MINIMUM OVERHEAD BURST SYNCHRONIZATION FOR OFDM BASED BROADBAND TRANSMISSION. Michael Speth, Dirk Daecke, Heinrich Meyr
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1 MINIMUM OVERHEAD BURST SYNCHRONIZATION FOR OFDM BASED BROADBAND TRANSMISSION Mchael Speth, Drk Daecke, Henrch Meyr Integrated Systems for Sgnal Processng (ISS) Aachen Unversty of Technology (RWTH) D Aachen, Germany ABSTRACT In ths paper the subject of tranng data overhead n burst orented transmsson systems usng OFDM s addressed. Prevous work has shown that burst synchronzaton for such scenaros s possble. Alas the tranng data needed n some cases wll sgnfcantly decrease the usable bandwdth. In order to mnmze overhead we analyze the mpact of synchronzaton errors on OFDM and derve a sutable optmzaton crteron. A novel tranng data format s ntroduced that allows to talor the overhead accordng to the actual requrements. Usng theoretcal analyss and smulaton the tranng data overhead can be decreased sgnfcantly wthout loss n performance. 1. INTRODUCTION OFDM (Orthogonal frequency dvson multplexng)s a well establshed technology for dgtal broadcastng applcatons [1]. Because of the numerous advantages of the OFDM prncple there s a growng nterest to use t for other applcatons [2, 3] as well. Some of the applcatons under consderaton such as wreless ATM requre a packet orented transmsson usng short data bursts [4]. OFDM s well known to be vulnerable to synchronzaton errors. Therefore the requrements for the accuracy of synchronzaton unts of the recever are extremely hgh. They are further aggravated by the partculartes of a burst orented transmsson: 1. The estmaton of all relevant parameters must be establshed by the evaluaton of a sngle preamble at a feasble complexty. 2. Whereas t s no bg topc n a contnuous transmsson, n a scenaro of very short bursts the tranng data needed for synchronzaton may reduce the usable bandwdth dramatcally. In the past several methods have been proposed that are capable to meet the requrements as far as accuracy and acquston tme are concerned [5, 6, 2, 7]. So far no Ths work was sponsored by the DFG under contract no. Me 651/14-1 partcular attenton has been pad to the synchronzaton overhead whch n some cases amounts to several OFDM symbols. It s obvous that for bursts consstng of few (possbly one) OFDM symbols ths overhead cannot be accepted. Therefore n ths artcle we show how the synchronzaton overhead can be systematcally reduced and adapted to the requrements of the applcaton. In order to quantfy the accuracy needed, we analyze the mpact of synchronzaton errors on the OFDM sgnal. A novel frame format s presented whch allows to talor the overhead used for synchronzaton accordng to these requrements. Further analyss of sutable algorthms shows how much tranng data s n fact requred. 2. SYSTEM MODEL 2.1. OFDM transmsson over selectve channels Data symbols a l k are transmtted va an OFDM system usng K u subcarrers. Let l be the OFDM symbol number and k be the number of the subcarrer. The resultng sgnal s descrbed by s(t) = + K u =2;1 l=; ;K u =2 a l k Ψ l k (t) (1) where Ψ l k (t) are the subcarrer pulses of length T s = T u +. Ψ l k (t) = e j2π Tu k (t; ;lts) u(t ; lt s ) u(t) = 1 0 t < Ts 0 else T u s the useful porton of the symbol whch s perodcally preceded by the guard nterval of length to compensate for nter symbol nterference (ISI). The transmtter s effcently mplemented usng an IFFT of sze N. The sgnal s transmtted over a frequency selectve channel h (t) δ(τ ; τ ) (3) h(τ t) = (2)
2 where h(τ t) comprses both the cr and the transmtter flter and has a maxmum dsperson of τ max. The receved sgnal sampled at tme nstants T = T u =N s gven by h (nt ) s(nt ; τ )+n(nt ) (4) r(n) = where n(nt ) denotes sampled whte Gaussan nose of varance σ N. We wll further assume that Efja l k j 2 g = Efjh j 2 g = 1 and the sgnal to nose rato averaged over all subcarrers s E s =N 1 0 = (5) σ N Takng all ths nto account the receved subcarrer symbols obtaned va the FFT are descrbed by z l k = a l k H l k + n l k (6) where n l k can be shown to be whte complex Gaussan nose and H l k = h (t)e 2πτ k Tu (7) 2.2. Transmsson Model and Recever Tasks Equaton (6) apples only under assumpton of deal synchronzaton of transmtter and recever. In general ths wll not be the case: The samplng tme T 0 of the recever wll be dfferent from T. The same holds for the carrer frequency leadng to a frequency devaton of f. In addton a symbol tmng offset of n ε T 0 has to be consdered. The resultng transmsson model comprsng all these effects s gven by [8, 5]: r(t n )=e j2π fnt h (nt 0 ) s((n ; n ε )T 0 ; τ )+n(nt 0 ) (8) In the recever the devatons have to be estmated and compensated to an extent where they have no nfluence on the BER. As man synchronzaton tasks symbol tmng synchronzaton, samplng clock synchronzaton and frequency synchronzaton can be dentfed. In order to determne the mportance of the sngle tasks, and to quantfy the accuracy needed, the mpact of synchronzaton errors on the OFDM sgnal must be analyzed. 3. IMPACT OF SYNCHRONIZATION ERRORS 3.1. Symbol Tmng Errors Identfyng the begnnng of an OFDM symbol and correctly removng the guard nterval s the frst task to be performed. The remanng N samples are fed nto the FFT for demodulaton. Due to the guard nterval some tmng offset can be tolerated as long as the samples wthn the FFT wndow are nfluenced by only one transmtted symbol. The subcarrer symbol dsturbed by an offset of n ε samples can be descrbed by [6]: nε j2πk z l k = e N ; n ε N N a l kh l k + n l k + n nε (l k) (9) where n ε (l k) can be assumed to be addtonal nose wth power P nε = jh (t)j 2 ; 2 ε 2 N ; ε (10) N and 8 < ε = : n ε ; τ T n ε T > τ τ ; T ; n ε 0 < n ε T < ;( ; τ ) 0 else Ths addtonal nose results from ISI and from nter channel nterference (ICI) caused by the loss of orthogonalty of the sgnal Frequency and Samplng Clock Errors A statc frequency offset f wll lead to a phase rotaton of the subcarrer symbols and to addtonal ICI. The receved symbols are descrbed by [9] z l k = e j2π fl(t s) a l k s(π ft u )H l k +n l k +n f (l k) (11) where n f (l k) can be assumed to be nose wth power P f π2 3 ( ft u) 2 (12) Takng nto account the typcal accuracy of oscllators frequency synchronzaton s mandatory for OFDM recevers.. Consderng a relatve samplng-clock offset of γ T 0 ; T = T the mpact on the receved subcarrer symbols s (13) Ts j2πkγl z l k = e Tu a l k s(πkγ)h l k + n l k + n γ (l k) (14) where n f (l k) agan s addtonal nose wth power P γ π2 3 (kγ)2 (15) Comparng these results to equatons (11) and (12) we see that the effects are comparable to those caused by a frequency offset f k = k γ ncreasng wth the subcarrer ndex k. In addton the symbol tmng poston wll change. Under wreless transmsson condtons P γ can usually be neglected. No explct samplng clock synchronzaton s needed.
3 4. REQUIREMENTS OF A BURST ORIENTED TRANSMISSION The ultmate requrement for the frame structure of a system (and the synchronzaton algorthms mpled by ths structure) s that the system performance should never be bounded by the achevable qualty of the synchronzaton. In order to systematcally mnmze the requred overhead we need to specfy an adequate crteron to measure the mpact of the synchronzaton on the system performance. From the analyss n the prevous secton we see that all synchronzaton errors bascally have two consequences: 1. A phase rotaton of the receved subchannel symbols. 2. Addtonal nose due to loss of sgnal power but more mportantly due to loss of orthogonalty. The phase rotatons cannot be dstngushed from those caused by the channel transfer functon. Hence they wll be compensated n the same way by ether a channel estmaton or by the use of a dfferental modulaton scheme. If we attrbute the synchronzaton effects to a resultng transfer functon Hl k R the followng modfed system model apples: z l k = a l k Hl k R + n l k + n s (l k) (16) where n s (l k) s the addtonal nose caused by all synchronzaton errors wth power P sync (m) =Efjn f j 2 g + Efjn γ j 2 g + Efjn nε j 2 g (17) and we assume that a synchronzaton parameter s held constant durng a burst wth burst number m. Thus the task of the recever s to reduce P sync (m) to an extent where ts mpact on decodng s neglgble. In a transmsson scenaro wth small bursts we can assume that the energy of the channel s constant for the duraton of one burst. If the power of the sgnal at the recever s held constant by a gan control the average power of the channel nose P C (m) wll change for every burst m and we defne: P C (m) =Efjn(l k)j 2 g (18) The synchronzaton effects are neglgble f the power of n s (l k) s sgnfcantly smaller than the power of the channel nose. Ths ntutve requrement can be expressed as follows: P sync (m) 1 K P C(m) (19) The mplct bound for the accuracy of the recever components gven by (19) s more approprate than the usual requrement that the synchronzaton error has to be wthn certan lmts. It mplctly takes nto account, that f the SNR of a specfc burst s too low for relably decodng the data, addtonal nose caused by synchronzaton errors may be qute large too. Thus the absolute devatons may be qute large wthout degradng the overall system performance. We defne a synchronzaton falure as the event that the lmt defned by (19) s exceeded: P f = P[P sync (m) > 1=K P C (m)] (20) The choce of K and P f depends on the modulaton and codng used and on the frame loss rate tolerable by the applcaton. Havng decded for specfc values the synchronzaton overhead can now be systematcally dmensoned. 5. FRAME FORMAT An effcent and relable burst synchronzaton requres the use of tranng data dedcated to synchronzaton [8] (For methods relyng solely on the evaluaton of the guardnterval as n [10, 11], correct synchronzaton cannot be guaranteed n the case of ISI). Generally ths tranng data can be provded n the frequency doman, embedded nto the subcarrer symbols, or n the tme doman as explct sequence. The sole use of frequency doman tranng data s problematc as far as the system acquston s concerned: Due to the lack of orthogonalty at the begnnng of the synchronzaton procedure the subcarrer symbols are subject to sever ICI. In order to acheve the necessary accuracy the synchronzaton must be performed teratvely whch contradcts the requrement of an nstantaneous acquston. Therefore ths opton wll not be treated any further. Apart from explct tranng data as guard nterval tranng sgnal T u n ε estmator wndow Fgure 1: Frame format for burst synchronzaton n [7, 12] perodc random data may be appled [6]. All these methods have n common that perodc sgnals are evaluated for synchronzaton. Most methods proposed use complete OFDM symbols as tranng data. Ths lmts the choce of the frame format and one may be forced to use much more overhead than actually requred. We therefore propose the frame format depcted n fgure 1 whch allows to freely choose the amount of symbol energy used for synchronzaton [13]. The frst symbol of
4 every burst s not only preceded by the guard nterval but also by an addtonal perodc part of L S samples (The remanng symbols of the burst are stll only preceded by the usual guard nterval). Thus we explot the perodcty nherent n every OFDM symbol and are able to effcently synchronze even bursts consstng of sngle symbols. L S can be chosen strctly accordng to the requrements of the system. For samplng-clock synchronzaton and the detecton of large frequency offsets addtonal tranng data can be nserted at subcarrer level [7]. 6. OPTIMIZATION OF THE FRAME STRUCTURE meet ths requrement can be derved va the tal probablty of a Gaussan dstrbuton wth varance σ ˆϕ : P[ϕ res > ϕ max ] ; 1 σ ϕ2 max ˆϕ 2σ p e 2ˆϕ (24) 2π ϕ max 1 ϕ 2 ; max 2 e 2σ 2ˆϕ (25) Usng (12) and (20) we can express the probablty for a synchronzaton falure as a functon of the synchronzaton overhead L S. Usng the approxmaton (25) we obtan: P f = e ; 6L S K (26) Note that equaton (26) s ndependent of both E s =N 0 We wll further regard the worst case of a burst consstng of a sngle OFDM symbol. As example we wll assume the transmsson of a broad-band sgnal of 8 Mhz bandwdth over a GSM hlly-terran channel as gven n [6] usng an OFDM system wth N = For the assumed accuracy of the samplng clock oscllators no synchronzaton of ths parameter s necessary even for hgh E s =N 0 of more than 20 db Frequency Synchronzaton A frequency offset can be dvded nto an offset of multples of the subcarrer spacng 1=T u and a fractonal offset of ϕ. f ϕ k ε = + (21) 2πT u T u The orthogonalty s only dsturbed by the fractonal offset ϕ. An nteger porton wll only lead to a shft of all subcarrers whch must be detected. Snce ths can be done relably wth only few addtonal synchronzaton symbols [6, 7, 5] we wll focus on the more crtcal task of estmatng the fractonal porton. An estmate for ϕ can be obtaned by averagng over the phase dfferences of the perodc portons of the sgnal [14, 11] L S ;1 ˆϕ = argf =0 r(n + + N) r (n + )g (22) Assumng that the estmate s Gaussan dstrbuted ts varance can easly be shown to be σ ˆϕ 1 N P E s =N 0 (23) Though n the strct sense ths result apples only for the AWGN channel t also proves to be accurate for frequency selectve channels. Snce the frequency offset can never be compensated completely, from equaton (12) we determne an allowable maxmum ϕ max for the resdng frequency offset ϕ res after correcton wth the estmate obtaned va equaton (22). The probablty that we fal to Fgure 2: Probablty of a falure of the frequency synchronzaton as functon of the synchronzaton overhead. and N. The accuracy of ths result can be seen n fgure 2 where we compare analyss wth a stochastc smulaton (The two theoretcal curves are due to the two approxmatons for the tal probablty). For flat fadng channels the smulaton results are well wthn the theoretcal bounds. For selectve channels the approxmatons necessary to obtan equaton (23) are too optmstc. Nevertheless the synchronzaton error stll has the property of beng ndependent of the SNR. One can draw the followng conclusons for the desgn of the frame structure: 1. By provdng a certan L S one can always guarantee a certan qualty of the frequency estmate ndependently of the momentary SNR. 2. Snce the choce of L S s ndependent of N there are no restrctons as far as the number of subcarrers s concerned Tmng-/Frame- Synchronzaton Snce at the begnnng of the synchronzaton procedure we have to assume the frequency offset to be unknown,
5 tmng synchronzaton va correlaton s the most feasble alternatve [14, 6, 7, 13]. The metrc used n [14] s gven by Λ(n t ) = L S ;1 jr(n t + + N)j 2 + jr(n t + )j 2 =0 L S ;1 =0 ;2 r(n t ++N)r (n t +) (27) From ths metrc the correct startng pont of the symbol can be estmated va mn(λ(n t )) ;! ˆn ε (28) n t The metrc gven n (27) has a fundamental advantage compared to the common correlaton metrc as gven n [7]. The sze of the correlaton wndow L S can be arbtrarly small whereas the correlaton metrc requres a large L S to average out the effects of random data. The error probablty for the symbol estmaton cannot be derved wth passable effort. For evaluaton we therefore rely on smulaton: In analogy to [13] for random channels, dstrbuted accordng to the channel profle under consderaton, the symbol offset s estmated usng the proposed algorthm. From the resdng offset after correcton wth the estmated value the addtonal nose s calculated usng (10) and the synchronzaton falure s determned accordng to (20). Fgure 4: Probablty of a falure of the symbol synchronzaton for an average SNR of 20dB. The accuracy of the synchronzaton cannot be ncreased beyond a certan lmt even f L S s further ncreased. For large values of L S t even decreases. The mnmum s reached for rather small values of L S. Thus for hgh SNR cases there may be a tradeoff between the qualty of frequency and symbol synchronzaton. The mechansm behnd ths behavor can be explaned wth a close analyss of the metrc and wll be subject of further publcatons. For many applcatons the achevable performance of the algorthm wll suffce. Alas for hgh synchronzaton requrements combned wth a low frame loss rate, symbol synchronzaton may turn out to be the system bottleneck. Ths may be resolved n several ways: Insertng multple tranng sequences and averagng over several metrcs. Ths of course wll conflct wth the concept of a sngle symbol burst The use of a pror nformaton about the channel. Fgure 3: Probablty of a falure of the symbol synchronzaton for an average SNR of 10dB. The results obtaned are qute dfferent from those of the frequency estmaton: The performance of the algorthm s no longer ndependent of the E S =N 0. A comparson of fgure 3 and 4 shows that though the absolute accuracy of the estmate wll be better for a hgh SNR the mpact on the receved sgnal s less for the low SNR case. Applyng more sophstcated (though more complex) methods for symbol synchronzaton [13, 15]. 7. RESULTS AND CONCLUSION For the applcaton example under consderaton we can conclude the followng: Snce a burst orented scenaro wll usually not be a hgh SNR scenaro we see that wth a choce of K = 10, L S 25 may already be suffcent. In ths case P f (m) wll be n the same order of magntude for both frequency and symbol synchronzaton at a low level of 10 ;6 (For the channels under consderaton one can expect the decodng of a burst to fal more frequently). Even f we consder the addtonal tranng data needed to
6 detect a shft of the subcarrers, we stll acheve a consderable reducton of synchronzaton overhead compared to [2, 7]. As far as the performance of the synchronzaton algorthms s concerned the followng was observed: 1. For frequency synchronzaton the probablty of a synchronzaton falure s ndependent of the E b =N 0 and thus of fadng effects. A certan qualty can always be guaranteed, f suffcent tranng data s provded. 2. The common correlaton based symbol synchronzaton scheme shows a bottomng of the performance f a too large number of samples are wthn the correlator wndow. For very large values of L S the performance wll even decrease. Ths mples that performance for some systems may be lmted by the accuracy of symbol synchronzaton. As long as the accuracy of the correlaton based tmng synchronzaton suffces the burst format presented here allows synchronzaton wth mnmum overhead. If hgher accuracy s needed ths can be acheved wth the use of of a sngle-carrer tranng sequence as proposed for frequency synchronzaton n [12]. Applyng the results of [15] these sequences can also be used for symbol synchronzaton enablng powerful and mplementatonally smple algorthms. The use of these algorthms s at the cost of an ncreased synchronzaton overhead snce the length of the synchronzaton sequence needed amounts to multples of the guard nterval. REFERENCES [1] ETSI, Dgtal broadcastng systems for televson, sound and data servces: DRAFT pr ETS , Mar [2] T. Keller and L. Hanzo, Orthogonal Frequency Dvson Multplex Synchronsaton Technques For Wreless Local Area Networks, n Proceedngs of the IEEE Internatonal Symposum on Personal, Indoor, and Moble Rado Communcatons, [3] V. Engels and H. Rohlng, Rado Access to an ATM Network Wth a TDD/TDMA-OFDM system, n Proceedngs of the IEEE Internatonal Conference on Vehcular Technology, [4] D. Petras and A. Hettch and A. Krämlng, Support of ATM servce classes n Wreless ATM, n ACTS Moble Communcaton Summt 1997, Aalborg,Denmark, Oct [5] M. Speth, S. Fechtel, G. Fock, and H. Meyr, Broadband Transmsson Usng OFDM: System Performance and Recever Complexty, n Internatonal Zürch Semnar on Broadband Communcatons, (Zurch), IEEE, Feb [6] F. Claßen, Systemkomponenten für ene terrestrsche dgtale moble Bretbandübertragung. Shaker Verlag, Aachen, Dssertaton at the RWTH-Aachen, ISBN [7] T.Schmdl and D. Cox, Robust Frequency and Tmng Synchronzaton for OFDM, IEEE Transactons on Communcatons, vol. 45, Dec [8] H. Meyr, M. Moeneclaey and S. Fechtel, Dgtal Communcaton Recevers: Synchronzaton and Channel Estmaton Algorthms. John Wley and Sons, New York, [9] F. Classen and H. Meyr, Frequency Synchronzaton Algorthms for OFDM Systems sutable for Communcatons over Frequency Selectve Fadng Channels, n Proceedngs of the IEEE Internatonal Conference on Vehcular Technology, (Stockholm, Sweden), pp , June [10] J. van de Beek, M. Sandell, M. Isaksson, and P. Börjesson, Low-Complex Frame Synchronzaton n OFDM Systems, n Proc. of the ICUPC, [11] F. Daffara and O. Adam, A Novel Carrer Recovery Technque for Orthogonal Multcarrer Systems, European Transactons on Telecommuncatons, vol. 8, July [12] U. Lambrette, M. Speth, and H. Meyr, OFDM Burst Frequency Synchronzaton based on sngle Carrer Tranng Data, IEEE Communcatons Letters, vol. 1, Mar [13] M. Speth, F. Classen, and H. Meyr, Frame synchronzaton of OFDM systems n frequency selectve fadng channels, n Proceedngs of the IEEE Internatonal Conference on Vehcular Technology, [14] P. Chevllat, D. Mawald, and G. Ungerboeck, Rapd tranng of a voceband data modem recever employng an equalzer wth fractonal T-spaced coeffcents, IEEE Transactons on Communcatons, vol. 35, pp , Sept [15] U. Lambrette, J. Horstmannshoff, and H. Meyr, Technques for frame synchronzaton on unknown frequency selectve channels, n Proceedngs of the IEEE Internatonal Conference on Vehcular Technology, May 1997.
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