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Long term evolution (LTE) is designed for high speed data rate, higher spectral efficiency, and lower latency as well as high-capacity voice support. LTE uses single carrier frequency division multiple access (SC-FDMA) scheme for the uplink transmission and orthogonal frequency division multiple access (OFDMA) in downlink. The one of the most important challenges for a terminal implementation are channel estimation (CE) and equalization. In this paper, a minimum mean square error (MMSE) based channel estimator is proposed for an OFDMA systems that can avoid the ill-conditioned least square (LS) problem with lower computational complexity. This channel estimation technique uses knowledge of channel properties to estimate the unknown channel transfer function at non-pilot subcarriers.

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Low Complexity MMSE Based Channel EstimationTechnique for LTE OFDMA Systems
Md. Masud Rana
1
and Abbas Z. Kouzani
21
Department of Electronics and Radio EngineeringKyung Hee University, South Korea
2
School of Engineering, Deakin University, Geelong, Victoria 3217, AustraliaEmail: mrana928@yahoo.com
Abstract
—Long term evolution (LTE) is designed for highspeed data rate, higher spectral efﬁciency, and lower latencyas well as high-capacity voice support. LTE uses single carrier-frequency division multiple access (SC-FDMA) scheme for theuplink transmission and orthogonal frequency division multipleaccess (OFDMA) in downlink. The one of the most importantchallenges for a terminal implementation are channel estimation(CE) and equalization. In this paper, a minimum mean squareerror (MMSE) based channel estimator is proposed for anOFDMA systems that can avoid the ill-conditioned least square(LS) problem with lower computational complexity. This channelestimation technique uses knowledge of channel properties toestimate the unknown channel transfer function at non-pilot sub-carriers.
Index Terms
—Channel estimation, LTE, least-square,OFDMA, SC-FDMA.
I. I
NTRODUCTION
The 3rd generation partnership project (3GPP) membersstarted a feasibility study on the enhancement of the universalterrestrial radio access (UTRA) in December 2004, to improvethe mobile phone standard to cope with future requirements.This project was called evolved-UTRAN or long term evolu-tion [1], [22]. The main purposes of the LTE is substantiallyimproved end-user throughputs, low latency, sector capacity,simpliﬁed lower network cost, high radio efﬁciency, reduceduser equipment (UE) complexity, high data rate, and signiﬁ-cantly improved user experience with full mobility [2].3GPP LTE uses orthogonal frequency division multiplexingaccess (OFDMA) for downlink and single carrier-frequencydivision multiple access (SC-FDMA) for uplink. SC-FDMAis a promising technique for high data rate transmissionthat utilizes single carrier modulation and frequency domainequalization. Single carrier transmitter structure leads to keepthe peak-to average power ratio (PAPR) as low as possible thatwill reduced the energy consumption. SC-FDMA has similarthroughput performance and essentially the same overall com-plexity as OFDMA [1]. A highly efﬁcient way to cope withthe frequency selectivity of wideband channel is OFDMA. Itis an effective technique for combating multipath fading andfor high bit rate transmission over mobile wireless channels.In OFDMA system, the entire channel is divided into manynarrow subchannels, which are transmitted in parallel, therebyincreasing the symbol duration and reducing the intersymbol-interference (ISI) [2], [4]. Channel estimation (CE) plays animportant part in LTE OFDMA systems. It can be employedfor the purpose of detecting received signal, improving thecapacity of OFDMA systems by cross-layer design, and im-proving the system performance in terms of symbol errorprobability (SEP) [4], [5].A key aspect of the wireless communication system isthe estimation of the channel and channel parameters. CEhas been successfully used to improve the performance of LTE OFDMA systems. It is crucial for diversity combination,coherent detection, and space-time coding. Improved channelestimation can result: improved signal-to-noise ratio, channelequalization, co-channel interference (CCI) rejection, mobilelocalization, and improved network performance [1], [2], [3],[18].Many CE techniques have been proposed to mitigate inter-channel interference (ICI) in the downlink direction of LTEsystems. In [3], the LS CE has been proposed to minimizethe squared differences between the receive signal and es-timation signal. The LS algorithm, which is independent of the channel model, is commonly used in equalization andﬁltering applications. But the radio channel is varying withtime and the inversion of the large dimensional square matrixturns out to be ill-conditioned. In [19], Wiener ﬁltering basedtwo-dimensional pilot-symbol aided channel estimation hasbeen proposed. Although it exhibits the best performanceamong the existing linear algorithms in literature, it requiresaccurate knowledge of second order channel statistics, whichis not always feasible at a mobile receiver. This estimatorgives almost the same result as 1D estimators, but it requireshigher complexity. To further improve the accuracy of theestimator, Wiener ﬁltering based iterative channel estimationhas been investigated [4]. However, this scheme also requirehigh complexity.In this paper we proposed a channel estimation methodin the downlink direction of LTE systems. This proposedmethod uses knowledge of channel properties to estimate theunknown channel transfer function at non-pilot sub-carriers.These properties are assumed to be known at the receiver forthe estimator to perform optimally. The following advantages
(IJCSIS) International Journal of Computer Science and Information Security,Vol. 8, No. 8, November 201052http://sites.google.com/site/ijcsis/ISSN 1947-5500
Fig. 1. OFDM transceiver system model.
will be gained by using this proposed method. Firstly, theproposed method avoids ill-conditioned problem in the inver-sion operation of a large dimensional matrix. Secondly, theproposed method can track the changes of channel parameters,that is, the channel autocorrelation matrix and SNR. However,the conventional LS method cannot track the channel. Oncethe channel parameters change, the performance of the conven-tional LS method will degrade due to the parameter mismatch.Finally, the computational complexity of the proposed methodis signiﬁcantly lower than existing LS and Wiener CE method.We use the following notations throughout this paper:bold face lower and upper case letters are used to representvectors and matrices, respectively. Superscripts
x
†
denote theconjugate transpose of the complex vector
x
, diag(x) is thediagonal matrix that its diagonal is vector
x
; and the symbol
E
(
.
)
denotes expectation.The remainder of the paper is organized as follows: sec-tion II describes LTE OFDMA system model. The proposedchannel estimation scheme is presented in section III, and itsperformance is analyzed in section IV. Section V concludesthe work.II. S
YSTEM DESCRIPTION
A. System model
A simpliﬁed block diagram of the LTE OFDMA transceiveris shown in Fig.1. At the transmitter side, a baseband modu-lator transmits the binary input to a multilevel sequences of complex number
m
(
n
)
in one of several possible modulationformats including binary phase shift keying (BPSK), quandaryPSK (QPSK), 8 level PSK (8PSK), 16-QAM, and 64-QAM[1]. CE usually needs some kind of pilot information as a pointof reference. CE is often achieved by multiplexing knownsymbols, so called, pilot symbols into data sequence [15].These modulated symbols, both pilots and data, are perform aN-point inverse discrete Fourier transform (IDFT) to producea time domain representation [1]:
s
(
m
) =1
√
N
N
−
1
n
=0
m
(
n
)
e
j
2
πnmN
,
(1)where
m
is the discrete symbols,
n
is the sample index, and
m
(
n
)
is the data symbol. The IDFT module output is followedby a cyclic preﬁx (CP) insertion that completes the digitalstage of the signal ﬂow. A cyclic extension is used to eliminateintersymbol-interference (ISI) and preserve the orthogonalityof the tones.
B. Channel model
Channel model is a mathematical representation of thetransfer characteristics of the physical medium. These mod-els are formulated by observing the characteristics of thereceived signal. According to the documents from 3GPP [15],in the mobile environment, a radio wave propagation canbe described by multipaths which arise from reﬂection andscattering. If there are L distinct paths from transmitter tothe receiver, the impulse response of the wide-sense station-ary uncorrelated scattering (WSSUS) fading channel can berepresented as [4]:
w
(
τ,t
) =
L
−
1
l
=0
w
l
(
t
)
δ
(
τ
−
τ
l
)
,
(2)where fading channel coefﬁcients
w
l
(
t
)
are the wide sensestationary i.e.
w
l
(
t
) =
w
(
m,l
)
, uncorrelated complex Gaus-sian random paths gains at time instant
t
with their respectivedelays
τ
l
, where
w
(
m,l
)
is the sample spaced channel re-sponse of the
l
th path during the time
m
, and
δ
(
.
)
is the Diracdelta function. Based on the WSSUS assumption, the fadingchannel coefﬁcients in different delay taps are statisticallyindependent. Fading channel coefﬁcient is determined by thecyclic equivalent of sinc-fuctions [7]. In time domain fadingcoefﬁcients are correlated and have Doppler power spectrumdensity modeled in Jakes [13] and has an autocorrelationfunction given by [5]:
E
[
w
(
m,l
)
w
(
n,l
)
†
] =
σ
2
w
(
l
)
r
t
(
m
−
n
)=
σ
2
w
(
l
)
J
0
[2
πf
d
T
f
(
m
−
n
)]
,
(3)where
w
(
n,l
)
is a response of the
lth
propagation pathmeasured at time
n
,
σ
2
w
(
l
)
denotes the power of the channelcoefﬁcients,
f
d
is the Doppler frequency in Hertz,
T
f
isthe OFDMA symbol duration in seconds, and
J
0
(
.
)
is thezero order Bessel function of the ﬁrst kind. The term
f
d
T
f
represents the normalized Doppler frequency [5].
C. Received signal model
At the receiver, the opposite set of the operation is per-formed. We assume that the synchronization is perfect. Then,the cyclic preﬁx samples are discarded and the remaining Nsamples are processed by the DFT to retrieve the complexconstellation symbols transmitted over the orthogonal sub-channels. The received signal can be expressed as [5]:
r
(
m
) =
L
−
1
l
=0
w
(
m,l
)
s
(
m
−
l
) +
z
(
m
)
,
(4)where
s
(
m
−
l
)
is the complex symbol drawn from a con-stellation
s
of the
lth
paths at time
m
−
l
, and
z
(
m
)
is theadditive white Gaussian noise (AWGN) with zero mean andvariance
x
. After DFT operation, the received signal at pilot
(IJCSIS) International Journal of Computer Science and Information Security,Vol. 8, No. 8, November 201053http://sites.google.com/site/ijcsis/ISSN 1947-5500
locations is extracted from signal and the corresponding outputis represented as follows:
R
(
k
) =
M
−
1
m
=0
r
(
m
)
e
−
j
2
πmkM
=
M
−
1
m
=0
[
w
(
m,l
)
s
(
m
−
l
) +
z
(
m
)]
e
−
j
2
πmkM
(5)The received signals are demodulated and soft or hard valuesof the corresponding bits are passed to the decoder. Thedecoder analyzes the structure of received bit pattern andtries to reconstruct the original signal. In order to achievegood performance the receiver has to know the impact of thechannel.
D. OFDMA waveform
The frequencies (sub-carriers) are orthogonal, meaning thepeak of one sub-carrier coincides with the null of an adjacentsub-carrier. With the orthogonality, each sub-carrier can be
...
N
1
T
sub-carriers
Spacing
Fig. 2. Orthogonal overlapping spectral shapes for OFDMA system.
demodulated independently without ICI. In OFDM system,the entire channel is divided into many narrow sub-channels,which are transmitted in parallel, thereby increasing the sym-bol duration and reducing the ISI.Like OFDM, OFDMA employs multiple closely spaced sub-carriers, but the sub-carriers are divided into groups of sub-carriers. Each group is named a sub-channel. The sub-carriersthat form a sub-channel need not be adjacent. In the downlink,a sub-channel may be intended for different receivers. Finally,OFDMA is a multi-user OFDM (single user) that allowsmultiple access on the same channel. Despite many beneﬁtsof OFDMA for high speed data rate services, they suffer fromhigh envelope ﬂuctuation in the time domain, leading to largePAPR. Because high PAPR is detrimental to user equipment(UE) terminals, SC-FDMA has drawn great attention as anattractive alternative to OFDMA for uplink data transmission.III. CE
PROCEDURE
CE is the process of characterizing the effect of the phys-ical medium on the input sequence. The aim of most CEalgorithm is to minimize the mean squared error (MSE),while utilizing as little computational resources as possiblein the estimation process [2], [4]. CE algorithms allow thereceiver to approximate the impulse response of the channeland explain the behavior of the channel. This knowledgeof the channel’s behavior is well-utilized in modern mobileradio communications. One of the most important beneﬁtsof channel estimation is that it allows the implementation of coherent demodulation. Coherent demodulation requires theknowledge the phase of the signal. This can be accomplishedby using channel estimation techniques. Once a model has
43220191716….……11 Slot = 7 OFDM symbols = 0.5 ms2 Slots = 1 Sub-frame = 10 msOne radio frame = 20 Slots = 10 Sub-frames = 10 ms1765432
7 OFDM symbols
Cyclic prefix
1 resource elementPilot15
1 2 s u b - c a r r i e r s = 1 8 0 k H z
Resource block:
Short CP:7 symbols x 12 sub-carriersLong CP:6 symbols x 12 sub-carriers
Fig. 3. OFDMA generic frame structure.
been established, its parameters need to be estimated in orderto minimize the error as the channel changes. If the receiverhas a priori knowledge of the information being sent over thechannel, it can utilize this knowledge to obtain an accurateestimate of the impulse response of the channel.In LTE, like many OFDMA systems, known symbols calledtraining sequence, are inserted at speciﬁc locations in the timefrequency grid in order to facilitate channel estimation [10],[15]. As shown in Fig. 3, each slot in LTE downlink has apilot symbol in its seventh symbol [6] and LTE radio framesare 10 msec long. They are divided into 10 subframes, eachsubframe 1 msec long. Each subframe is further divided intotwo slots, each of 0.5 msec duration. The subcarrier spacing inthe frequency domain is 15 kHz. Twelve of these subcarrierstogether (per slot) is called a physical resource block (PRB)therefore one resource block is 180 kHz [2], [3], [6]. Sixresource blocks ﬁt in a carrier of 1.4 MHz and 100 resourceblocks ﬁt in a carrier of 20 MHz. Slots consist of either 6or 7 ODFM symbols, depending on whether the normal orextended cyclic preﬁx is employed [10], [15], [17].Channel estimates are often achieved by multiplexing train-ing sequence into the data sequence [18]. These trainingsymbols allow the receiver to extract channel attenuations andphase rotation estimates for each received symbol, facilitatingthe compensation of channel fading envelope and phase. Gen-eral channel estimation procedure for LTE OFDMA system isshown in Fig. 4. The signal
S
is transmitted via a time-varyingchannel
w
, and corrupted by an additive white Gaussian noise(AWGN)
z
before being detected in a receiver. The referencesignal
w
est
is estimated using LS , Wiener based, or proposedmethod. In the channel estimator, transmitted signal
S
isconvolved with an estimate of the channel
w
est
. The errorbetween the received signal and its estimate is
e
= (
r
−
r
1
)
.
(6)
(IJCSIS) International Journal of Computer Science and Information Security,Vol. 8, No. 8, November 201054http://sites.google.com/site/ijcsis/ISSN 1947-5500
Channel coefficient(w)with AWGN (z)Actual receivedsignal (r)Estimated signal(r1)Estimationalgorithm (LS,winner, ect.)Transmittedsequence (s)+
+-
Error signale=r-r1Estimated channelCoefficient
(
W
est
)
Fig. 4. General channel estimation procedure.
The aim of most channel estimation algorithms is to minimizethe mean squared error (MMSE), while utilizing as littlecomputational resources as possible in the estimation process.The equation (4) can be written as vector notation as [1]:
r
=
Sw
+
z
,
(7)where
r
= (
r
0
,r
1
,......,r
L
−
1
)
†
,
S
=
diag
(
s
0
,s
1
,......,s
L
−
1
)
,
w
= (
w
0
,w
1
,......,w
L
−
1
)
†
, and
z
= (
z
0
,z
1
,......,z
L
−
1
)
†
.The least-square estimate of such a system is obtained byminimizing square distance between the received signal andits estimate as [3]:
J
= (
Sr
−
w
)
2
= (
r
−
Sw
)(
r
−
Sw
)
†
.
(8)We differentiate this with respect to
w
†
and set the resultsequal to zero to produce [3]:
w
LS
= (
α
I
+
SS
†
)
−
1
S
†
r
,
(9)where
α
is regularization parameter and has to be chosen suchthat the resulting eigenvalues are all deﬁned and the matrix
(
α
I
+
SS
†
)
−
1
is the least perturbed. Where the channel isconsidered as a deterministic parameter and no knowledge onits statistics and on the noise is needed. The LS estimator iscomputationally simple but problem that is encountered in thestraight application of the LS estimator is that the inversionof the square matrix turns out to be ill-conditioned. So, weneed to regularize the eigenvalues of the matrix to be invertedby adding a small constant term to the diagonal [3]. If thetransmitted signal is more random, the performance of the LSmethod is signiﬁcantly decrease. Also the LS estimate of
w
est
is susceptible to Gaussian noise and inter-carrier interference(ICI). Because the channel responses of data subcarriers areobtained by interpolating the channel responses of pilot sub-carriers, the performance of OFDM system based on comb-type pilot arrangement is highly dependent on the rigorousnessof estimate of pilot signals. The successful implementation of the LS estimator depends on the existence of the inverse matrix
(
SS
†
)
−
1
. If the matrix
(
SS
†
)
is singular (or close to singular),then the LS solution does not exist (or is not reliable).To improve the accuracy of the estimator, Wiener ﬁlteringbased iterative channel estimation has been investigated [4],[7]:
w
est
=
R
ww
F
†
S
†
[(
SFR
ww
F
†
S
†
) +
x
I
]
−
1
w
ls
(10)where
R
ww
is the autocovariance matrix of
w
,
F
is theDFT matrix, and
x
denotes the noise variance. However, thisscheme also requires higher complexity.IV. P
ROPOSED
MMSE
BASED
CE
TECHNIQUE
The equation (7) can we rewritten as [22]:
w
1
=
rS
+
zS
=
w
2
+
z
1
,
(11)where actual channel value is
w
2
=
r
/
S
, noise contribution
z
1
=
z
/
S
, and
w
1
is the result of direct estimated channel.The proposed channel estimation is
w
prop
=
L
−
1
k
=0
a
†
k
w
1
(
k
)=
L
−
1
k
=0
a
†
k
[
w
2
(
k
) +
z
1
(
k
)]
w
prop
=
a
†
.
w
3
,
(12)where
a
k
= (
a
0
,a
1
...,a
L
−
1
)
†
is the column vector ﬁltercoefﬁcients, and
w
3
=
∑
L
−
1
k
=0
[
w
2
(
k
) +
z
1
(
k
)]
. The meansquare error (MSE) for the proposed LTE channel estimation is
J
= (
w
−
w
prop
)
2
. In order to calculate the optimal coefﬁcient,taking the expectation of MSE and partial derivative withrespect to channel coefﬁcient:
∂E
(
J
)
∂
a
†
=
∂ ∂
a
†
(
E
[(
w
−
w
prop
)(
w
−
w
prop
)
†
])
.
(13)Now putting the value of
w
prop
=
a
†
w
3
into the aboveequation to produce:
∂E
(
J
)
∂
a
†
=
∂ ∂
a
†
(
E
[(
w
−
a
†
w
3
)(
w
−
a
†
w
3
)
†
])=
∂ ∂
a
†
(
E
[(
w
−
a
†
w
3
)(
w
†
−
aw
†
3
)])=
∂ ∂
a
†
(
E
[
ww
†
−
a
†
w
3
w
†
−
aw
†
3
w
+
a
†
w
3
w
†
3
a
])=
E
[
−
w
3
w
†
+
w
3
w
†
3
a
]
.
(14)Now putting the partial derivative equal to zero in the aboveequation and after some manipulations we get the coefﬁcientas:
a
=
E
[(
w
3
w
†
)](
E
[(
w
3
w
†
3
)])
−
1
= [
E
(
w
2
+
z
1
)
w
†
][
E
((
w
2
+
z
1
)(
w
2
+
z
1
)
†
)]
−
1
= [
E
(
w
2
w
†
+
z
1
w
†
)][
E
((
w
2
+
z
1
)(
w
†
2
+
z
†
1
))]
−
1
=
E
(
w
2
w
†
+
z
1
w
†
)[
E
(
w
2
w
†
2
+
z
1
w
†
2
+
w
2
z
†
1
+
z
1
z
†
1
)]
−
1
.
(15)In this paper we assume that mean of the AWGN is zero i.e.
E
(
z
) = 0
and variance is
x
i.e.
E
(
zz
†
) =
x
. So, the aboveequation is simpliﬁed as:
a
=
E
(
w
2
w
†
)[
E
(
w
2
w
†
2
) +
E
(
z
1
z
†
1
)]
−
1
=
E
(
w
2
w
†
)[
E
(
w
2
w
†
2
) +
x
]
−
1
=
w
cross
∗
(
W
auto
+
x
)
−
1
,
(16)
(IJCSIS) International Journal of Computer Science and Information Security,Vol. 8, No. 8, November 201055http://sites.google.com/site/ijcsis/ISSN 1947-5500

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