Suppression of ISI Caused by Sampling Time Offset in IFDMA Systems

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1 Suppression of ISI Caused by Samping Time Offset in IFDA Systems Aexander Arkhipov, ichae Schne German Aerospace Center (DLR), Inst. of Communications and Navigation, D-82234, Wessing, Germany. Phone/e-mai: Abstract In this artice, we investigate the infuence of samping time offset on the bit error rate (BER) performance in intereaved frequency-division mutipe-access (IFDA) upink systems. It is shown that even sma samping time offset resuts in inter-symbo interference (ISI) and in signa-to-noise ratio (SNR) degradation. To avoid this, a soft ISI suppression agorithm is proposed which aows to significanty improve the system performance. The proposed agorithm can be appied to both IFDA upink systems and to conventiona orthogona frequency-division mutipeaccess (OFDA) upink systems. I. INTRODUCTION Recenty, IFDA attained significant importance and is considered as an air interface candidate for 4G mobie communications [1] [2]. IFDA is equivaent to an OFDA- CD [3] scheme with bock intereaved frequency aocation and Fourier spreading [4] [5]. Compared to conventiona OFDA [6], IFDA seems more attractive due to its ower compexity, since IFDA requires no discrete Fourier transform (DFT) at the transmitter. oreover, IFDA shows a significanty ower peak-to-average power ratio (PAPR) than conventiona OFDA. In a rea IFDA upink system, samping time offsets and frequency offsets are different for different users. Frequency offsets occur because of a non-zero reative speed between a base station and mobie terminas or because of sighty different osciator frequencies at the receiver and the transmitter. Frequency offset estimation in IFDA systems is of the scope of this artice and is considered in [7]. IFDA system with rectanguar puse-shaping exhibits an inefficient power density spectrum [8]. Appication of a puseshaping fiter with acceptabe spectra characteristics reduces excess bandwidth, but such an IFDA system requires fine synchronization in time. If puse-shaping is appied, the probem of correct samping arises [8]. Samping time offset resuts in SNR degradation and ISI. Both these effects ead to the performance degradation in IFDA systems. In addition, different users have different samping time offsets which makes the probem of samping time offset estimation more difficut. In this contribution, it is shown that ISI is responsibe for the main part of IFDA system performance degradation, especiay if the samping time offset is arge. In this contribution, we propose a soft agorithm for ISI suppression. The agorithm estimates the reiabiity of received code bits, reconstructs and eiminates the ISI. Since soft vaues are used, the quaity of the ISI reconstruction can be enhanced substantiay. The proposed agorithm requires an estimate of the samping time offset. Such an estimate can be obtained by performing an oversamping at the receiver as described in [8]. We use the foowing notation: variabes denoting signas in time domain are written in sma etters, variabes denoting signas in frequency domain are written in capita etters. Bod variabes designate matrices or vectors. The remainder of the paper is organized as foows. Section II introduces the IFDA scheme. In Section III, the infuence of samping time offset on the system performance is studied. Section IV describes the proposed agorithm for soft ISI suppression. Simuation resuts are discussed in Section V. Finay, Section VI concudes the paper. II. INTERLEAVED FREQUENCY-DIVISION ULTIPLE ACCESS (IFDA) SCHEE In the foowing, IFDA is described as a specia case of OFDA-CD. For additiona descriptions of the IFDA scheme refer to [4] [9]. The standard OFDA-CD [3] upink transmission system is abe to support up to simutaneousy active users. Assume that N u users (N u ) transmit simutaneousy. Each OFDA-CD user i = 0,..., N u, performs a bocked transmission of Q compex-vaued symbos is obtained after the moduation of the qth independent data stream coming from the qth channe encoder as shown in Fig. 1. Such a coding scheme aows an iterative interference canceation scheme, as described in [3], and is used for the ISI suppression in this contribution. The average energy of the transmitted data d (i) q, q = 0,..., Q 1. Each symbo d (i) q symbo d q (i) is unity and the symbo duration is T s. The Q symbos are arranged to buid the symbo vector d (i) of user i d (i) = (d (i) 0, d(i) 2,..., d(i) Q 1 ). (1) The symbo vector d (i) is first seria-to-parae converted. Then, a code-division mutipexing (CD) component is introduced by spreading each symbo with a different spreading code c q, q = 1,..., Q, of ength L Q and adding together the resuting Q spread symbos. After summation, the resuting vector s (i) can be represented by s (i) n = Q q=1 c n,q d (i) q, n = 0,..., L 1, (2)

2 Channe encoder Compression d d x Channe q P/S and X CP encoder repetition Up-samping... Channe encoder... Fig. 1. d 0 dq e 2 j i The IFDA transmitter for user i where c n,q is the n-th component of the spreading code c q, q = 0,..., Q 1. Finay, an inverse DFT (IDFT) with userspecific frequency mapping is performed for the row vector s (i). Bock intereaving achieves optima frequency diversity, since it distributes the L spread symbos of the Q data symbos of user i equay over the whoe transmission bandwidth. Note, OFDA-CD excusivey assigns to each of the users a set of L frequencies of a possibe N c = L subcarriers. If a subcarriers assigned to user i are uniformy spaced over the whoe avaiabe transmission bandwidth at a distance N c /, the time domain transmit signa x (i), = 0,... N c 1, obtained after the IDFT operation in the transmitter, can be represented by x (i) = e j 2π i 1 L 1 n=0 Tx fiter s (i) n e j 2π L n. (3) As in standard OFDA, a guard interva arger than the maximum channe deay is added as a cycic prefix (CP) in OFDA-CD in order to avoid interference from preceding OFDA-CD transmission symbos. IFDA as a specia case of OFDA-CD can be reaized if a fuy oaded system, i.e. L = Q, is considered and Fourier codes with components c n,q = {e j 2π Q nq }, n = 0,..., L 1, q = 0,..., Q 1, are used for spreading. In this case, the Fourier codes for spreading and the rotation factors of the Fourier transform cance and the transmit signa given in (3) reduces to = e j2π }{{ i 1 } d (i) user specific phase factor x (i) mod L }{{} transmitted chips, = 0,..., N c 1. (4) Comparing (4) and [10] [9] it foows that IFDA is equivaent to OFDA-CD with bock intereaved frequency aocation and can be competey generated in the time domain with using the Fourier transform. The time domain generation of IFDA uses compression and repetition as described in detai in [9]. Note, the mutipication with the user specific phase factor in (4) ensures the user discrimination by assigning to each user i a set of subcarriers orthogona to a other users subcarrier sets. Each sampe x (i) represents the transmitting chip, = 0,..., N c 1. The duration of the resuting chips is T c = T s /. The simuation mode for the IFDA is shown in Fig. 1. After addition of CP, the obtained signa is up-samped. This up-samping is impemented by adding zero sampes between successive sampes x (i). After up-samping, the puseshaping is performed by a transmit fiter. After anaog-todigita (A/D) conversion, we assume transmission over a timedispersive mobie radio channe. At the receiver, we consider an oversamping per transmitted chip x (i). After samping, signa is fitered by a receive fiter, which is matched to the transmit puse-shaping fiter. In Fig. 2, the IFDA signa after the receive fiter is represented, with a dotted ine. In the down-samping operation one sampe per transmitted chip is chosen for equaization, despreading and estimation of the transmitted data. For the sake of simpicity, the convion of the receive and transmit fiters is represented by a samped function g(t). In the foowing, function g(t) is a Nyquist puse ( ) t cos(παt/tc ) g(t) = sinc T c 1 4α 2 t 2 /Tc 2, (5) where α denotes the ro-off factor. For the sake of simpicity, ony one received sampe y per transmitted chip x (i) is considered in the foowing. Therefore, we assume that channe has an impuse response described by a vector h (i) of dimension with components h (i) m, m = 1,...,. Assume that vaue y represents the th eement of received vector y, which can be represented as N u y = ĥ (i) z (i) (τ (i) ) + n, (6) i=1 where vector n denotes sampes of additive white Gaussian noise (AWGN). The channe matrix ĥ (i) h (i) 1 h (i) h (i) 1 h (i) 0 ĥ (i) = (7) 0... h (i) 1... h (i) h (i) 1... h (i) is the N c N c right circuar matrix whose rows are cycicay shifted versions of the vector h (i). The vector h (i) is obtained by appending N c zeros to h (i). The eements z (i) (τ (i) ) of the vector z (i) (τ (i) ) in (6) can be represented as z (i) (τ (i) ) = e j 2π d (i) i(+ τ(i) Tc ) 1 (8) mod L (τ g (i)) N c 1 ( ) + d (i) p mod L g τ (i) + (p )T c p=0 p } {{ } ISI. The normaized time offset τ (i) can take on vaues in the range T c /2 τ (i) T c /2. The orthogonaity between users is not vioated since τ (i) does not introduce any frequency offset. However, ISI appears if a samping time offset τ (i) is present

3 optimum samping points () i T c misaigned samping points Fig. 2. Exampe of the IFDA signa after the receive fiter. Samping time offset τ (i) causes SNR degradation and eads to the ISI; d (i) = [1, 1, 1, 1] T ; L = Q = 4; α = 0.25; ony user i = 0 is active; AWGN channe with a negigibe noise power. as shown in Fig. 2. The optimum samping points correspond to a situation where τ (i) = 0. In this case, the received signa y of user i is ISI-free. Other users transmit their data on separated orthogona subcarriers and their infuence is not considered in the foowing. Thus, we omit subscript i for simpicity, and focus on the data of user i. III. ISI AND SNR DEGRADATION DUE TO THE SAPLING TIE OFFSET We consider vector z(τ) in our anaysis of ISI. ISI appears if a samping time offset τ is present as shown in (8). If L is arge enough, the variance of the ISI for chip x can be approximated as σ 2 ISI(τ) = 1 N c 1 p=0 p g 2 (τ + (p )T c ). (9) If operator E{.} denotes the expectation, the energy of the usefu signa in (8) decreases with τ according to E{ d mod L g (τ) 2 }/ = g 2 (τ) /. (10) Additiona phase rotation in (8) can be mitigated by a channe estimation agorithm and does not have any negative impact on the system performance. IV. SOFT ISI SUPPRESSION The soft ISI suppression scheme for the symbo d q, q = 0,..., Q 1 is shown in Fig. 3. It is assumed that a main part of the ISI comes from the symbo d (q and the symbo d (q+. A reconstruction of the ISI is performed in the upper part, whereas the fina decoding of a data stream corresponding to the data symbo d q is done in the ower part. A reconstruction of the ISI is performed as foows. The received time domain signa y is converted into frequency domain, by appying a DFT of ength N c. The obtained t frequency domain vector Y is then frequency demapped. The frequency demapping assumes that ony the subcarriers κ = n +i, n = 0,..., L 1 are taken for despreading. After despreading, the equaization is performed. In the foowing, a minimum mean square (SE) equaization technique is considered [3]. Despreaidng assumes a mutipication by a code, which is compex conjugate to the code c (q. After symbo demapping and deintereaving, the og-ikeihood ratio (LLR) of received bits is cacuated as described in [11]. The put of the LLR bock is the LLR vaue λ (j 1) (q for each coded bit, where j = 1,..., J designates the iteration number and J denotes the tota number of iteration. Vaues λ (0) (q denote LLR vaues of bits corresponding to the data stream (q obtained after the initia iteration. The soft in/ channe decoder performs maximum a posteriori probabiity estimation for code bits [11]. Thus, the put of this decoder are re-encoded og-ikeihood vaues LLR re. These vaues are cacuated for each code bit. The soft bit vaue w [12] is defined as w = tanh{llr re /2}. (11) The soft bit w can take on vaues in the interva [-1,1]. Note that we omitted index q in (11). After the soft symbo mapping, compression and repetition is performed as described in the previous section. utipication with the vector u assures a correct weighting of the obtained ISI. The eements u, = 0,..., N c 1 of the vector u are defined as u = 1 g(t c + τ)e j 2π i(+ τ Tc +1). (12) A convion with the channe impuse response h is reaized by a mutipication with the channe matrix ĥ. However, this convion can be efficienty reaized by using ony two DFT operations and one vector mutipication. The reconstructed ISI of the symbo d (q is subtracted from the frequency-domain signa Y. The foowing remarks are of interest: Proposed soft ISI suppression scheme requires an estimation of the samping time offset τ. This estimation can be performed as described in [8]. The ISI coming from the data symbo d (q+ must aso be reconstructed and subtracted. A reconstruction of the ISI is performed exacty in the same way as for the data symbo d (q, ony the sign of τ must be changed in (12). For sma vaues of the ro-off factor α in (5) or for arge vaues of τ, the subtraction of ISI coming from ony one preceding and ony one foowing data symbo is not enough. In this case, the performance of the considered system can be improved if the ISI from other interfering symbos is subtracted as we. utipe iterations can improve the performance of the soft ISI suppression agorithm significanty. Obtained vaues λ (j) q, q = 0,..., Q 1 can be used in succeeding iterations as input of the soft in/ decoder.

4 Freq. demapping. Detect. Despreding c* ( q- Symbo demap. LLR ( j- 1) ( q- 1) modq Soft in/ decoder IFFT Conv. h X u Compress and repeat. Soft symbo map. w dtanh(.) LLR re ( q- Y Freq. demapping. Detect. Despreding c* q mod Q Symbo demap. LLR ( j ) q mod Q Channe decoder ( q+ Fig. 3. Iterative scheme for the ISI suppression for symbo d q, q = 0,..., Q 1 V. SIULATION RESULTS The transmission system has a bandwidth of 20 Hz and the carrier frequency is 5 GHz. The number of subcarriers is N c = The spreading ength is L = 64 and the maxima number of users is = 16. A conviona code with rate 1/2 and memory 6 is used in our simuations. The frame consists of 24 IFDA symbos. QPS moduation aphabet is used. The ro-off factor α changes from 0.25 to Infuence of the received and the transmit fiter is modeed by the function g(t), which is non-zero ony in the range 3T c < t < 3T c. Therefore, if samping time offset occurs, each transmitted chip x experiences ISI from three preceding and three foowing chips. A mutipath channe mode is considered, which consists of a tapped deay ine with = 11 statisticay independent Rayeigh fading taps. The average power for each channe component h m, m = 1,...,, is modeed as E{ h m 2 } = m + 1 (db). (13) Additionay, the average channe attenuation is normaized to unity in our simuations. It is known, that system performance depends on the channe diversity. If we increase a mobie termina speed the system performance improves, since channes gets more time diversity. Two different mobie termina speeds are considered. The first one is equa to 0 km/h and corresponds to a sowy changing mobie channe, whereas the second one is equa to 250 km/h and corresponds to the fast changing mobie channe. The bit error rate (BER) curves versus SNR are presented in Fig. 4 for the case of τ = 4 18 T c, τ = 7 18 T c and sowy changing channe. As a reference, the curve for the case τ = 0 is shown. It is seen that the system performance degrades if τ increases. The soid ine curves in Fig. 4 denote the system performance with a SE detector. The dotted ines denote ower bounds which are obtained by shifting the reference curves to the right. This shift is cacuated from (10) and represents the SNR degradation due to the samping time offset τ. For the BER equa to 10 3 and τ = 7 18 T c a performance gap between the ower bound curve and the SE curve is ab 8.5 db. For τ = 4 18 T c, the performance degradation is ab 2dB. The dashed ine represents performance of the ISI suppression agorithm. For the case τ = 4 18 T c, the ower bound can be reached. For τ = 7 18 T c, the BER performance can be improved approximatey by 6.5 db. However, the performance gap between the ower bound curve and the dashed curve is sti ab 2 db. The probem is that ISI from one successive and one foowing symbo is subtracted in Fig. 4. The residua ISI stems from other data symbos and this ISI is party responsibe for the remaining performance gap of 2 db. The suppression of the residua ISI is thoroughy investigated in Fig. 5. Two different sets of curves are simuated for two different speeds of mobie terminas in order to iustrate the performance of the ISI suppression agorithm in dependance on a channe diversity. In each simuation set two cases are considered. In the first case, the ISI coming from one successive and one foowing data symbo is subtracted ony, i.e the ISI from d (q and d (q+. The curves corresponding to this case are marked as 1 symbo in Fig. 5. The case 2 symbos corresponds to a situation, where ISI coming from the data symbos d (q, d (q+, d (q 2) mod Q and d (q+2) mod Q is subtracted. As a reference, the ower bound curve for the fast changing channe and τ = 0 is depicted in Fig. 5. It is seen that additiona subtraction of the ISI coming from d (q 2) mod Q and d (q+2) mod Q improves the BER performnce. However, this performance gain is ab 1 db for the sowy changing channe. It is seen that the BER system performance improves if we increase channe diversity. However, this improvement is of a minor importance. It is seen that the performance gap between the ower bound and the case of ISI suppression with two symbos is sti ab 2 db. This effect can be expained as foows. At the high vaues of samping time offset, e.g., τ = 7 18 T c, the SNR degrades and ISI increases drasticay. Thus, the prob-

5 Bit Error Rate 10-2 Bit Error Rate km/h 250 km/h τ= 7/18 Τ c, SE 10-3 τ = 7/18 Τ c, ISI supp. τ = 7/18 Τ c, ower bound τ= 4/18 Τ c, SE τ = 4/18 Τ, ISI supp. c τ = 4/18 Τ c, ower bound τ= 0, SE τ = 7/18 Τ c, ISI supp., 1 Symbos τ = 7/18 Τ c, ISI supp., 2 Symbos τ = 7/18 Τ c, ISI supp., 2 Symbos, 2 Iter. τ = 0, ower bound SNR in db SNR in db Fig. 4. The BER performance versus SNR for different vaues of samping time offset τ; IFDA system with the soft ISI suppression agorithm; 1 iteration; sowy changing channe Fig. 5. The BER performance versus SNR for a different number of subtracted interfering symbos and different number of iterations; IFDA system with the soft ISI suppression agorithm abiity to distinguish between two neighboring data symbos decreases. oreover, two neighboring data symbos experience exacty the same infuence of the transmission channe, e.g., can be deepy faded. If this situation, the probabiity to reconstruct the ISI correcty decreases tremendousy. Thus, the quaity of the reconstructed ISI decreases and, as a resut, some residua ISI remains. In this instance, data stream with subtracted ISI cannot be decoded perfecty since this data stream experiences exacty the same bad channe condition. The ogica countermeasure can be to use mutipe iterations in the ISI suppression agorithm. This performance of the ISI suppression agorithm with mutipe iterations is shown in Fig. 5. This resuts verifies our approach. If samping time offset τ is arge it is usefu to appy mutipe iterations in order to improve the IFDA system performance. Ony one additiona iteration aows to improve the system performance by 1.5 db and cosey approach the ower bound. VI. CONCLUSIONS The ISI appears because of the samping time offset which causes remarkabe performance degradation. A time offset equa to the one haf of the chip duration makes successfu data transmission impossibe. In this contribution, we propose the efficient agorithm for the soft ISI suppression. The proposed agorithm aows to achieve an optimum performance and competey eiminate the ISI for the sma vaues of the samping time offset. For arge vaues of samping time offset, the performance improvement is significant and the IFDA system performance can reach the ower bound at the price of a high compexity. ACNOWLEDGENTS The work presented in this paper is carried in the framework of the 4ORE (4G C-CDA mutipe antenna system On chip for Radio Enhancements) project [2], which is supported by the European Commission within FP6 under the contract number IST The authors woud ike to acknowedge this support and this opportunity to conduct the research work. REFERENCES [1] H. Atarashi and. Sawahashi, Broadband wireess access based on VSF-OFCD and VSCRF-CDA and its experiments, In Proc. uti- Carrier Spread Spectrum & Reated Topics (C-SS), Sept [2] IST 4ORE project, web site [3] S. aiser, OFD code division mutipexing in fading channes, IEEE Transactions on Communications, vo. 50, no. 8, pp , Aug [4] A. Arkhipov and.schne, Intereaved frequency-division mutipeaccess system with frequency domain equaization, Internationa OFD Workshop 2004, Dresden, Germany, Sep [5]. Bruninghaus and H. Rohing, uti-carrier spread-spectrum and its reation to singe-carrier transmission, In Proc. of the IEEE VTC 98, Ottawa, Canada, [6] R.V. Nee and R. Prasad, OFDA for Wireess utimedia Communications, Artech House, [7] A. Arkhipov and. Schne, Frequency offset estimation for IFDA upink systems, IEEE GLOBECO 06, San Francisco, Caifornia, USA, Nov [8] A. Arkhipov and.schne, Samping time offset estimation for IFDA upink systems, IEEE Internationa Conference on Communications (ICC 2007), Submitted. [9]. Schne, I. De Broeck, and U. Sorger, A promising new wideband mutipe-access scheme for future mobie communications systems, European Transactions on Teecommunications (ETT), vo. 10, No. 4, pp , Ju./Aug [10] U. Sorger, I.De Broeck, and. Schne, Intereaved FDA - a new spread-spectrum mutipe-access scheme, In Proc. of IEEE Internationa Conference on Communications (ICC 98), pp , June [11] J. Proakis, Digita Communications, cgraw Hi Higher Education, Dec [12] S. aiser, uti-carrier CDA obie Radio Systems - Anaysis and Optimization of Detection, Decoding and Channe Estimation, Düssedorf: VDI Verag, Fortschritt-Berichte VDI, series 10, no. 531, 1998.

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