lW_Jals aMsgWoLs 6s lVLeLs l`s JLQ_LJsGgs. P^Hc. . )/103$*0I G_Js #s Wgs hVLs .s #s. 'J. 8o. O^(EXc. . P] P7ds P,V 7ds. ac. 4 ]GheWms 0o. lVLeLs P Wgs hVLsMa[[alW_Us Ia[j]_s kLIhaes. w. D @ @ T. /o. . . O^\c. -o. fs. Yo. o. {. Pfs. . 9IN7e s N7ses 6k sN7ses .s %6k6I. =VLs]GheWms#seLbeLgL_hgshVLsYaW_hsLOLIhsaMshVLs lVLeLs 6ks jbgG]b[W_Us lWhVs MGIhaes 'o G_Js hVLs IWeIj[Ges Ia_ka[jhWa_s UWkL_s Hns LdjGhWa_s #o . P^(EXc. ECSP>\ $ 2P8KQJERR>P\8P;DER>;RSP>\ RD>\AHR>P\!L\ :HM;G\ ;MPP>QNMK<Q\ RM\ 8\Q;8H9\ JSHRENHE;8REMK\ M?\ >8;D\ QRP>8J\ :W\ !\% 4. ,,,

(48) s :&!&-A&;s .. "223.\. ,_s beGIhWILs lLs Ia_gWJLes Gs JWUWhG[s kLegWa_s aMs jes hVGhs Wgs gn_hVLgWoLJsMea]s Whgs gG]b[Lgs =\s j[6kslWhVs 6ks . =\s. . lVLeLs .s. . 3Vs. I=` \;-[sa.s `2s. . *o. 4 G_Js j` \sWgsUWkL_s Hns. ECSP>\ ( "R>P8RET>\ P>;>ET>P\ 8P;DER>;RSP>\. +o. ,_shVWgsbGbLes lLsIa_gWJLesG_sWhLeGhWkLseLILWkLesHGgLJsa_shVLs hjeHas LdjG[WoGhWa_s hLIV_WdjLs JLgIeWHLJs W_s C#-Do =VLs eLILWkLes.

(49) [v "c. ZN "c %H. 4. [v n. ? ?. S. Qv s. 6^Zo. Dc$c. Qv l. @c. ? ?. Qv I. [v &IC. 4. B. S. W^ _ M _ l _ IC. H. 4. ?. BLc. ?.

(50) . @7;Zc. 4. B. ? ?. S. S. ECSP>\ ) "2\ EJNH>J>KR8REMK\ M?\ RD>\ HEK>9\ ))0\ >OS8HEX>P\ UERD\ Sc -.&,.&:. GeIVWhLIhjeLs Wgs JLbWIhLJs W_s "3.\ (o Whs Wgs HGgLJs a_s Gs [W_LGes 1Lhs J]s HLs hVLs [L_UhVs 4 JLQ_LJs Ggs J]s 2W_W]j]s 2LG_s <djGeLs %eeaes 22<%s LdjG[WoLes jgW_Us Go G_Js hVLs ]GheWms rsGeLsUWkL_s Hns _bP\bPo W_Mae]GhWa_s Mea]sGs<,<5s JLIaJLe

(51) s. J: rV#g#J]s V qs. Kc. 7. . 3l_bKffP\[o \Lo gOKo XG__Kbo. s

(52)

(53)

(54) s 17s Kc 4 #+o. #-o 4 s V24 1!/4 =VLs 22<%s LdjG[WoLes W_bjhgs GeLs aHgLekGhWa_gs Mea]s hVLs iD#g#s " -

(55) s rs #.o IVG__L[s

(56) ]LG_s %!4 G_JskGeWG_ILs !4 eLbeLgL_hW_UshVLs Go _bP\bPo JWgheWHjhWa_s a_s Bs %!4 G_Js !4 GeLs Ia]bjhLJs Mea]s hVLs 1aUs 1WZL[WVaaJs:GhWas 11:s ! 4 V 4 Hns hVLs]GbbLe

(57) s=VLs]GbbLes ,hs IG_s HLs GfUjLJs hVGhs _as ]GhIVLJs Q[hLes VGgs HLL_s Ja_Ls has WgsWJL_hWIG[shashVLsa_LsJLgIeWHLJsW_s C#-D1o ]LG_gsG_JskGeWG_ILgs aHhGW_s hVLsIVG__L[s ]aJL[s aMsLdjGhWa_s /o ,_s MGIhs ]j[hWb[WIGr aMsgn]Ha[gsGeLsUWkL_s Hns hVLs Ma[[alW_UsgLhs aMsLdjGhWa_gs hWa_gsHns #gsW_sLdjGhWa_s #*o IaeeLgba_JshashVLsGbb[WIGhWa_saMsGs IWeIj[Ges]GhIVLJsQ[hLesMa[[alLJsHnsGsJal_gG]b[W_UsaMsMGIhaes 4 #!o !,4 .I"-",4 "! 4 IaeeLgba_JW_UshasgG]b[W_UsGhs eGhLs !*4 =VWgsghLbsWgsIa_gWJLeLJs !4 HnsJLMGj[hsW_s C#'Do G_Js C#(Do ValLkLeshVLsIaeeL[GhWa_saMshVLs_aWgLs 4 0!,4 .I ("4 !, -",4 "! 4 ##o GhshVLsajhbjhsaMshVLs]GhIVLJsQ[hLesWgs_ahsIa_gWJLeLJshasJLgWU_s !4 hVLs22<%sLdjG[WoLe

(58) s,hsIG_sHLsMjehVLes_ahLJshVGhs rVsLdjGhWa_s -Vs #*o IaeeLgba_Jgs has hVLs 22<%s LdjG[WoLes LmbeLggWa_s lVL_s Gs s #'o IaeeL[GhLJs _aWgLs lWhVs IaeeL[GhWa_s]GheWms 4Wgs Ia_gWJLeLJ

(59) s !,4 !4 .I .s ,4 3als lLs gVals hVGhs LdjGhWa_gs #*#.o IG_s HLs LMQIWL_h[ns =as Ia]bjhLs hVLgLs LdjGhWa_gs a_Ls _LLJgs -",4 "! 4 W]b[L]L_hLJsW_shVLsSLdjL_InsJa]GW_

(60) s,_JLLJsWhsIG_sHLs_ahLJs hVGhs hVLs ]GheWms 4 #gs#s Wgs Gs IWeIj[G_hs ]GheWms aMs gWoLs lVWIVs Wgs JLQ_LJs Ggs 4 ac 4 lWhVsQeghs[W_Ls M7ssM7s"*

(61) 4 M7s 4 &

(62) "*

(63)

(64) 4 bVs eu *'! 3.'4 +L_ILs rVs Wgs G[gas Gs IWeIj[G_hs ]GheWms G_Js ]j[hWb[WIGhWa_gs Hns s s #(o 4 G_Js rVs GeLs LdjWkG[L_hs has IWeIj[Ges Ia_ka[jhWa_gs hVGhs IG_s -",4 "! 4 ,I '4 s eu 4 ! 3.'44 HLs W]b[L]L_hLJs jgW_Us''=sG_Js,''=

(65) s,_sbGehWIj[Ges Q`sIG_sHLs eLleWhhL_sGgs lVLeLs "4 ]GbbW_Us* ]s

(66)

(67)

(68) 4 4*. )4 . . . . . . . ;. #/o. 3l_bKffP\[o \Lo gOKo <<@3o KahGTPmKbo kPgOo Gs beWaeWs. =VLs IVG__L[s ]aJL[s aMsLdjGhWa_s /o JaLgs _ahs IaeeLgba_Js has %djGhWa_s #/o IG_s HLs W]b[L]L_hLJs Ma[[alW_Us hVLs H[aIZs JWGr Gs IWeIj[Ges Ia_ka[jhWa_s gW_ILs hVLs eLILWkLJs gWU_G[s Wgs gG]b[LJs Ghs UeG]s UWkL_s W_s "3.\ *o lVLeLs ,4 Wgs UWkL_s Hns LdjGhWa_s hW]Ls ValLkLes hVLs 22<%s lWhVs Go _bP\bPo IG_s ghW[[s HLL_s -o G_Js4,4 Wgs Ia]bjhLJs jgW_Us hVLs gG]Ls ghLbgs Ggs W_s C#-Do =VLs ajhbjhs gaMhs LghW]GhLs aMs B`sWgs JL_ahLJsHns Q`sG_Js Wgs UWkL_s Hns ,Vs. #0o ,4 .I M7s*"*4# & +$

(69) 4 B`s #*o >`s #g# %!4 4 /%!24 4 +. . . .

(70) >gW_UshVLsMGIhshVGhshVLs]GheWms rVsA}A WgsGsIWeIj[G_hs]GheWms sIG_sG[gasHLsLmbeLggLJs jgW_Us 5o( `s Ggs. ,Vs. s BI .I =o. <. 54

(71) Vo. V 2s /4 iE54

(72) Vo. #. '!o. 3l_bKffP\[o \Lo gOKo IKXG__Kbo. ,_s C#.Do Whs Wgs gVal_s hVGhs E`s Wgs Gs HWGgLJs LghW]Ghaes aMs B`s HLIGjgLs '#o L` \ss *C` \s <\s. # #. . t. #. o o. #. #. lVLeLs <\sWgs Gs _aWgLshLe]s lWhVs kGeWG_ILs @Is I 0 q

(73) s =GZW_UsW_has GIIaj_hs hVWgs HWGgs hLe]s W_has hVLs JL]GbbLes LmbeLgr gWa_s lLs VGkLs. #. #. #. #. #. #. #. #. #. >5#>:%c. ECSP>\ \ 5"2\ ;D8PRQ\ ?MP\ Nc 9c Y \ \ \

(74) \ Z\ 8K<\ ?MP\ RD>\ (MC%.\ <>;M<>P\ M?\ RD>\ ;MKTMHSRET>\ ;M<>\ UERD\ NMHWKMJE8H\ \ , 4 ?MP\. .I. Jo. 'W!m2 Vn0s. V U Vs. =R[c. 9?$]YSo=c. +IJWQ;F &2n` Qo. . =\ ;MKQE<>PEKC\ 8K\ EKK>P\ ;M<>\ M?\ P8R>\ P . RTs. 14. #. lVLeLs XCaZseLbeLgL_hgs hVLs gn]Ha[s GggaIWGhLJs lWhVs [GHL[s. Zs. #. ,@

(75) s. 1")3(2"+*\ : 03(20\. ,_s hVWgs gLIhWa_s lLs VWUV[WUVhs hVLs bLeMae]G_ILgs aMs hVLs bear bagLJs heG_g]WhhLe eLILWkLes GeIVWhLIhjeLgs Maes hVLs a_ka[jhWkLs aJLs ICIG_JsMaes1als"L_gWhns6GeWhns VLIZs1"6 sIaJLg

(76) s =VLs Q[hLes NesWgs Gs :aahs :GWgLJs agW_Ls :: s Q[hLes lWhVs Gs ea[[saOs IaLMQIWL_hs aMs

(77) s G_Js Ia_gWJLeW_UsGs 82s]aJj[Gr hWa_

(78) s BLs Ia_gWJLes IaJLlaeJgs gbG__W_Us 4s - gjHIaJLlaeJgs aMs JjeGhWa_s =o s s gn]Ha[gs UWkW_Us IaJLlaeJgs aMs gWoLs Gs

(79) s 'Weghs lLs beabagLs has G_G[noLs hVLs bLeMae]G_ILgs aMs hVLs beabagLJs ]LhVaJs Maes hVLs s C>I =VLs GggaIWGhLJs <aMhs ,_bjhs <aNis 5jhbjhs <,<5s JLIaJLes Wgs Gs HWh lWgLs 2GmW]j]s s 6aghLeWaeWs 26s 1aU /:s GV[s aIZLs /L[W_LZs :GkWks G[UaeWhV]

(80) s ,_s "3.\ +o lLs UWkLs hVLs %CheW_gWIs ,_Mae]Gr hWa_s =eG_gMLes %C,=s IVGehgs Maes hVLs beabagLJs LdjG[WoLes Maes s = p

(81) s

(82) s

(83) s

(84) s

(85) qs Maes Gs <WU_G[s has 3aWgLs :GhWas sK

(86) s=VLs%C,=sIVGehsaMshVLs<,<5sJLIaJLesaMshVLs sWgs G[gasbeakWJLJ

(87) sBLsaHgLekLshVGhsMaesGs<3:saMs sKskG[jLgs aMss s

(88) shVLsWhLeGhWkLsJLIaJW_UsgVaj[JsIa_kLeULslVW[LsMaes ss

(89) s Whs Wgs _ahs hVLs IGgL

(90) s =VWgs HLVGkWaes Wgs IaeeaHaeGhLJs Hns hVLs Whs%eeaes:GhLs IjekLgsUWkL_sW_s "3.\ -o ,_s "3.\ .o lLs Ia]bGeLs gbLIheG[s LPIWL_Ins aMs JWOLeL_hs IaJW_Us gIVL]Lg

(91) s =VLs IjekLs lWhVs _as ]GeZLes eLbeLgL_hgs hVLs GIVWLkGH[Ls gbLIheG[s LMQIWL_Ins Maes W_JLbL_JL_hs G_Js WJL_hWIG[[ns JWgheWHjhLJs )GjggWG_s IaJLHaaZg

(92) s =VLs IjekLs lWhVs Ieaggs ]GfZr Legs Wgs hVLs W_Mae]GhWa_s eGhLs Maes >_WMae][ns G_Js ,_JLbL_JL_h[ns "WgheWHjhLJs #,"s 82sW_bjhsG[bVGHLhgsa_shVLs\<,sIVG__L[s IaeeLgba_JW_Us has ss

(93)

(94) s =VWgs IjekLs VGgs HLL_s Ia]bjhLJs jgW_UshVLs<VG]GWs1GfaWGs a_YLIhjeLs<1 sgLLs C#/Do =VLsIjekLs lWhVsheWG_U[Ls]GeZLegseLbeLgL_hgshVLsW_Mae]GhWa_seGhLsaHhGW_LJs HnsIa]bjhW_Us hVLsGeLGs j_JLeshVLs %C,=s IVGehs aMshVLsbeabagLJs <,<5sLdjG[WoLe

(95) s. #. c. "# #

(96) #. %o co # # # # #. ECSP>\ + .\ TQ\. #. ?MP\ Nc. #. 9c. #. #. 04 hmd:. #. #. #. #. #. Y$\ \ Z\ 8B>P\ \ ER>P8REMKQ\. BLs aHgLekLs hVGhs hVLs beabagLJs gIVL]Ls gjOLegs aMs Gs bLeMaer Ia]bGeLJs has hVLs ]G_ILs JLUeGJGhWa_s Maes VWUVs kG[jLgs aMs <1

(97) sBLsgjbbagLshVGhshVWgsbLeMae]G_ILs[aggsWgsJjLshashVLsW]r bagLJs[W_LGesghejIhjeLsaMsajesLdjG[WoLe

(98) s'aesLkLenskG[jLsaMs lLsVGkLsIa]bjhLJshVLs%C,=sIVGehgsaMsajes<,<5sLdjG[WoLesG_Js lLs VGkLs Maj_Js hVLs abhW]G[s 1als "L_gWhns 6GeWhns VLIZs IaJLs beaQ[LsjgW_UshVLs]LhVaJsbeabagLJsW_s C#0Do 'ea]shVLgLsbeaQ[Lgs lLs VGkLs Ia]bjhLJs hVLs IaeeLgba_JW_Us W_Mae]GhWa_s eGhLgs jgW_Us LdjGhWa_s .o =VLseLgj[hW_UsIjekLsVGgsgdjGeLs]GeZLeg

(99) sBLs_ahLs hVGhshVLsbLeMae]G_ILs[aggsIa]bGeLJshashVLsGeLGsj_JLeshVLs%C,=s IVGehsWgs[al

(100) sBLs G[gasbeakWJLshVLs#,"sW_Mae]GhWa_seGhLsMaes. 82s]aJj[GhWa_sGhsGs3ndjWghseGhLs ss IlWhVseaj_Js]GeZLegs G_Js aHgLekLs hVGhs Maes LdjWkG[L_hs '=3s G[[algs gWU_WQIG_hs UGW_gsW_sgbLIheG[sLMQIWL_In

(101) s=lasIaaeJW_GhLgsIaeeLgba_JW_Ushas hVLs s Maes ss

(102) s G_Js ss

(103) s GfLs beakWJLJs Maes Gs hGeULhs %:saMs

(104) s.

(105) 2016 9th International Symposium on Turbo Codes & Iterative Information Processinj 7 6 N. :r: ::;';;;-. REFER ENCES Gaussian spectral efficiency, FTN r = 0. 35 - - Shama i Laroia Conjecture, FTN r = 0. 35 --+- Area une! er EXIT char ts, FT N T = 0. 35 --e- LDPC optimization, FT N r = 0. 35 --e-- UID information rate, Nyquist T = 1. 3. .s >, ". t. 4. ". "' ·;::;. f:E. IÏl. <e. .::u. "'o.. ifJ. 10. Eb in d B No. Figure 7. Comparison of severa! spectral efficienci es for {3 = 0. 35.. T. 0. 35 and. V. CONCLUSION. To conclude, in this paper we consider a circular pulse shaped FTN signaling. An architecture based on FFTIIFFT operations is proposed that avoids the use of a cyclic prefix at the transmitter. We then propose an iterative receiver architecture based on the sampling of the received signal at twice the symbol rate. Finally, we propose simulation results to show the performances of the proposed transmitter/receiver architectures and observe that significant gains can be achieved using FTN. Furthermore, with the proposed iterative receiver scheme, we observe that for target BER below 10- 5 compression factors as low as 0. 35 can be used with a performance loss less than 0. 5dB compared to the Nyquist case with T = 1. APPENDIX A AUTOCORRELATION OF. x (t). In order to derive the PSD of x (t) , we start by computing its autocorrelation function R x(t , 5) = lE [x (t) x* (t- 5)]. From equation (3) , after sorne calculation steps (using the fact that symbols a p,m are iid) and after remarking that x(t) is wide sense cyclo-stationary for a period of T , the average autocorrelation function of x(t) is equal to 2 M - 1. R x(5) =. T;a L. 1. m= O. T. hr(t- mT8 )hT(t - 5- mTs)Wr (t - 5)dt. 0. (22). For 5 = 0 we obtain 2 M- 1. 1 T. ;;; L hr (t T;,a;·+oo -oo lh(t)1 2 dt. mTs)hY, (t - mT8 )dt. s m=O 0. 2. O"~g(O). Th. (23). 245. [ 1] J. Salz, "Optimum mean-square decision feedback equalization," Bell System Technical Journal, vol. 52, no. 8, pp. 1341- 1373, 1973. [2] J. E. Mazo, "Faster-than-nyqui st signaling;• Bell System Technical Journal, vol. 54, no. 8, pp. 1451 - 1462, 1975. [3] A. D. Liveris and C. N. Georghiades, "Exploiting faster-than-nyquist signaling," IEEE Trans. Commun., vol. 51 , no. 9, pp. 1502- 1511 , 2003 . [4] F. Rusek and J. Anderson, "Receivers for faster-than-nyqui st signaling with and without turbo equali zation," IEEE Trans. !nf Theory, pp. 19931997. 2006. [5] F. Rusek, A. Prlja, O. Kapetanovic, and J. B. Anderson, "Faster-thanNyquist modulation based on short finite pulses," in Radiovetenskaplig konjerens 2008 (RVK '08). RVK conference, 2008, pp. 166-170. [6] A. Barbieri , D. Fertonani, and G. Colavolpe, "Time-frequency packing for 1inear modulations: spectral efficiency and practical detection schemes," IEEE Trans. Commun. , vol. 57, no. 10, pp. 2951- 2959, 2009. [7] F. Rusek and J. B. Anderson, "Constrained capacities for faster-thanNyquist signaling," IEEE Trans. !nf Theory, vol. 55, no. 2, pp. 764- 775, 2009. [8] G. Colavolpe, T. Foggi , A. Modenini, and A. Piemontese, "Faster-thannyquist and beyond: how to improve spectral efficiency by accepting interference," Optics express, vol. 19, no. 27, pp. 26600-26609, 2011. [9] D. Arnold, H.-A. Loeliger, P. Yontobel, A. Kavcic, and W. Zeng, "Simulation-based computation of information rates for channels with memory," IEEE Trans. !nf Theory, vol. 52, no. 8, pp. 3498- 3508, Aug 2006. [lü] G. Ungerboeck, "Adaptive maximum-likelihood receiver for carriermodulated data-transmission systems," IEEE Trans. Commun. , vol. 22, no. 5, pp. 624-636, May 1974. [Il] J. B. Anderson and A. Prlja, "Turbo equalization and an m-bcjr algorithm for strongly narrowband intersymbol interference," in Information Theory and ils Applications (ISITA), 2010 International Symposium on. IEEE, 2010, pp. 261- 266. [12] S. Sugiura, "Frequency-domain equali zation of faster-than-Nyquist signaling," vol. 2, no. 5, pp. 555- 558, 2013. [13] S. Sugiura and L. Hanzo, "Frequency-domain-equali zation-aided iterative detection of faster-than-nyqui st signaling;' IEEE Trans. Veh. Technol. , vol. 64, no. 5, pp. 2122- 2128, 2015. [14] P. Sen, T. Aktas, and A. O. Yilmaz, "A low-complex ity graph-based LMMSE receiver designed for colored noise induced by FTN-signaling," in 2014 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2014, pp. 642- 647. [15] H. Lin, N. Lahbabi, P. Siohan, and X. Jiang, " An efficient FTN implementation of the OFDM/OQAM system;' in 2015 IEEE International Conference on Communications (!CC). IEEE, 2015, pp. 4787-4792. [16] M. Tüchler and A. Singer, "Turbo Equalization: An Overview," IEEE Trans. !nf Theory, vol. 57, no. 2, pp. 920- 952, Feb 2011. [17] C. Laot, R. Le Bidan, and D. Leroux, "Low-complexity mmse turbo equalization: a possible solution for edge," Wireless Communications, IEEE Transa ctions on, vol. 4, no. 3, pp. 965- 974, 2005. [18] S. Shamai and R. Laroia, "The intersymbol interference channel: lower bounds on capacity and channel precoding loss," IEEE Trans. !nf Theory, vol. 42, no. 5, pp. 1388- 1404, Sep 1996. [19] R. Tajan, B. Benammar, C. Poulliat, and M.-L. Boucheret, "On coding for Faster-Than-Nyquist signaling," in 2015 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom) . IEEE, 2015, pp. 92- 96..

(106)