Performance of Extended Super-Orthogonal Space -Time Trellis Coded OFDM system

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1 Prformanc of Etndd Supr-Orthogonal Spac -im rllis Codd OFDM systm Ilsanmi B. Oluwafmi, Studnt Mmbr,IEEE, and Stanly H. Mnny, Mmbr IEEE School of Elctrical, Elctronic and Computr Enginring Univrsity of KwaZulu-Natal, Durban, 44, South Africa and Abstract: In this papr, th prformanc of tndd supr orthogonal spac tim trllis codd orthogonal frquncy division multipling systm is invstigatd in frquncy slctiv widband wirlss channls. Nw 6, 3 and 64 stats full rat tndd supr orthogonal spac tim trllis cods for quadratur phas shift kying is proposd using th gnrator matri notation and thir fram rror rat prformanc valuatd by computr simulation. Rsults shows an improvd prformanc ovr its spac tim trllis cod and supr orthogonal spac tim trllis cod countrpart with quivalnt dlay lngth in typical urban channl condition. I. INRODUCION h convrgnc of computr and tlcommunication systms with th intgration of srvics such as voic, data and vido transmission has ld to th vr- incrasing dmand for widband high data rat wirlss communication systms. With this vr-incrasing dmand for wirlss broadband srvics coupld with th limitd radio frquncy and harsh mobil nvironmnt, dsigning wirlss communication systms that guarant incrasd spctral fficincy and improvd link rliability bcoms a challnging task. Divrsity tchniqus hav bn usd tnsivly to mitigat th ffct of multipath fading and to nhanc th rliability of wirlss transmission without sacrificing bandwidth or incrasing transmittd powr. Employing multipl-input and multipl-output (MIMO) tchniqu has provd to b a significant tchniqu that guarants capacity gain of numrous incrass in achivabl spctral fficincy and data rat [, ]. Spac-tim coding (SC), is on of th approachs that mak possibl th us of multipl transmit antnnas and (optionally) multipl rciv antnnas [3, 4] to guarant high data rats and dpndabl communication ovr fading channls, through th combinations of modulation, coding and spatial divrsity [5]. SCs ar dsignd to guarant targtd divrsity and coding gain in quasi-static, flat fading narrow band channls [6]. Howvr, widband wirlss channls ndd for broadband srvics ar frquncy slctiv in natur and in such channls SC communication systms suffrs prformanc dgradation as a rsult of intr-symbol intrfrnc (ISI) [3]. Improving th prformanc of SC communication systms in frquncy slctiv fading channl thrfor rquirs additional procssing to rmov or prvnt ISI. Orthogonal frquncy division multipling (OFDM) has bn adoptd in litratur as a good tchniqu in mitigating th ffct of ISI in multipath fading channl [6, 7]. OFDM divids frquncy slctiv fading channl into narrow band paralll subchannls, thrby th symbol duration is incrasd and ISI as a rsult of multipath is liminatd [8]. In OFDM, ach subcarrir is orthogonal with vry othr subcarrir, a proprty that diffrntiats it from th commonly usd frquncy division multipling (FDM). OFDM is a popular mthod for high data rat wirlss transmission and its combination with multipl-input, multipl- output (MIMO) tchnology is a promising tchniqu that holds th potntial to guarant improvd spctral fficincy and link rliability for nt gnration fid and mobil wirlss communication systms. OFDM tchniqus hav bn adoptd in many wirlss standards such as th IEEE8.a, th IEEE8.6a, th digital audio broadcasting (DAB) and th digital vido broadcasting (DVB) standards. h first SC codd OFDM systm was introducd in [6] whr a 6 stats Spac im rllis Cod (SC) was considrd. Aftr this pionr work, rsarch into SC codd OFDM took cntr stag. In [9], th two factors affcting th prformanc of SC-OFDM systm wr invstigatd whr som optimizd SCs wr proposd. h first factor is th channl intrlavr whil th scond factor is th ffctiv cod lngth, which should b as larg as possibl to attain high multipath divrsity. In [], supr orthogonal spac tim trllis (SOSC) was proposd to provid full rat, full spatial divrsity and improvd coding gain ovr SC. hs cods wr howvr dsignd for flat fading channls and it was shown in [] that thy princ prformanc dgradation in frquncy slctiv fading channls. In ordr for ths cods to ploit multipath divrsity th supr-orthogonal spac-tim frquncy trllis codd OFDM was proposd. h work points out that for SOSC to achiv multipath divrsity, paralll transition must b avoidd by incrasing th numbr of th trllis stats. It shows that to prvnt paralll transition in a full rat SOSC with a quadratur phas shift kying (QPSK) signal constllation, at last a6 stats trllis cod is rquird. In this papr, th prformanc of tndd supr orthogonal spac-tim trllis codd (ESOSC) OFDM systm which provids multipath divrsity is considrd. ESOSC is an tnsion of SOSC whr th constllation is rotatd with an additional rotational paramtr. Nw 6, 3 and 64 stats full rat ESOSC for QPSK ar proposd using th gnrator matri notation approach of [] with th dsignd rul givn in [].h fram rror rat (FER) of th proposd 6, 3 and 64 stats full rat ESOSC-OFDM for QPSK systms ar valuatd by computr simulation. h 6 stats ESOSC- OFDM show an improvd prformanc ovr th corrsponding full rat 6 stats supr-orthogonal spac tim

2 frquncy trllis codd OFDM (SOSFC-OFDM) givn in [] and th 6 stats SC-OFDM givn in [6] with quivalnt dlay lngth undr th sam channl condition. h papr is organizd as follows. Sction II introducs th systm modl. In sction III th various spac tim coding schms in OFDM nvironmnt ar prsntd, whil in sction IV simulation rsults ar shown to dmonstrat th prformanc of our schm. In sction V, th complity of th proposd schm is calculatd and compard with isting schm and th papr concluds in sction VI. II. SYSEM MODEL A MIMO OFDM CHANNEL MODEL Considr an OFDM communication systm with K subcarrirs quippd with N antnnas at th transmittr and N R antnnas at th rcivr. h fading channl is assumd to b frquncy slctiv and quasi-static which is constant during on OFDM codword and changs indpndntly from on codword to anothr. Lt f dnot th subcarrir spacing. h L-tap channl impuls rspons btwn th i-th transmit and th -th rciv antnna is givn by [4] h i ( ) L i ( ) ( D t ), () whr i () is th compl path gain from transmit antnna i to rciv antnna of th -th tap, t s =/K f is th sampling intrval of th OFDM systm and D is an intgr which rprsnts th -th path s dlay sprad normalizd by t s. h lngth of th cyclic prfi symbols should not b lss th D L- to avoid ISI. h channl frquncy rspons (IDF) btwn th i-th transmit antnna and th -th rciv antnna for th k- th subcarrir with propr cyclic tnsion and tolrabl lakag as wll as prfct sampl timing is givn by [5] H i ( L h i whr P K = p(-π/k). s kd ( ) P, () K For a spac tim codd OFDM systm, th rconstructd signal of th -th rcivd antnna at th n-th symbol priod and at th k-th subcarrir is givn by[5] r ( n, N i E s H i ( b ( n, i ( n,, whr b i (n, dnots th transmittd symbol from th i-th transmit antnna at th k-th subcarrir, ( n, dnots th indpndnt sampl of zro-man compl aussian noiss with varianc N / pr dimnsion at th -th rciv antnna for th k-th subcarrir, and E s dnots th transmittd symbol nrgy. B ENCODER SRUCURE h block diagram of th proposd ESOSC OFDM systm with two transmit antnna is givn in Fig... For a (3) two dimnsional M-PSK signal constllation of siz M= b and, for ach subcarrir, N s b= b data bits ar input to th ncodr. h data bits ar first mappd to two modulation symbol and and to a rotation angls θ and φ by th trllis ncodr rlatd to its currnt stat. At th ESOSC ncodr output, and ar transmittd from th first antnna, at th first tim and scond tim intrvals. Similarly, and ar transmittd from th scond antnna at th first and scond tim intrval. h srial output from th ESOSC ncodr is first convrtd to paralll and thraftr applid to th channl intrlavr. At th ncodr sid, invrs fast Fourir transform (IFF) is prformd on th corrsponding symbol takn from ach of th output of th intrlavr for ach subcarrir and cyclic prfi (CP) is addd bfor transmission from th antnnas. C. DECODER SRUCURE h Block diagram of th singl antnna rcivr for th proposd ESOSC OFDM with two transmit antnna is shown in Fig... At th rcivr, th cyclic prfi is rmovd and Fast Fourir ransformd (FF) is prformd on th rcivd signal to dtrmin th rcivd sampl of ach subcarrir. hraftr, th rcivd signals ar dintrlavd and convrtd from paralll to srial bfor bing snt to th Vitrbi dcodr. III. SPACE IME CODIN SCHEME IN OFDM ENVIRONMEN A. SPACE-IME RELLIS CODED OFDM SCHEME. Spac tim trllis cod (SC) was proposd in [5] as an tnsion to th rat on dlay divrsity schm by ointly dsigning modulation, channl coding, transmit divrsity and optional rciv divrsity to raliz maimum divrsity gain and suboptimal coding gain at th cost of rlativly high dcoding complity. In [6], th appaling trllis form of SC was transformd to a mor flibl gnrator form. As an ampl, a QPSK 6 stats SC from [5] can b rprsntd in its gnrator matri form as Many SC-OFDM communication systms hav bn dployd in litratur. In [7], it was shown that using th pairwis rror probability analysis in a frquncy slctiv fading channl, spac-tim codd OFDM systms can potntially provid a divrsity ordr of N t N r K. In [9], th ffct of dlay sprad on th prformanc of SC-OFDM was invstigatd whr it was pointd out that dlay sprad has significant ffct on th minimum dtrminant of SC in multipath nvironmnt. B. SUPER ORHOONAL SPACE-IME RELLIS CODED OFDM SCHEME. Supr Orthogonal spac tim trllis cod (SOSC) is a nw class of SCs introducd in [] to provid full divrsity and improv coding gain ovr th SC. SOSC is a concatnation of a supr st of orthogonal SBC with SC whos transmission matri is givn by [].

3 X sourc bit Etndd Supr-Orthogonal Spac im rllis Cod Encodr N= N= N= Intrlavr Intrlavr IFF and CP Addition X N= IFF and CP Addition Fig.. Encodr block diagram of ESOSC-OFDM systm for two transmit antnna FF and CP rmoval N= N= P/S P/S y y Vitrbi Dcodr Fig.. Dcodr block diagram for ESOSC-OFDM systm for on rciv antnna. C(,, ), (4) whr for M-PSK signal constllations, th signals and l M can b rprsntd by, l=,,,m- and θ can tak on th valus θ =πl /M, whr l =,,,M-. h gnrator matri notation for SOSC was rcntly introducd in [] to allow for systmatic and haustiv computr sarch for optimal cods with a highr numbr of stats. SOSCs ar dsignd basd on th rank and dtrminant critria and thir trllis structur has a larg numbr of paralll transitions. In [3], it was shown that SOSC cannot tak advantag of th multipath divrsity in frquncy slctiv fading channl bcaus of th incras in th numbr of paralll transitions of th dcoding trllis and hnc princ loss in rror rat prformanc in such fading channls. o prvnt paralll transitions in a full rat SOSC with QPSK signal constllation, at last a 6-stats trllis is rquird [7, ]. A 6-, 3- and 64-stats trllis was dsignd for SOSC OFDM in [] that fully ploit th spatial and multipath divrsity of th cod whil in [7] known 6-stats SOSC was invstigatd in an OFDM nvironmnt with dlay sprad btwn adacnt multipaths. C. EXENDED SUPER-ORHOONAL SPACE-IME RELLIS CODED OFDM SCHEME. In a bid to improv its prformanc SOSC was multiplid by an additional rotational paramtr to obtain th ESOSC in [8]. With th additional rotational paramtr, th transmission matri of (4) is transformd to C,,, ) (. (5) whr can b any ral valu btwn and π. ESOSC is similar to SOSC cpt for th utilization of tra rotation paramtr in addition to θ in ordr to pand th innr orthogonal SBC. h st partitioning for ESOSC is idntical to that of SOSC [8]. h dsign rul for ESOSC was proposd in [3] which is an tnsion of th gnrator matri notation of [].h proposd rul is applid in th dsign of our ESOSC cod so that th st partitioning ruls of [9] ar satisfid. First, full rats SOSCs for QPSK constllation ar dsignd and thn multiplid with an tra rotation paramtr. h gnrator matri for our 6, 3 and 64 stats SOSC ar, 3 3, and rspctivly. W obtaind th ESOSC by multiplying th SOSC with = and = π/ for vn and odd stats, rspctivly. Fig. 3. shows th trllis structur of our 6 stats ESOSC. In th figur, th QPSK symbols ( and ) ar dnotd by,,, 3 corrsponding to,,- and rspctivly. h valu of th rotation angl θ is dnotd by and corrsponding to and π rspctivly. Also, w rprsntd th valu of th tra rotation paramtr by and which also corrspond to and π/ rspctivly. IV. PERFORMANCE RESULS. h fram rror rat prformanc of th 6, 3 and 64 stats ESOSC- OFDM is valuatd for two transmit and on rciv antnna using 64 subcarrirs through computr simulation. h OFDM systm is assumd to hav a bandwidth of 8 khz with a subcarrir spacing of.5 khz and FF duration of µs.h guard band is µs and th symbol duration is 8µs. In analyzing our systm prformanc, a typical urban si path (U6) channl modl rportd in [] is considrd for simulation. h wirlss channl involvd is assumd to b quassi-static i.. th multipath channls is constant ovr on OFDM codword but varis from on codword to anothr. W also assumd that

4 FER FER S S stats 3 stats 64 stats SNR[dB] Fig. 4. FER Prformanc of 6, 3 and 64 stats ESOSC- OFDM for two transmit and on rciv antnna. SC-OFDM SOSC-OFDM ESOSC-OFDM Fig.3.. h trllis structur of th 6 stats ESOSC ( bits/s/hz, N t =). th rcivr has prfct knowldg of th channl stat information and that thr is prfct tim and frquncy synchronization btwn th transmittr and th rcivr. h FER for th 6, 3 and 64 stats ESOSC is as shown in Fig.4.. As shown on th plot, th prformanc of th ESOSC incrass with incras in th numbr of stats. his is bcaus th ffctiv cod lngth of SC is a function of th numbr of stats and th prformanc of SC OFDM incrass with incras in ffctiv cod lngth. For comparison purpos w show th FER of 6 stats SC-OFDM and 6 stats SOSC-OFDM with our 6 stats ESOSC in Fig. 5.. For th SC_OFDM, th 6 stats SC cod from [6] was usd and in ordr to hav th sam numbr of symbol pr fram and th sam dlay lngth for both systms, th numbr of subcarrirs for th SC- OFDM is chosn to b 8 which is twic that of ESOSC. For th SOSC-OFDM, w usd th sam numbr of 64 subcarrirs. h ESOSC is sn to outprform th SC- OFDM by about db at FER of - and also slightly outprform th SOSC-OFDM with. db at th sam FER. V. DECODIN COMPLEXIY h dcoding complity for SC-OFDM and SOSC- OFDM was discussd in [] whr th total numbr of flops pr dcodd bit was calculatd. Hr, w tnd th dcoding SNR[dB] Fig. 5. FER Prformanc of 6 stats SC-OFDM, SOSC-OFDM and ESOSC-OFDM for two transmit and on rciv antnna. complity to th ESOSC OFDM systm. Not that th trllis dcoding is a two stp opration which consist of branch mtric calculation and th add, compar, slct (ACS) opration. h numbr of ACS oprations pr dcodd sourc bit is givn as [] ACS= m ( q -)/q, (6) whr m rprsnt th numbr of ncodr mmory lmnts and q is th numbr of sourc bits pr coding stp. It was calculatd as 4 ACS/bit for SC, 6 ACS/bit for SOSC and 6 ACS/bit for ESOSC. Each ACS opration corrspond to two floating point oprations(flops), which is th sum of addition, comparison, subtraction and multiplication of ral valu. h branch mtric calculation complity is rlatd to th branch mtric quation and th numbr of branch mtric for ach sourc symbol. In [], th computation complity for

5 compl multiplication, addition and squard modulo was takn as 6, and 3 flops rspctivly which rsultd in 9 flops for SC and th branch mtric computation was givn by[] as Branch mtric (SC) = 9 b /q which rsults in 5flop/ bit. For th SOSC branch mtric computation is givn by[] Branch mtric (SOSC) = 7 b /q. his sum up to 8 flop/bit for SOSC with QPSK signal constllation. h diffrnt btwn th branch mtric calculation for SOSC and ESOSC is ust th multiplication of th tra rotational paramtr which is ust four tra multiplications as compard with that of SOSC. From th aformntiond, th branch mtric computation complity of ESOSC is Branch mtric (ESOSC) = 94 b /q. his amount to 376 flop/bit for ESOSC with QPSK signal constllation. h total dcoding complity for th 6 stats SC is thrfor flops/bit, for 6 stats SOSC is 4 flops/bit and for 6 stats ESOSC it summd out to b 496 flops/bit which is 9.35% highr than that of SOSC. V. CONCLUSION In this papr, th prformanc of nw ESOSC cods in OFDM systm hav bn invstigatd in widband frquncy slctiv fading channls using OFDM systms. Nw 6, 3and 64 stats, full rat QPSK ESOSC for OFDM systm for two transmits antnna wr dsignd, and thy hibits improvd prformanc through computr simulation ovr its full rat SC-OFDM and SOSC-OFDM countrpart with quivalnt dlay lngth undr th sam channl condition. h dcoding complity of th proposd ESOSC- OFDM hav bn calculatd and compard with that of SC- OFDM and SOSC-OFDM systms. VII. REFERENCES. []. V. arokh, H. Jafarkhani, and A. R. Caldrbank, Spac tim block cods from orthogonal dsigns, IEEE rans. Inform. hory, vol. 45, July999, pg []. J.N.Pillai and S.H Mnny: urbo Dcoding of Supr Orthogonal spac tim trllis Cods in Fading Channls ; Wirlss Prsonal Communications, No 37 pg [3]. Oludar Sokoya and B Mahara, Prformanc of Supr- Orthogonal Spac tim rllis cold in a Multipath nvironmnt, in IEEE Africon 7 Procdings. [4]. B. Vuctic and J. Yuan, Spac im Coding, John Willy and Sons Ltd, Wst Suss England 3, st dition, pp 49. [5]. V. arokh, N. Sshadri, and A. R. Caldrbank, Spac tim cods for high data rat wirlss communication; Prformanc critrion and cod construction, IEEE rans. Inform. hory, vol. 44, pp , Mar [6]. D. Agrawal, V. arokh, A. Naguib and N. Sshadri, Spac im Codd OFDM for high Data-rat Wirlss Communication Ovr widband Channls, IEE VC998, pp [7]. O.Sokoya and B.. Mahara, Prformanc of spac tim codd Orthogonal Frquncy Division Multipling Schm with Dlay Sprads In Procdings MELECON 8, pg [8] L. J. Cimini Jr., Analysis and Simulation of a Digital Mobil Channl Using Orthogonal Frquncy Division Multipling, IEEE ransaction on Communications Vol.Com.33, No 7, July 985. [9] B., Lu, and X. Wang: A spac-tim trllis cod dsign mthod OFDM systms, Wirl. Pr. Comm., 3, 4, pp [] H Jafarkhani and N Sashadri, Supr orthogonal Spac im rllis Cods, IEE transaction on Information hory, Vol.49, No4, April 3, pg [] K.aksoy and U. Aygolu, Supr Orthogonal spac tim frquncy trllis codd OFDM, IE communications 7 pg [] M. Bal t al, Computr Dsign of Supr-Orthogonal Spac im rllis Cod IEEE rans. Wirlss Comm. vol. 6 No. Fb. 7. [3] E.R. Hartling and H.Jafarkhani, Dsign Ruls for Etndd Supr-Orthogonal Spac im rllis cods in Procdings of CCECE 8 pg 6-66 May 8. [4] J.. Proakis and M. Salhi, Digital communications, Mc raw- Hill. Nw York, NY, USA, 5th dition. 8. [5] Y. Hong and Z.Y. Dong, Prformanc analysis of spac tim trllis codd OFDM systm, Intr. Journal of applid Math and Comp.Sc. Vol..No. pg Spring 6. [6] S. Baro,.Bauch and A. Hansmann, Improvd Cods for Spac im rllis-codd Modulation IEEE Comm..Lt.. vol., 4, No. Jan. Pp -. [7] Yi Hong, Jinhong Yuan and Xun Shao, Robust Spac- im rllis Cods for OFDM Systms ovr Quassi-static Frquncy Slctiv Fading Channl in Procdings IEEE in Intr. Symposium on prsonal indoor and mobil radio comm.. 3 pg [8] Y. Zhu and H. Jafarkhani, Diffrntial Supr-Orthogonal Spac im rllis Cods IEEE rans. On Wirl. Comms. Vol.5. No Dc. 6.pp [9]. Ungrbock, Channl Coding with Multilvl/Phas Signal, IEEE ransactions on Information thory, VOL. I- 8, No, Jan 98 pgs [] Digital Land Mobil Radio Communications, Commission of th Europan Communitis, Lumbourg, Blgium, COS 7, 989. Ilsanmi B. Oluwafmi rcivd th B.Eng dgr in Elctrical and Elctronic Enginring from Univrsity of Ado Ekiti, Nigria in. H obtaind th Mastr of Enginring dgr in Elctronic and lcommunication from Univrsity of Bnin, Nigria in 5. H is currntly pursuing a PhD dgr in Elctronic Enginring at th school of Elctrical, Elctronic and Computr Enginring, at th Univrsity of KwaZulu-Natal. His rsarch intrsts ar in th ara of wirlss communication including spac-tim coding, channl coding, MIMO and OFDM systms. Stanly H. Mnny obtaind his B.Sc.(Hons) Eng. Dgr from th Univrsity of Scinc and chnology, Kumasi, hana in 976. In 979 h compltd his M.ASc. from th univrsity of oronto in Canada. In a Nuffic fundd proct by th Nthrlands govrnmnt h mbarkd on a sandwich Ph.D programm btwn th Eindhovn Univrsity of chnology and th Univrsity of Dar s Salaam, th lattr awarding th dgr in 988.H currntly holds th position of profssor and Had of School of Elctrical, Elctronic and Computr Enginring at th Univrsity of KwaZulu-Natal. His rsarch intrsts includ wirlss ntworks, rural tlcommunication srvics, digital signal procssing and imag procssing.

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