ESTIMATION OF SAMPLING TIME MISALIGNMENTS IN IFDMA UPLINK

Transcription

1 ESTIMATION OF SAMPLING TIME MISALIGNMENTS IN IFDMA UPLINK Aexander Arkhipov, Michae Schne German Aerospace Center DLR) Institute of Communications and Navigation Oberpfaffenhofen, 8224 Wessing, Germany Abstract This artice investigates the infuence of samping time offset on the performance of an intereaved frequency-division mutipe-access IFDMA) upink scheme for mobie radio transmission. It is shown that samping time offset causes signa-to-noise ratio SNR) degradation and eads to inter-symbo interference ISI). In addition, an efficient agorithm is proposed which is capabe to estimate samping time offset by appying oversamping at the receiver. The proposed agorithm requires ony three-times oversamping, does not use any piot symbos, and is independent from the transmission channe and moduation aphabet. 1. Introduction Compared to conventiona OFDMA [1], IFDMA seems more attractive due to its ower compexity, since IFDMA requires no discrete Fourier transform DFT) at the transmitter. Moreover, IFDMA shows a significanty ower peak-to-average power ratio PAPR) than conventiona OFDMA. If a transmit fiter is appied, the correct samping at the receiver becomes important. Severa studies have been accompished to estimate the time offset for OFDMA upink systems [2] []. In these works, rectanguar puse shaping is assumed, and the probem of correct samping is not considered. Standard samping time offset estimation agorithms for singe-carrier systems [4] cannot be appied to an IFDMA receiver. First, in an IFDMA receiver, equaization is preferaby performed in the frequency domain. Second, the infuence of a time-dispersive mobie radio channe must be taken into account. Third, received upink signas from different users are distorted by different transmission channes.

2 A.Arkhipov, M. Schne In this artice, we investigate the performance of an IFDMA upink system for mobie radio transmission in the presence of samping time offset misaignment and propose an agorithm for samping time offset estimation. We assume that samping time offset is equa or ess than the chip duration. The base station receives data from different users simutaneousy and, ideay, a users are perfecty aigned in time. However, in our investigation, we consider that a users can have random time deays, which have to be ess than the chip duration. The obtained estimates of the samping time offsets of each user can be used for the correcting of samping time instances at the base station receiver, or to transmit time correction vaues back to the mobie terminas in order to fine-tune users in time. We use the foowing notation in this artice: 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 this artice is organized as foows. In section II IFDMA scheme is briefy renewed. Section describes the proposed samping time offset estimation agorithm and simuation resuts are discussed in section 4. Finay, section 5 concudes this artice. 2. Intereaved Frequency-Division Mutipe Access Scheme In the foowing, IFDMA is described as a specia case of OFDMA- CDM. For additiona descriptions of the IFDMA scheme refer e.g to [5] [6]. The standard OFDMA-CDM [7] upink transmission system is abe to support up to K simutaneousy active users. Assume that N u users N u K) transmit simutaneousy. Each OFDMA-CDM user, i = 1,..., N u, performs a bocked transmission of Q compex-vaued symbos d i) q, q = 1,..., Q, which are assumed to be equay ikey and are taken from the underying moduation aphabet. The average energy of the transmitted data symbo d i) q 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) 1, di) 2,..., di) Q )T. 1) The symbo vector d i) is first seria-to-parae converted. Then, a codedivision mutipexing CDM) 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 vectors. After summation, we obtain vector s i) which is referred as a vector of the spread symbos.

3 Estimation of Samping Time Misaignments in IFDMA Upink Sexp{ j2 i/n } C i) d Compresion and repetition ) x i C/P up-samping Tx fiter D/A i) Channe h A/D Rx fiter y down-samping FFT -C/P Y Equa. Despread. c* ˆd Figure 1. Simuation mode for IFDMA upink It can be represented by its components s i) n, n = 0,..., L 1 as s i) n = Q q=1 c n,q d i) q, n = 0,..., L 1, 2) where c n,q is the nth component of the spreading code c q. Finay, an inverse DFT IDFT) with user-specific frequency mapping is performed for the vector s i). Bock intereaving achieves optima frequency diversity, since it distributes the L spread symbos s i) n of the Q data symbos of user i equay over the whoe transmission bandwidth. Note, OFDMA- CDM excusivey assigns to each of the K users a set of L frequencies out of a possibe N c = KL subcarriers. If a subcarriers assigned to user i are uniformy spaced over the whoe avaiabe transmission bandwidth at a distance N c /K, 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 Nc i 1 Nc L 1 n=0 s i) n e j 2π L n. ) As in standard OFDMA, a guard interva arger than the maximum channe deay is added as a cycic prefix CP) in OFDMA-CDM in order to avoid interference from preceding OFDMA-CDM transmission symbos. IFDMA as a specia case of OFDMA-CDM 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 = 1,..., Q, are used for spreading. In this case, the Fourier codes for spreading and the rotation factors of the Fourier transform cance out and the transmit signa given

4 A.Arkhipov, M. Schne in ) reduces to x i) = e j2π Nc }{{ i } user specific phase factor 1 d i) K mod L, = 0,..., N c 1. 4) Comparing 4) and the IFDMA signa generation as described in [5] [6] it foows that IFDMA is equivaent to OFDMA-CDM with bock intereaved frequency aocation and can be competey generated in the time domain without using the Fourier transform. The time domain generation of IFDMA uses compression and repetition as described in detai in [5]. 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 transmission chip, = 0,..., N c 1. The duration of the resuting chips is T c = T s /K. The simuation mode for IFDMA is shown in Fig. 1. After addition of CP, the obtained signa is up-samped. Up-samping is impemented by adding zero sampes between successive sampes x i). After up-samping, puse-shaping is performed by a transmit fiter. After digita-to-anaog D/A) conversion, we assume transmission over a time-dispersive mobie radio channe. At the receiver, we consider oversamping per transmitted chip x i). After samping, the signa is fitered by a receive fiter, which is matched to the transmit puse-shaping fiter. In Fig. 2, an exampe of the IFDMA signa after the receive fiter is represented. The soid ines represent the puse-shapes corresponding to the different chips and the dotted ine is the sum signa. In the down-samping operation at east one sampe per transmitted chip is chosen for performing equaization, despreading and estimation of the transmitted data. For the sake of simpicity, the convoution of the receive and transmit fiters is represented by the function gt), which is chosen as a Nyquist puse ) t cosπαt/tc ) gt) = sinc T c 1 4α 2 t 2 /Tc 2, 5) where α denotes the ro-off factor. In this section ony one receive sampe y, = 0,..., N c 1 per transmitted chip x i) is considered. We assume that the channe has an impuse response described by the vector h i) of dimension M with components h i) m, m = 1,..., M. Without oss of generaity, we assume that N c > M, in the foowing.

5 Estimation of Samping Time Misaignments in IFDMA Upink Assume that y represents the th eement of the received vector y, which can be written as N u y = ĥ i) zτ i) ) + n, 6) i=1 where the vector n denotes the sampes of the additive white Gaussian noise AWGN). The channe matrix ĥ 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 M zeros to h i). The eements z τ i) ) of vector zτ i) ) in 6) can be represented as z τ i) ) = e j 2π τi) i+ Nc Tc ) 1 7) K d i) mod L g τ i)) }{{} usefu signa ) d i) p mod L g τ i) + p )T c. p=0 p }{{} ISI N c 1 + 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 as shown in Fig. 2. The optimum samping points correspond to a situation where τ i) = 0. In this case, the received signa of user i is ISI-free. Defining W as a N c N c DFT matrix, the frequency domain representation Y of the received signa y can be written as N u Y = H i) Zτ i) ) + N, 8) i=1 where H i) = Wĥ i) is a N c N c diagona matrix, which is the DFT transformation of the channe impuse response ĥi). The received signa of user i in the frequency domain is defined as Zτ i) ) = Wzτ i) ) and N = Wn. The vector Y can be used for the estimation of the transmitted data. User i transmits its L spread symbos s i) n on subcarriers κ = nk +i, n = 0,..., L 1. 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. After

6 A.Arkhipov, M. Schne 1.5 optimum samping points T c misaigned samping points 1 K t -0.5 i) Figure 2. Exampe of the IFDMA signa after the receive fiter. Samping time offset τ i) causes SNR degradation and eads to 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. frequency domain equaization, the L received vaues Y κ can be despread with the compex-conjugate Fourier codes IDFT operation of ength L) to create an estimation ˆd of the symbo vector d. The considered receiver is equivaent to the conventiona OFDMA-CDM receiver [7], ony Fourier codes are used instead of Wash-Hadamard codes.. Time offset estimation Our goa is to estimate the time offset τ without any additiona piot symbos. In the foowing, we propose an agorithm which aows to estimate τ using tree times oversamping per transmitted chip. Thus, we consider the case where samping is performed with a period Tc and in addition to vector y we introduce two vectors y and y. If we omit the infuence of other users, y and y can be defined as y = ĥz τ T ) c + n 9) and y = ĥz τ + T ) c + n, 10)

7 Estimation of Samping Time Misaignments in IFDMA Upink respectivey. We introduce aso two additiona frequency domain vectors Y = Wy and Y = Wy. Note, ony the eements Y κ and Y κ, κ = nk + i, n = 0,..., L 1 of vectors Y and Y represent data of user i. Thus, we have three frequency domain vectors Y, Y and Y. The expectations of the eements of these vectors Y κ, Y κ and Y κ are given as E{ Y κ 2 } = E{ H κ,κ 2 }E{ Z κ τ) 2 } + σ 2 n, 11) E{ Y κ 2 } = E{ H κ,κ 2 }E { Z κ τ T ) } c 2 + σn 2 12) and E{ Y κ 2 } = E{ H κ,κ 2 }E { Z κ τ + T ) } c 2 + σ 2 n, 1) where σn 2 is the variance of the fitered noise, Z κ τ), Z κ τ Tc ) and Z κ τ + Tc Tc Tc ) are the components of vectors Zτ), Zτ ) and Zτ + ) taken at κ = nk + i, n = 0,..., L 1. The fading coefficients H κ,κ, κ = nk + i, n = 0,..., L 1 are the diagona eements of H. It can be noted that H κ,κ are the same in 11), 12) and 1). This assumption can be considered as reaistic, since system design rues assume that fading coefficients remain constant over a duration of one IFDMA symbo, i.e, during a time period equa to N c T c. The expectations E{ Y κ 2 }, E{ Y κ 2 } and E{ Y κ 2 } can be approximated as averages of the energies of the received data Y κ, Y κ and Y κ. For exampe, such an averaging can be performed over the whoe transmission frame. The DFT operation does not change the energy of the signa, i.e. E{ Z κ τ) 2 } = K E{ z τ) 2 }. Therefore, the vaue E{ Z κ τ) 2 } can be approximated as E{ Z κ τ) 2 } = E s τ) = N c/2 p= N c/2 g 2 τ + pt c ). 14) Taking into account 11), 12), 1) and 14) and introducing new variabes A = E{ Y κ 2 }-E{ Y κ 2 }, B = E{ Y κ 2 }-E{ Y κ 2 } and C = E{ Y κ 2 }- E{ Y κ 2 }, the estimate ˆτ of the normaized time offset τ can be found as ˆτ = 15) arg min τ AE s τ T ) c + BE s τ + T ) c + CE s τ).

8 A.Arkhipov, M. Schne The foowing remarks are of interest: The estimation in 15) does not require the knowedge of the transmission channe and the moduation aphabet. The estimation in 15) can be performed ony if Tc 2 τ Tc 2, since function E s τ) is periodic with a period of T c. The proposed estimation requires ony one dimensiona search over possibe vaues of τ. Vaues E s τ) can be precacuated at the receiver according to formua 14). One of the vectors Y, Y and Y can be used for despreading and data demoduation. 4. Simuation Resuts The transmission system considered for simuations has a bandwidth of 20 MHz and the carrier frequency of 5 GHz. The number of subcarriers is N c = The spreading ength is L = 64 and the tota number of users is K = 16. A minimum mean square error MMSE) detector is used as described in [7]. For the channe coding, a convoutiona code with rate 1/2 and memory 6 is used in our simuations. The transmission frame consists of 24 IFDMA symbos. QPSK is used for moduation. Infuence of the receive and the transmit fiter is modeed as the Nyquist puse gt), which assumed to be non-zero ony within T c < t < T c. Therefore, if samping time offset is present, each transmitted chip x experiences ISI from three preceding and three foowing chips. The ro-off factor α varies from 0.25 to A mutipath channe mode is considered, which consists of a tapped deay ine with M = 11 statisticay independent Rayeigh fading taps. The average power for each channe component h m, m = 1,..., M, is modeed as E{ h m 2 } = m + 1 db). 16) Additionay, the average channe attenuation is normaized to unity in our simuations. We evauate the system performance in terms of biterror rate BER) and mean square error MSE) of the samping time offset estimate. In Fig. the system performance versus SNR is present for samping time offsets τ = 4 18 T c and τ = 7 18 T c. As a reference, the idea case with τ = 0 is presented. It is shown that the performance of the system degrades with increasing τ, due to the increase of ISI and SNR degradation. However, SNR degradation does not pay a significant roe in the performance oss. According to 2), SNR degradation is -0.74

9 Estimation of Samping Time Misaignments in IFDMA Upink Bit Error Rate τ= 7/18 Τc τ= 4/18 Τc τ= SNR in db Figure. BER versus SNR for the different vaues of samping time offset τ; α = α=0.25, 1 frame 10 - MSE α=0.75, 1 frame τ= 7/18 Τ τ= 4/18 Τ c c α=0.75, 2 frames SNR in db Figure 4. MSE of the samping time offset estimate versus SNR db for τ = 4 18 T c and -2.6 db for τ = 7 18 T c. Therefore, ISI is responsibe for the residua performance degradation. The MSE of the samping time offset estimation in 15) is presented in Fig. 4 for τ = 4 18 T c and τ = 7 18 T c as we as for different vaues of α equa to 0.25 and For α = 0.25, the performance of the proposed agorithm degrades if τ increases. In contrast, the performance of the agorithm is independent from τ if α = Cose inspection of the function E s τ) expains this fact. If α = 0.25, the function E s τ) is

10 A.Arkhipov, M. Schne reativey fat. Hence, the function in 15) does not have a distinct minimum, and the obtained estimation is easiy affected by noise. The situation changes competey, if we increase α. The difference between the maximum and minimum vaue of E s τ) is neary two times arger for α = 0.75 than for α = If α = 0.75, the function E s τ) increases steepy and this steepness remains neary constant with increasing τ. Therefore, MSE is independent of τ for α = How it is seen from Fig. 4, the required SNR to achieve a MSE of 10 is 14 db ess for α = 0.75 than for α = The precision of the estimate can be improved if averaging in 11), 12) and 1) is performed over the frame with a arge size or over many frames. In Fig. 4 this averaging is performed over two frames for the case of α = It can be seen that the performance is improved by db. However, such an improved averaging eads to a deay in the samping time offset estimation and is not desirabe. 5. Concusions The performance of the IFDMA upink system is investigated in the presence of samping time offset. It has been shown that samping time offset resuts in ISI and SNR degradation. Moreover, we have proposed an agorithm for samping time offset estimation using three times oversamping at the receiver. The proposed agorithm is independent from the transmission channe and moduation aphabet. References [1] R.V. Nee and R. Prasad. OFDMA for Wireess Mutimedia Communications. Artech House, [2] M. Morei. Timing and frequency synchroniozation for the upink of an OFDMA system. IEEE Transactions on Communications, 52, no. 2:286 06, Feb [] M. Park, K.Ko, H.Yoo, and D.Hong. Performance anaysis of OFDMA upink systems with symbo timing misaignment. IEEE Communications Letters, 7:76 79, Aug [4] J. Proakis. Digita Communications. McGraw Hi Higher Education, Dec [5] M. Schne, I. De Broeck, and U. Sorger. A promising new wideband mutipeaccess scheme for future mobie communications systems. European Transactions on Teecommunications ETT), 10, No. 4: , Ju./Aug [6] U. Sorger, I.De Broeck, and M. Schne. Intereaved FDMA - a new spreadspectrum mutipe-access scheme. IEEE Internationa Conference on Communications ICC 98), pages , June [7] S. Kaiser. OFDM code division mutipexing in fading channes. IEEE Transactions on Communications, 50, no. 8: , Aug