Channel estimation for LTE uplink in high doppler spread WCNC2008

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings Channel Estimation for LTE Uplink in High Doppler Spread Bahattin Karakaya H¨useyin Arslan Hakan Ali C ¸ ırpan Department of Electrical Engineering Istanbul University Istanbul, 34320, Turkey Email: bahattin@istanbul.edu.tr Department of Electrical Engineering University of South Florida Tampa, FL, 33620 USA Email: arslan@eng.usf.edu Department of Electrical Engineering Istanbul University Istanbul, 34320, Turkey Email: hcirpan@istanbul.edu.tr A Frame Abstract—Long Term Evolution (LTE) systems are expected to use Single Carrier Frequency Division Multiple Access (SCFDMA) for the uplink Being very similar to the OFDMA technology, SC-FDMA is sensitive to frequency offsets, which leads to inter-carrier interference (ICI) In this paper, we propose an interpolation algorithm based on adaptive order polynomial fitting for LTE uplink channel estimation to mitigate ICI in high Doppler spread Simulation results show that the proposed method has better performance compared to the conventional schemes #1 Slot #2 Slot #i Slot #1 Symb #2 Symb #j Slot # 19 Slot # 20 Slot # Symb A Subframe Cyclic Prefix Fig Data Reference Signal ( Training Symbol ) An LTE Uplink type frame structure with extended CP I I NTRODUCTION 3GPP Long Term Evolution (LTE) is the name given to a project within the Third Generation Partnership Project to improve the UMTS mobile phone standard to cope with future requirements The LTE project is not a standard, but it will result in the new evolved release of the UMTS standard, including mostly or wholly extensions and modifications of the UMTS system Release 8’s air interface is assumed to use OFDMA for the downlink and Single Carrier FDMA (SCFDMA) for the uplink [1] SC-FDMA is introduced in order to keep the peak to average power ratio (PAPR) as low as possible SC-FDMA has similar throughput performance and essentially the same overall complexity as OFDMA Furthermore, it can be viewed as DFT-spread OFDMA, where time domain data symbols are transformed to frequency domain by a discrete Fourier transform (DFT) before going through OFDMA modulation [2] Hence, similar to OFDMA, SC-FDMA is highly sensitive to frequency offsets caused by oscillator inaccuracies and the Doppler shift, which destroy the subcarrier orthogonality and give rise to ICI Several channel estimation techniques have been proposed to mitigate ICI in OFDM In [3], receiver antenna diversity has been proposed, but it is less effective in high normalized Doppler spread In [4], the proposed method is based on a piece-wise linear approximation for channel time-variations, but it tracks the channel variations by employing a comb-type pilot subcarrier allocation scheme In LTE uplink, however, pilot symbols are used instead As shown in Fig 1, each slot in LTE Uplink has a pilot symbol in its fourth symbol [1] In [5] Modified Kalman Filter based time-domain channel estimation approach for OFDM with fast fading channels have been proposed The proposed receiver structure models the time-varying channel as AR-process tracks the channel with MKF, uses curve fitting, extrapolation and MMSE time domain equalizer In contrast to [5], we propose a Kalman Filter based channel estimation method with interpolation that employs frequence domain equalizer Interpolation is applied with polynomial fitting, whose order is determined adaptively according to the amount of Doppler shift and signal-to-noise ratio (SNR) In this method, first, frequency domain least squares (LS) channel estimation is applied to pilot symbols in consecutive slots to obtain channel estimates Then, estimated channels taps are used as initial values for tracking the tap variation within the pilots by employing a Kalman filter Finally, adaptive order polynomial fitting is applied to channel estimates in consecutive slots in order to estimate the channel taps for the data symbols between the pilot symbols II S YSTEM M ODEL Fig shows the discrete baseband equivalent system model We assume an N -point DFT for spreading pth users time domain signal d(n) into frequency domain: D(p) (κ) = √ N N −1 d(p) (n)e−j2πnκ/N (1) n=0 After spreading, D(p) (κ) is mapped to the k th subcarrier S (p) (k) as follows S (p) (k) = 1126 1525-3511/08/$25.00 ©2008 IEEE D(p) (κ), 0, (p) k = ΓN (κ) otherwise (2) This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings Data processing d(n) D( Enco de d gn ip pa m re rir ac bu S DFT da ta se que nce S(k) s(m) IFFT Data processing Add CP da ta data h(m,l) Tx ngi pp a m re rir ac bu S DFT Zado ff - Chu se quence IFFT Y(k) y(m) Add CP w(m) Rem CP FFT Su bc ar rie rm ap pi ng FFT Su bc ar rie rm ap pi ng X( x(n) FDE IDFT LS Est Fi lte rin g D em od ul at io n data Rx + pilot pilo t Rem CP Ka lm an In te r p o la ti o n Pilo t pro ce ssing Pilot processing Fig SC-FDMA transceiver system model (p) where ΓN (κ) denotes N-element mapping set of pth user If it has consecutively arranged elements, the type of mapping is called localized Otherwise, it is called distributed mapping, which is used for frequency diversity [1] The transmitted single carrier signal at sample time m is given by s(p) (m) = √ M M −1 S (p) (k)ej2πmk/M (3) By using (3) in (6), the received signal becomes y(m) = √ M P −1 L−1 (4) (p) E{h(p) (m, l)h(p)∗ (n, l)} = σh2 (p) (l) J0 (2πfd Ts (m − n)) (5) where σh2 (p) (l) denotes the power of the channel coefficients (p) of pth user and fd is the Doppler frequency of pth user (p) in Hertz The term fd Ts represents the normalized Doppler frequency J0 (.) is the zeroth order Bessel function of the first kind In this paper, we assume that there is a single user, P = 1, so (4) becomes L−1 h(m, l)s(m − l) + w(m) y(m) = l=0 (6) h(m, l)ej 2πk(m−l) M + w(m) (7) l=0 L−1 −j2πlk/M , l=0 h(m, l)e y(m) can M −1 S(k)H(k, m)ej2πmk/M + w(m) (8) k=0 The FFT output at kth subcarrier can be expressed as p=0 l=0 where h(p) (m, l) is the sample spaced channel response of the lth path during the time m of pth user, L is the total number of paths of the frequency selective fading channel, and w(m) is the additive white Gaussian noise (AWGN) with zero mean and variance E{|w(m)|2 } = σw The fading channel coefficients h(m, l) are modeled as zero mean complex Gaussian random variables Based on the Wide Sense Stationary Uncorrelated Scattering (WSSUS) assumption, the fading channel coefficients in different delay taps are statistically independent In time domain fading coefficients are correlated and have Doppler power spectrum density modeled in Jakes [6] and has an autocorrelation function given by k=0 y(m) = √ M k=0 h(p) (m, l)s(p) (m − l) + w(m), L−1 S(k) By defining H(k, m) = be written as The received signal at base station can be expressed as y (p) (m) = M −1 Y (k) = = √ M M −1 y(m)e−j2πmk/M m=0 S(k)H(k) + I(k) + W (k), (9) where H(k) represents frequency domain channel response as H(k) = M M −1 H(k, m), (10) k=0 I(k) is ICI caused by the time-varying nature of the channel given as I(k) = M M −1 M −1 H(i, m)ej2πm(i−k)/M , S(i) i=0,i=k (11) m=0 and W (k) represents Fourier transform of noise vector w(m) W (k) = √ M M −1 w(m)e−j2πmk/M (12) m=0 Because of the I(k) term, there is an irreducible error floor even in the training sequences since pilot symbols are also corrupted by ICI Time varying channel destroys the orthogonality between subcarriers Therefore, channel estimation should be performed before the FFT block In order to compensate for the ICI, a high quality estimate of the channel impulse response is required in the receiver In this paper, the proposed channel estimation is done in time domain, where 1127 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings time varying channel coefficients are tracked by Kalman filter within the training intervals Variation of channel taps during the data symbols between two consecutive pilots is found by interpolation We assume that equalization is performed in frequency domain after the subcarrier demapping block Data are obtained after the demapping as ˆ h(m + 1) can be obtained by a set of recursions ˆ e(m) = y(m) − yˆ(m) = y(m) − sT (m)h(m) + sT (m)P(m)s∗ (m) K(m) = βP(m)s∗ (m) σw (13) X(κ) = Y (k), k = ΓN (κ) = D(κ)H(k) + I(k) + W (k) , k = ΓN (κ) We use frequency domain least squares estimation to find the initial values of the Kalman filter Below, (.)0 denotes the initial value Channel frequency response, which corresponds to used subcarriers, can be found by the following equation k = ΓN (κ) l=0 M M −1 H (23) C Adaptive order polynomial fitting In matrix notation, the equation for polynomial fitting is given by [11] ˆ T (l) ˆ T (l), h h i j (14) where Dt (κ) is a training sequence known by receiver L−1 ˆ h(m) − h(m) (22) P(m + 1) = β βI − K(m)sT (m) P(m) + Q(m + 1) (24) A Frequency Domain Least Squares Estimation H(k) = −1 ˆ ˆ h(m + 1) = β h(m) + K(m)e(m) III C HANNEL E STIMATION ∗ ˆ (k) = X(κ)Dt (κ) , H |Dt (κ)|2 ˆ h(m) − h(m) where P(m) = E (21) h(m, l)e−j2πkl/M , (15) m=0 M −1 defining h(l) = M m=0 h(m, l), to find initial values for ˆ (k) Kalman filtering in time domain, we can write IFFT of H as ˆ (l) = ˆ (k)ej2πkl/M (16) H h N k=ΓN (κ) = ΘTi , ΘTj T a, (25) where a = [a0 , a1 , , ak ]T are the polynomial coefficients, k is the order of the polynomial, i and j deˆ i (l) = note consecutive slot numbers depicted in Fig 1, h T ˆ i,0 , l), , h(m ˆ i,M −1 , l) are estimated ith slot pilot’s h(m lth channel tap vector, mi,b and Θi is given as  mi,0  mi,1  Θi =   B Kalman Filtering Time varying channel taps can be expressed in the form of an autoregressive (AR) process, in the case of the first order AR model the vector form of the channel is given in [7] and [8] as h(m + 1) = βh(m) + v(m + 1) (17) T is time index along ith slot pilot, m2i,0 m2i,1 m2i,M −1 mi,M −1 ··· ··· mki,0 mki,1 ··· mki,M −1      (26) By the matrix equation in (25), we can find polynomial coefficients according to the least squares as a = ΘT Θ −1 ˆ ΘT h(l) (27) where h(m) = [h(m, 0), · · · , h(m, L − 1)] Equation (17) is called process equation in Kalman filtering [9] v(m) and βIL are called process noise and state transition matrix, respectively Correlation matrix of process noise and state transition matrix can be obtained through the Yule-Walker equation [10] In this paper, we claim that the order of the polynomial can be selected adaptively Fig illustrates the appropriate polynomial orders according to maximum Doppler shift versus SNR ) Q(m) = (1 − β )diag(σh(m) (18) β = J0 (2πfd Ts ), (19) Channel taps through the η symbols, which are between the ith and j th slot pilots, can be found by polynomial coefficients as ¯ T T = ΘT , · · · , ΘT T a ¯ T (l), · · · , h (28) h 2 2 is the = σh(m,0) , σh(m,1) , , σh(m,L−1) where σh(m) power delay profile of the channel The equivalent of (6), which is a measurement equation in the state-space model of Kalman filter, can be shown in vector form as y(m) = sT (m)h(m) + w(m), D Interpolation 1 η η Proper polynomial orders are determined using the following mean squared identification error (MSIE) equation for various Doppler shift and SNR values via simulation (20) where s(m) = [s(m), s(m − 1), · · · , s(m − L + 1)] The channel estimate T 1128 M SIE = L l M ¯ |h(m, l) − h(m, l)|2 m (29) This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings Polynomial Fitting Order dB −5 dB 800 Hz 3rd Order Region −10 dB 700 Hz −15 dB 2nd Order Region −20 dB 500 Hz MSIE Maximum Doppler Shift 600 Hz −25 dB 400 Hz 1st Order Region −30 dB 300 Hz −35 dB 200 Hz −40 dB 100 Hz Hz dB −45 dB dB 10 dB 20 dB 30 dB SNR 40 dB 50 dB Interpolation v=60 km/h Interpolation v=120 km/h Extrapolation v=60km/h Extrapolation v=120 km/h dB 10 dB 15 dB 60 dB Fig The orders of polynomials appropriate for being used are shown in separate regions 20 dB 25 dB 30 dB 35 dB SNR Fig MSIE performance comparisons of the proposed method (Interpolation) and prediction method (Extrapolation) with different velocities TABLE I LTE U PLINK S IMULATION PARAMETERS −1 10 3, 84.106 Hz 2, 5M Hz 256 144 64 QP SK 2Ghz −2 10 BER Parameters Sampling frequency, fs Transmission bandwidth, FFT size, M DFT size, N Cyclic Prefix size Modulation type Carrier frequency −3 10 −4 10 IV S IMULATION R ESULTS We consider the generic frame structure, constant amplitude zero autocorrelation (CAZAC) pilot sequences, and extended cyclic prefix size for LTE uplink [12] As shown in Fig 1, frames have 20 slots, and each slot has symbols 4th symbol in each slot is a pilot symbol, and the rest are data symbols Simulation environments are shown in Table I In each simulation iteration, one frame (100 data symbols) is transmitted We consider a three-tap Rayleigh channel It has a normal2 = ized exponentially decaying power delay profile l σh(m,l) 1 and path delays τ = [0, 1, 2] fs We consider an MMSE equalizer for frequency domain equalization In Figs and 5, Extrapolation denotes the algorithm which is proposed in [5] and Interpolation denotes our proposed algorithm Fig shows the MSIE comparisons and Fig shows the BER comparisons of the proposed algorithm and the existing algorithms at the relative velocities, v = 60km/h, 120km/h, respectively V C ONCLUSION −5 Extrapolation v=60 km/h Extrapolation v=120 km/h Interpolation v=60 km/h Interpolation v=120 km/h dB dB 10 10 dB 15 dB 20 dB 25 dB 30 dB 35 dB SNR Fig BER performance comparisons of the proposed method (Interpolation) and prediction method (Extrapolation) with different velocities order polynomial fitting is applied to channel estimates in consecutive slots in order to estimate the channel taps for the data symbols between the pilot symbols The proposed method is shown to improve the BER performance of LTE systems considerably, especially in rapidly-varying channels, via the simulation results provided ACKNOWLEDGMENT The authors would like to thank WCSP group members at USF for their insightful comments and helpful discussions[] Future wireless communication systems such as LTE aim at very high data rates at high speeds However, many of these systems have an OFDM based physical layer, and hence, they are very sensitive to ICI In this paper, we propose a channel estimation method for wireless systems that transmit only block-type pilots (training symbols) In this method, adaptive 1129 R EFERENCES [1] 3GPP, TR 25.814 ”Physical Layer Aspects for Evolved UTRA” [Online] Available: www.3gpp.org [2] H G Myung, J Lim, and D J Goodman, “Single carrier FDMA for uplink wireless transmission,” IEEE Vehicular Technology Magazine, vol 1, no 3, pp 30–38, Sept 2006 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings [3] M Russell and G Stuber, “Interchannel interference analysis of OFDM in a mobile environment,” Vehicular Technology Conference, 1995 IEEE 45th, vol 2, 1995 [4] Y Mostofi and D Cox, “ICI Mitigation for Pilot-Aided OFDM Mobile Systems,” Wireless Communications, IEEE Transactions on, vol 4, no 2, pp 765–774, 2005 [5] K Han, S Lee, J Lim, and K Sung, “Channel estimation for OFDM with fast fading channels by modified Kalman filter,” Consumer Electronics, IEEE Transactions on, vol 50, no 2, pp 443–449, 2004 [6] W Jakes and D Cox, Microwave Mobile Communications Wiley-IEEE Press, 1994 [7] L Davis, I Collings, and R Evans, “Coupled estimators for equalization of fast-fading mobile channels,” Communications, IEEE Transactions on, vol 46, no 10, pp 1262–1265, 1998 [8] M Tsatsanis, G Giannakis, and G Zhou, “Estimation and equalization of fading channels with random coefficients,” Signal Processing, vol 53, no 2-3, pp 211–229, 1996 [9] S Haykin, “Adaptive filter theory,” Prentice-Hall Information And System Sciences Series, p 989, 1996 [10] B Porat, “Digital processing of random signals: theory and methods,” pp 152–181, 1994 [11] N Draper and H Smith, Applied Regression Analysis New York, 1967 [12] 3GPP, TS 36.211 ”Physical Channels and Modulation” [Online] Available: www.3gpp.org 1130