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.. In [4], the pro
Trang 1Channel Estimation for LTE Uplink in High
Doppler Spread
Bahattin Karakaya
Department of Electrical Engineering
Istanbul University
Istanbul, 34320, Turkey
Email: bahattin@istanbul.edu.tr
H¨useyin Arslan Department of Electrical Engineering University of South Florida Tampa, FL, 33620 USA Email: arslan@eng.usf.edu
Hakan Ali C ¸ ırpan Department of Electrical Engineering
Istanbul University Istanbul, 34320, Turkey Email: hcirpan@istanbul.edu.tr
Abstract—Long Term Evolution (LTE) systems are expected
to use Single Carrier Frequency Division Multiple Access
(SC-FDMA) 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.
I INTRODUCTION 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 8 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
(SC-FDMA) 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
# 2 Slot
# 1 Slot
# j
Slot
# i
Slot
# 20 Slot
# 19 Slot
Data Cyclic Prefix Reference Signal ( Training Symbol )
# 1 Symb.
# 2 Symb. Symb.#
A Frame
A Subframe
Fig 1 An LTE Uplink type 1 frame structure with extended CP.
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 SYSTEMMODEL Fig 2 shows the discrete baseband equivalent system model
We assume an N -point DFT for spreading p th users time
domain signal d(n) into frequency domain:
D (p) (κ) = √1
N
N −1
n=0
d (p) (n)e −j2πnκ/N . (1)
After spreading, D (p) (κ) is mapped to the k th subcarrier
S (p) (k) as follows
S (p) (k) =
D (p) (κ), k = Γ (p) N (κ)
Trang 2Su bc ier m ap g IFFT
Data processing
Pilot processing
Encoded
data sequence
Zadoff - Chu
sequence
data
pilot
Tx
Su bc ier m ap g IFFT
Sub carr ier m app ing FFT
Pilot processing
data data
pilot Rx
Rem CP
Sub carr ier m app ing FFT Est.LS
Rem CP
FDE IDFT
+
h ( m,l ) w ( m )
y(m) Y(k) X( x(n)
Kalm
an
Filte ring
In te ola tio n
De mo dula tion
Fig 2 SC-FDMA transceiver system model.
where Γ(p) N (κ) denotes N-element mapping set of p thuser 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) = √1
M
M −1
k=0
S (p) (k)e j2πmk/M (3) The received signal at base station can be expressed as
y (p) (m) =
P −1
p=0
L−1
l=0
h (p) (m, l)s (p) (m − l) + w(m), (4)
where h (p) (m, l) is the sample spaced channel response of the
l th path during the time m of p th 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} = σ2
w
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
coeffi-cients are correlated and have Doppler power spectrum density
modeled in Jakes [6] and has an autocorrelation function given
by
E{h (p) (m, l)h (p)∗ (n, l)} = σ2
h (p) (l) J0(2πf d (p) T s (m − n)).
(5)
where σ2h (p) (l) denotes the power of the channel coefficients
of p th user and f d (p) is the Doppler frequency of p th user
in Hertz The term f d (p) T srepresents 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
y (m) =
L−1
l=0
By using (3) in (6), the received signal becomes
y (m) = √1
M
M −1
k=0
L−1
l=0
h (m, l)e j 2πk(m−l) M + w(m) (7)
By defining H(k, m) = L−1
l=0 h (m, l)e −j2πlk/M , y(m) can
be written as
y (m) = √1
M
M −1
k=0
S (k)H(k, m)e j2πmk/M + w(m) (8) The FFT output at k th subcarrier can be expressed as
M
M −1
m=0
y (m)e −j2πmk/M
where H (k) represents frequency domain channel response as
H (k) = 1
M
M −1
k=0
I (k) is ICI caused by the time-varying nature of the channel
given as
I (k) = 1
M
M −1
i=0,i=k
M −1
m=0
H (i, m)e j2πm(i−k)/M , (11)
and W (k) represents Fourier transform of noise vector w(m)
W (k) = √1
M
M −1
m=0
w (m)e −j2πmk/M . (12)
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 orthog-onality 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
Trang 3time 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
do-main after the subcarrier demapping block Data are obtained
after the demapping as
= D(κ)H(k) + I(k) + W (k) , k = Γ N (κ).
III CHANNELESTIMATION
A Frequency Domain Least Squares Estimation
We use frequency domain least squares estimation to find
the initial values of the Kalman filter Below,(.)0denotes the
initial value Channel frequency response, which corresponds
to used subcarriers, can be found by the following equation
ˆ
H0(k) = X (κ)D ∗ t (κ)
where D t (κ) is a training sequence known by receiver.
H (k) =
L−1
l=0
1
M
M −1
m=0
h (m, l)e −j2πkl/M , (15)
defining h (l) = 1
M
M −1
m=0 h (m, l), to find initial values for
Kalman filtering in time domain, we can write IFFT of ˆH0(k)
as
ˆh0(l) = 1
N
k=Γ N (κ)
ˆ
H0(k)e j2πkl/M (16)
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
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]
where σ h(m)2 = σ h(m,0)2 , σ2h(m,1) , , σ h(m,L−1)2
is the 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
where s(m) = [s(m), s(m − 1), · · · , s(m − L + 1)] T The
channel estimate
ˆh(m + 1) can be obtained by a set of recursions
e (m) = y(m) − ˆy(m) = y(m) − s T (m)ˆh(m) (21)
where P(m) = E
C Adaptive order polynomial fitting
In matrix notation, the equation for polynomial fitting is given by [11]
ˆhT
i (l), ˆh T
j (l)T = ΘT
i ,ΘT j
T
where a = [a0, a1, , a k]T are the polynomial
coeffi-cients, k is the order of the polynomial, i and j
de-note consecutive slot numbers depicted in Fig 1, ˆhi (l) =
ˆh(m i,0 , l ), , ˆh(m i,M −1 , l)T are estimated i th slot pilot’s
l th channel tap vector, m i,b is time index along i thslot pilot, andΘi is given as
i,0
i,1
1 m i,M −1 m2i,M −1 · · · m k
i,M −1
. (26)
By the matrix equation in (25), we can find polynomial coefficients according to the least squares as
In this paper, we claim that the order of the polynomial can be selected adaptively Fig 3 illustrates the appropriate polynomial orders according to maximum Doppler shift versus SNR
D Interpolation
Channel taps through the η symbols, which are between the
i th and j thslot pilots, can be found by polynomial coefficients as
¯hT
1(l), · · · , ¯h T
η
T
= ΘT
1, · · · , Θ T
η
T
Proper polynomial orders are determined using the following mean squared identification error (MSIE) equation for various Doppler shift and SNR values via simulation
L
l
1
M
m
Trang 40 dB 10 dB 20 dB 30 dB 40 dB 50 dB 60 dB
0 Hz
100 Hz
200 Hz
300 Hz
400 Hz
500 Hz
600 Hz
700 Hz
800 Hz
Polynomial Fitting Order
SNR
1st Order Region
2nd Order Region
3rd Order Region
Fig 3 The orders of polynomials appropriate for being used are shown in
separate regions.
TABLE I LTE U PLINK S IMULATION P ARAMETERS
Parameters
Sampling frequency,f s 3, 84.106Hz
Transmission bandwidth, 2, 5MHz
FFT size, M 256
DFT size, N 144
Cyclic Prefix size 64
Modulation type QP SK
Carrier frequency 2Ghz
IV SIMULATIONRESULTS
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 6 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
normal-ized exponentially decaying power delay profile
l σ h(m,l)2 =
1 and path delays τ = [0, 1, 2]1
f s We consider an MMSE equalizer for frequency domain equalization In Figs 4 and
5, Extrapolation denotes the algorithm which is proposed in
[5] and Interpolation denotes our proposed algorithm Fig 4
shows the MSIE comparisons and Fig 5 shows the BER
com-parisons of the proposed algorithm and the existing algorithms
at the relative velocities, v = 60km/h, 120km/h, respectively.
V CONCLUSION 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
−45 dB
−40 dB
−35 dB
−30 dB
−25 dB
−20 dB
−15 dB
−10 dB
−5 dB
0 dB
SNR
Interpolation v=60 km/h Interpolation v=120 km/h Extrapolation v=60km/h Extrapolation v=120 km/h
Fig 4 MSIE performance comparisons of the proposed method (Interpola-tion) and prediction method (Extrapola(Interpola-tion) with different velocities.
10−5
10−4
10 −3
10−2
10−1
SNR
Extrapolation v=60 km/h Extrapolation v=120 km/h Interpolation v=60 km/h Interpolation v=120 km/h
Fig 5 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[]
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