A Low Complexity Trnsmitter Structure or OFD-FDA Uplink Systems Dirk Gld nd Hermnn Rohling Technicl University Hmburg-Hrburg, Deprtment o Telecommunictions Eißendorer Strße 40, 21073 Hmburg, Germny Elen Cost, Hrld Hs nd Egon Schulz SIEENS AG, IC N R ST 8 Werner-von-Siemens-Ring 20, 8630 Grsbrunn, Germny Abstrct The orthogonl requency division multiplex (OFD) trnsmission technique cn eiciently del with the eects o multi-pth propgtion in the brodbnd rdio chnnel. It lso hs high system inherent lexibility or designing multiple ccess scheme by combining the conventionl TDA, FDA nd CDA pproches with the OFD modultion scheme. The FDA multiple ccess scheme is especilly interesting or n uplink o communiction system since it cn completely void ny multiple ccess intererences (AI). oreover, the pek-to-verge rtio (AR) o the uplink OFD trnsmit signl cn be gretly reduced i this OFD-FDA multiple ccess scheme is dditionlly combined with dt spreding technique bsed on Discrete Fourier Trnsorm (DFT) spreding mtrix using only the user speciic subcrriers. Since the DFT spreding opertion nd the IDFT opertion used s prt o the OFD modultion scheme cncel out ech other the complexity o the trnsmitter structure or n OFD-FDA uplink cn be gretly reduced. Keywords OFD, FDA, CDA, Uplink, AR, DFT Spreding I. INTRODUCTION The brodbnd rdio chnnel is chrcterized by its requency selective ding due to multi-pth propgtion. In mobile communictions pplictions the rdio chnnel is dditionlly time-vrint due to the movement o the mobile terminl. The orthogonl requency division multiplexing (OFD) trnsmission technique cn cope with the eects o requency selectivity nd time vrince with low implementtion nd computtion complexity. Inter symbol intererences (ISI) s well s inter crrier intererences (ICI) cn be completely voided by dividing the totl system bndwidth into lrge number o spectrlly overlpping but mutully orthogonl non-requency selective nrrow-bnd subchnnels nd by introducing n dditionl gurd intervl into the OFD symbol. Even t the output o requencyselective chnnel this orthogonlity o the subcrriers cn be mintined. The equliztion o ech subchnnel is then reduced to single complex multipliction per subchnnel [1]. Recently, the combintion between the clssicl multiple ccess schemes TDA, FDA nd CDA nd the OFD trnsmission technique hve been intensively discussed [2]. For the synchronous downlink C-CDA or OFD-CDA cn oer good perormnce but due to the loss o orthogonlity o the used codes in requency selective rdio chnnel the receiver o mobile terminl hs to cope with AI by single or multi user detection (SUD, UD) scheme. The eect o AI is even incresed i OFD-CDA is used in the uplink due to the independent chnnels which ect the trnsmission o dierent mobile terminls. The subdivision o the trnsmission bndwidth into set o orthogonl subcrriers cn dditionlly be exploited by n OFD-FDA multiple ccess scheme. y llocting distinct sets o subcrriers to dierent users the vilble bndwidth cn be lexibly shred between dierent mobile terminls while voiding ny multiple ccess intererences (AI) between dierent users. The FDA multiple ccess scheme oers not only high lexibility or the rdio resource mngement (RR) but cn lso increse the bndwidth eiciency o the complete system by voiding the use o highly ttenuted subcrriers or speciic users bsed on the knowledge o the chnnel trnser unction [2]. oreover, the OFD-FDA multiple ccess scheme cn be dpted to the mesured rdio chnnel knowledge t the trnsmitter site using bit-loding techniques. I chnnel stte inormtion is not vilble the perormnce cn be incresed using n dditionl spreding over the subcrriers ssigned to one user. The resulting computtion complexity o the totl system cn by this mens be dopted to the given system requirements which is especilly o importnce or the mobile terminl nd in the uplink cse. The lterntive OFD-FDA multiple ccess scheme is thereore o importnce or the uplink cse nd cn be dvntgeous over OFD-CDA schemes becuse o its bility to void AI i idel crrier synchroniztion is ssumed or ll mobile terminls nd the bse sttion. Since the OFD trnsmit signl results rom the superposition o lrge number o independent dt symbols the envelope o the complex bsebnd time signl hs in generl lrge pek-to-verge rtio (AR). The lrgest output power vlue o the mpliier will limit the mximum mplitude o the signl in the trnsmitter. Thereore, non-liner distortions due to clipping nd mpliiction eects in the trnsmit signl will led to both in-bnd nd out-o-bnd emissions. In the pst dierent techniques or reducing the AR by chnging the trnsmit signl independently rom knowledge o other prts o the OFD trnsmitter hve been developed. ut the AR o the trnsmit signl envelope which employs n OFD-FDA multiple ccess scheme cn signiicntly be reduced i dditionl spreding techniques re pplied which spred the user dt over the llocted subcrrier only. In this cse n pproprite spreding technique must be designed re-
6 6 ( gnitude ^ E = gnitude E J = C IEEE Vehiculr Technology Conerence (VTC) Spring 2002,irminghm, Albm 2 odultion Spreding FDA- pping OFD- Trnsmitter DUC + DAC LO T (m+2) T (m+1) obile Terminl A se Sttion LO Decoder + Demodultion Equliztion + Detection FDA- Dempping OFD- Receiver DDC + ADC Fig. 1. sebnd system model or the OFD-FDA uplink with individul spreding o user dt ducing the AR to minimum vlue. It will be shown in this pper tht using the Discrete Fourier Trnsorm (DFT) mtrix s n orthogonl spreding technique will reduce the AR signiicntely [3]. Furthermore, the DFT bsed spreding opertion nd the IDFT bsed OFD modultion technique cncel out ech other which mens tht the trnsmitter structure cn be simpliied to single crrier trnsmitter with n dditionl gurd intervl in this speciic cse which helps to reduce the computtionl complexity o the trnsmitter o the mobile terminl. This pper shows how n OFD-FDA uplink system cn be combined with user dt spreding technique bsed on the DFT spreding mtrix to reduce the AR o the uplink signl without incresing the computtionl complexity o the trnsmitter. In Section II the structure o the nlyzed OFD-FDA system combined with DFT spreding mtrix is described or the uplink ppliction. In Section III the inluence o DFT mtrix pplied or dt spreding is nlyzed or n OFD-TDA multiple ccess scheme nd is extended to n OFD-FDA system in seprte subsection. The generl topic o non-linerities in n OFD system is reviewed in Section IV. Quntittive results re given in Section V nd SectionVI summrizes the ppers content. II. SSTE STRUCTURE The bsebnd system model o n OFD-FDA uplink with individul spreding o user dt is shown in Fig. 1. In this cse dierent users re considered nd ech user lloctes dierent subcrrier exclusively. The totl number o subcrrier in the considered trnsmission system is. The input dt strem or ech mobile user, "!"!"!#%$'&, is convolutionlly encoded in irst step. The bit sequence is then mpped onto complex modultion symbols ( -,. / "!"!"!# $0&, o coherent, higher-level modultion scheme. The modultion symbols re spred over the user speciiclly llocted subcrrier with n unitry spreding mtrix 1 243 resulting in complex trnsmit symbols -. The spreding opertion cn be denoted mthemticlly by the ollowing simple mtrix multipliction 1 273 gnitude (1) where ech complex trnsmit symbol - is clculted by the sum o user modultion symbols ( - weighted by 8 6 orthogonl code vectors - :9 8 - ;< 8 - ; = "!"!"!" 8 - ;-?> with. @ "!"!"!# $A& - @DC 8 F#G < - ;F ( F or. @ "!"!"!# $A&! (2) The trnsmit symbols - 9 > re then mpped onto o the vilble subcrrier which re exclusively llocted to user. In principle, the set o subcrrier ssigned to ech user cn be composed o ny out o H subcrrier tht hve not been ssigned to nother user. I spreding technique is employed including the user speciic subcrriers nd the spreding gin should be mximized then the selected subcrrier set should be more or less uncorrelted [4]. Thereore in this pper subset is considered where the selected subcrrier re plced on equidistnt subcrriers over the entire bndwidth, see Fig. 2. In this cse Subcrrier UserI Subcrrier Fig. 2. User K lloctes the equidistnt subset o subcrriers shit by K subcrriers in the requency domin the selected subcrrier set cn be ssumed to be mutully independent which leds to mximum spreding gin, the subcrrier selection is exclusive or ech user, which voids ny AI, nd the signlling overhed is minimized. Furthermore, it is ssumed in the sequel tht the set o equidistnt subcrrier re shited by subcrrier in the requency domin i the subset is ssigned to user. The proposed subcrrier selection nd modultion process does not need ny rdio chnnel stte inormtion in this cse. 8 Independent o the considered spreding mtrix but ssuming the equidistnt lloction o subcrrier over the entire bndwidth the resulting OFD time signl o user cn nlyticlly be described s L ON# Q R *TSVUXW & DC - N Q R - S - G < (3) or Z [$\],"!"!"!# "!"!"!# ] where denotes the length o the gurd intervl which is inserted into the trnsmit time signl. At the bse sttion the received time signl in the bse bnd is processed by removing the gurd intervl, clculting the Fourier trnsormtion (FFT) which splits the time signl into the orthogonl subcrrier chnnels nd inlly selecting the user speciic complex vlued symbols ^ - t the FFT output. The user speciic subcrrier set is locted t subcrrier _ ` "!"!"! ` 9 $b& > or user. The complex vlued symbols ^ - cn be described s - @c *,d - e - ` *,d - e! (4) UserJ
( t S/ 2 L 2 L DFT- Spreding IFFT G /S 1 IEEE Vehiculr Technology Conerence (VTC) Spring 2002,irminghm, Albm 3 denotes the complex chnnel trnser ctor on the complex Gussin noise with vrince U Q. For perectly time nd crrier synchronized system the received symbols re not inluenced by ISI nd ICI t ll. An estimte o dt symbols - cn then be clculted independently or ech user by pplying ny single- or multicode detection techniques. c where _ subcrrier o user nd III. DFT SREADING The spreding mtrix 1 273 o n OFD-FDA system is oten only chrcterized by its requency diversity properties. It thereore is chosen to be unitry in order to mke the detection process esier, to distribute the signl energy o the superimposed code symbols uniormly over ll subcrrier nd not to chnge the distnce o the code vectors. Thus, in mny OFD systems with dditionl spreding the Wlsh-Hdmrd (WH) mtrix is employed since it hs the dditionl dvntge tht it only consists o only +1 nd - 1 elements which cn reduce the computtionl complexity. The discrete Fourier mtrix is lso unitry but dditionlly hs n inluence on the AR o n OFD trnsmit signl. In this Section the inluence o such n Fourier speding mtrix on the resulting AR will be discussed. A. OFD-TDA with DFT Spreding In [3] the Discrete Fourier Trnsormtion 6 (DFT) mtrix hs been used or spreding the vector ( o length [ over ll subcrriers o n OFD system. I single user is ssumed in this OFD system the spreding opertion includes ll subcrrier within the entire bndwidth. In this cse the DFT spreding mtrix nd the IDFT opertion in the OFD modultion process cncel out ech other. The OFD trnsmitter structure with DFT spreding mtrix is thereore techniclly reduced to the seril sequence o complex trnsmit dt symbols ( to which gurd intervl is dded in the time domin s cyclic preix L ) = + ( * UXW or Z [$\],"!"!"!" "!"!"!# () where denotes the modulo opertion, s shown in Fig. 3. Fig. 3. Time signl o n OFD-TDA system with DFT spreding Since the trnsmit signl o this OFD system consist o sequence o complex modultion symbols ( it hs the sme AR s the modultion scheme employed or single crrier trnsmission techniques. Ater clculting the FFT in the receiver which splits the received time signl into the orthogonl sub-chnnel the sme single- or multi-code detection techniques cn be pplied which re well known rom OFD-CDA receiver structures. The sme bit error rte (ER) perormnce compred to system using Wlsh-Hdmrd spreding mtrix cn thereore be chieved i DFT spreding mtrix is considered insted. ut in cse o DFT spreding mtrix the resulting AR is signiicntly reduced. The generl structure o n OFD trnsmitter including DFT spreding is shown in Fig. 4. Interlever odultion "!#%$ & '!#($ & )!#($ * Add Gurd Intervl () OFD trnsmitter including DFT spreding over ll subcrriers +",-(. Interlever odultion / 0,-(. (b) Relistic but simpliied OFD trnsmitter structure Add Gurd Intervl Fig. 4. In n OFD system including DFT spreding mtrix nd n IFFT or the OFD modultion process both mtrices cncel out ech other.. OFD-FDA with DFT Spreding The dvntge o DFT spreding mtrix cn lso be exploited in the uplink o n OFD-FDA system. I the user dt is spred only over 243476 subcrriers then the DFT o length 2 used or spreding does not directly cncel out with the length 76 IDFT o the OFD modultor in generl. Only when the spreded symbols 8 = re mpped onto equidistnt locted subcrriers with spcing o >6@?A2CED the DFT spreding nd the OFD modultion cn be removed in the trnsmitter structure. This cn be seen by inserting Eqution (2) into Eqution (3) using the elements o the discrete Fourier mtrix FHGJI K the trnsmit signl o user X G G or u L 2ONQ KSR TUG K V W cn be written s = bdc e F = I eu = bdc e ]KSR TUG = V W KSR T 9 e ]^G ; = V W g hji k b Wmlon 9 e ]^G ; eqp Wr%s7tvuow (6) G : x y W (7) {z< Q}Q}Q}Q ~m Q}Q}Q}" {6 nd the periodic dirc pulse Wr%w. The trnsmit time signl in sequence p o user X n OFD-FDA uplink using DFT spreding mtrix nd n equidistnt subcrrier lloction results thereore in periodic repetition o the complex user dt symbol = sequence including n dded gurd intervl s cyclic preix,
S/ DFT- Spreding FDA-pping IFFT /S IEEE Vehiculr Technology Conerence (VTC) Spring 2002,irminghm, Albm 4 m m m m Fig.. Time signl o n OFD-FDA uplink system with DFT spreding is chrcterized by periodic repetition ( ) shown in Fig.. This periodic dt N Q R sequence *TSVUXW is multiplied by user speciic complex signl due to the user individul requency shit by subcrriers o the complete llocted subcrrier set. The number o periods inside single OFD symbol is equl to the spcing o the subcrriers llocted to user. The structure o the OFD trnsmitter cn be simpliied by this pproch since both the DFT spreding opertion nd the IFFT clcultion o the conventionl OFD trnsmitter cncel out nd cn be removed in the technicl reliztion completely nd will be replced by simple repetition process o the considered user dt ( -. The simpliied trnsmitter structure is depicted in Fig. 6. Any equidistnt subcr- IV. NON-LINEARITIES For suiciently lrge number o used subcrrier per o user given in Eqution (3) hs n pproximtely Gussin mplitude distribution due to the superposition o sttisticlly independent modultion symbols - on ll used subcrriers. The mximum pek-to-verge rtio (AR), deined by user the time discrete OFD signl L,.- ^ [&0/ 132 = <4 mx 976 L 98 > 6Q > Q 9 : 1 <; 3 (8) where Q 9 denotes the verge trnsmit power, occurs only i the identicl modultion symbol - is trnsmitted on ll used subcrriers. In this cse the AR is determined by the number o used subcrriers. A non-liner device is oten modelled by sot-limiter described by its non-liner mplitude modultion nd phse modultion chrcteristic s = 9?> > A@ > 6 >6DCE- < - < else (9) Interlever odultion Add Gurd Intervl () OFD-FDA trnsmitter with DFT spreding over equidistnt subcrriers Interlever odultion! "# $ Repetition Frequency Shit (b) Relistic but simpliied OFD trnsmitter structure Add Gurd Intervl Fig. 6. In n OFD-FDA uplink system including DFT spreding mtrix pplied to set o equidistnt subcrriers the DFT spreding mtrix nd the OFD IFFT trnsormtion cncel out ech other. rier lloction cn be used with the proposed FDA scheme since it only inluences the number o periods o the trnsmit signl. Thereore the user dt rte cn be lexibly djusted by ssigning the required number o subcrriers to ech user. With the sme rgumenttion the AR cn lso be reduced or the OFD-FDA downlink even though not the sme simple trnsmitter structure cn be used. The AR o the time signl is in this cse determined by the number o users (' insted o the number o used subcrrier nd will thereore in most cses be lower thn or conventionl OFD-FDA system without dditionl spreding. Since the time signl o the OFD-FDA uplink with DFT spreding is identicl to single crrier trnsmission dditionl techniques to reduce the AR originlly developed '+* or single crrier systems like the ) -QSK cn be employed. % "# & where > is the mgnitude o the time signl nd - < deines the mximum output mplitude o the device. When the OFD time signl is pssed through nonliner device s the high power mpliier o the trnsmitter lrge signl mplitudes will be clipped by tht devices i they exceed its rnge o liner opertion. A non-liner signl distortion will cuse both in-bnd nd out-o-bnd emissions o the trnsmit power spectrum. In-bnd distortions will only degrde the perormnce o the OFD system wheres outo-bnd emissions will lso disturb services in djcent trnsmission bnds. Especilly out-o-bnd emissions hve thereore to be reduced below certin power level to comply with given spectrum msk. Additionlly, becuse o identicl trnsmission bnds o dierent users in n OFD-FDA uplink system in-bnd emissions will led to multiple ccess intererences (AI) between dierent users. In order to void non-liner distortions even in the cse o highly liner power mpliier suicient input-bcko (IO) o the trnsmit signl to the mpliier hs to be used. Even though the clipping probbility o the OFD signl cn be reduced or even be voided or n IO lrger thn the AR system with lrge energy eiciency loss results. Alterntively, the eects which non-liner device cn hve on the trnsmit power spectrum cn be inluenced by reduction o the OFD trnsmit signl AR. Dierent techniques hve been developed which reduce the AR o the OFD signl by the mens o modiied chnnel coding [], n dditive [6] or multiplictive [7] correction unction or selective mpping o modultion symbols to subcrriers [8]. A mjority o these techniques hs high computtionl complexity due to the ct tht they nlyze the generted trnsmit signl nd modiy it either in the requency or time domin to reduce its pek mplitudes. For system employing coherent subcrrier modultion the AR cn lso be reduced i the dt symbols re spred by Fourier mtrix in requency direction [3].
IEEE Vehiculr Technology Conerence (VTC) Spring 2002,irminghm, Albm V. RESULTS & shred be- users. The continuous-time trnsmit signl We consider n OFD-FDA system with subcrriers ] nd gurd intervl o * tween & L 98 > is simulted by discrete-time signl oversmpled by ctor o nd bndlimited by root-rised cosine Nyquist ilter. The oversmpled nd iltered signl is then pssed through non-liner device modelled by sot-limiter s it hs been described in Section IV. The distorted signl L 98 > is then nlyzed by mesuring its power spectrl density (SD) nd the its clipping probbility. Since only the trnsmit signl is nlyzed in this pper no ssumption bout the chnnel hve to be mde. A. Out-o-bnd Rdition To evlute the impct o the proposed OFD-FDA trnsmitter structure on the out-o-bnd emission ter nonliner device the power spectrl density 99 9 > o the distorted trnsmit signl L 98 > o ech user is clculted. Fig. 7 shows the SD o the used subcrrier or n OFD- FDA uplink using DFT-spreding mtrix or n IO o 6 nd 9 d. For comprison the SD o conventionl OFD system pssed through the sme non-liner device is shown. It cn be concluded rom this plot tht the power eiciency cn be improved by more thn 3 d with this pproch. Φ ss (Ω) 10 0 10 20 30 40 0 60 70 9 d OFD TDA (QSK) OFD FDA with DFT Spreding (QSK) OFD FDA with DFT Spreding (π/4 QSK) 6 d r{ s(t) > A 0 } 10 0 10 1 10 2 10 3 10 4 10 OFD TDA (QSK) OFD FDA with DFT Spreding (QSK) OFD FDA with DFT Spreding (π/4 QSK) 0 1 2 3 4 6 7 8 9 10 11 A /σ [d] 0 s Fig. 8. Clipping probbility o conventionl OFD system nd n OFD- FDA system or the uplink versus the signl input bcko to sot limiter eiciency cn be incresed by 3.6 d or the OFD-FDA uplink with DFT spreding nd QSK modultion nd by '+* n dditionl 0.3 d or ) -QSK or probbilistic AR o & C. VI. SUAR In this pper n OFD-FDA system concept or the uplink o multi user communiction system hs been studied. It hd be shown tht i n OFD-FDA system with equidistnt subcrrier lloction is combined with user speciic spreding using n discrete Fourier trnsorm s spreding mtrix the trnsmitter structure cn be gretly simpliied without ny perormnce degrdtion. oreover, the pek-to-verge rtio o the trnsmit signl is reduced to the AR o the subcrrier modultion scheme which cn limit the out-o-bnd nd in-bnd emissions when the trnsmit signl is pssed through non-liner device. With the opportunity to independently djust the user dt rtes the proposed technique oers n interesting lterntive or reducing the complexity o the mobile terminl in the brodbnd rdio uplink. 80 0 0.1 0.2 0.3 0.4 0. 0.6 0.7 0.8 0.9 1 Ω Fig. 7. ower spectrl density o conventionl OFD system nd n OFD-FDA system or the uplink t the output o sot limiter Note tht or n OFD-FDA system with DFT spreding the AR nd thereore the non-liner distortions re independent rom the number o subcrriers per user wheres or conventionl OFD-FDA the it is not. The gin in trnsmit power is thereore inluenced by the subdivision o the system bndwidth mong the dierent users. While or conventionl OFD system the non-liner distortion is independent rom the used modultion scheme or the OFD- FDA uplink with DFT spreding it depends on the AR o the employed modultion scheme.. Amplitude Distribution The probbility tht the instntneous power 6 L 98 > 6 Q exceeds the threshold - < Q is depicted in Fig. 8 versus the normlized threshold. As cn be seen rom this Figure the power REFERENCES [1] J. A. inghm, ulticrrier modultion or dt trnsmission: An ide whose time hs come, IEEE Communictions gzine, 1990. [2] H. Rohling nd R. Grünheid, erormnce comprison o dierent multiple ccess schemes or the downlink o n OFD communiction system, in roc. o the IEEE VTC, hoenix, USA, 1997. [3] K. rüninghus nd H. Rohling, ulti-crrier spred spectrum nd its reltion to single crrier trnsmission, in roc. o the IEEE VTC 98,Ottw, Cnd, 1998. [4] J. rk, J. Kim, S. Choi, N. Cho, nd D. Hong, erormnce o C- CDA systems in non-independent ryleigh ding, in roc. o IEEE ICC 99, Vncouver, Cnd, 1999. [] A. Jones nd T. Wilkinson, Cobined coding or error control nd incresed robustness to system nonlinerities on OFD, in roc. o IEEE VTC 96, Atlnt, USA, 1996. [6] T. y nd H. Rohling, Reducing the pek-to-verge power rtio in OFD rdio trnsmission systems, in roc. o the IEEE VTC, Ottw, Cnd, 1998. [7]. uli nd H.-. Kuchenbecker, Reduzierung der durch Nichtlineritäten hervorgeruenen Au serbndstrhlung bei einem ehrträgerverhren, ITG Fchberichte 13 obile Kommuniktion, 199. (In germn). [8]. reiling, S. H. üller-weinurtner, nd J.. Huber, ek-power reduction in OFD without explicit side inormtion, in roc. o the th Int. OFD-Workshop (InOWo 00), Hmburg, Germny, 2000.