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Pilot-Assisted Channel Estimation for STBC-Based Wireless MIMO-OFDM Systems
Bo-Chiuan Chen
Dept. of Electrical Engineering National Chi Nan University Nantou, Taiwan 545, R.O.C.
Wen-Jeng Lin
Dept. of Electrical Engineering National Chi Nan University Nantou, Taiwan 545, R.O.C.
Jung-Shan Lin
∗
s3323527@ncnu.edu.tw
s3323541@ncnu.edu.tw
Dept. of Electrical Engineering National Chi Nan University Nantou, Taiwan 545, R.O.C.
jslin@ncnu.edu.tw
ABSTRACT
With equipping multiple antennas at both t

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Pilot-Assisted Channel Estimation forSTBC-Based Wireless MIMO-OFDM Systems
Bo-Chiuan Chen
Dept. of Electrical EngineeringNational Chi Nan UniversityNantou, Taiwan 545, R.O.C.
s3323527@ncnu.edu.twWen-Jeng Lin
Dept. of Electrical EngineeringNational Chi Nan UniversityNantou, Taiwan 545, R.O.C.
s3323541@ncnu.edu.twJung-Shan Lin
∗
Dept. of Electrical EngineeringNational Chi Nan UniversityNantou, Taiwan 545, R.O.C.
jslin@ncnu.edu.tw
ABSTRACT
With equipping multiple antennas at both transmitter andreceiver ends, the desired signals in the OFDM wireless com-munications could be transmitted and received through mul-tiple uncorrelated channels for achieving twofold beneﬁtsand high ﬂexibility. For this kind of MIMO-OFDM sys-tems, if the assistance of channel estimation is under con-sideration, the overall system performance is able to be fur-ther enhanced. This paper proposed a pilot-symbol-assistedchannel estimation technique for MIMO architecture by as-signing known pilot symbols orthogonally between diﬀerenttransmitting antennas. The mixed transmitted signals couldbe completely separated at the receiver end due to the or-thogonal property of pilot blocks. Some simulation resultsare given to illustrate the superior overall performance thatcan be achieved by the proposed channel estimation algo-rithm in MIMO-OFDM systems under COST 207 mobilewireless environments.
Categories and Subject Descriptors
G.1.1 [
Numerical Analysis
]: Interpolation—
interpolation formulas
General Terms
Algorithms, performance
Keywords
OFDM, MIMO, channel estimation, pilot symbols
1. INTRODUCTION
The idea of multi-carrier modulation (MCM) techniquesis a good transmission concept that can be adopted to gain
∗
J.-S. Lin is also with the Graduate Institute of Communi-cation Engineering, National Chi Nan University, R.O.C.
Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for proﬁt or commercial advantage and that copiesbear this notice and the full citation on the ﬁrst page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior speciﬁcpermission and/or a fee.
IWCMC’07,
August 12–16, 2007, Honolulu, Hawaii, USA.Copyright 2007 ACM 978-1-59593-695/07/0008 ...$5.00.
many advantages instead of conventionalsingle-carrier cases.The optimal schemes of MCM techniques are orthogonalfrequency division multiplexing (OFDM) [1, 2] transmis-sion techniques which have widely attracted for researchand application nowadays. OFDM systems could cope withfrequency-selective fading eﬀect caused by multipath prop-agation delay spread through dividing available bandwidthinto many sub-bands to create a frequency-ﬂat fading chan-nel condition. Then, each portion of data is carried througheach subcarrier for signals transmission. Therefore, theband-width could be saved quite a little due to orthogonally over-lapped subcarriers. In addition, OFDM could be easily im-plemented by manipulating fast Fourier transform (FFT)algorithm with an acceptable cost.Multiple man-made uncorrelated or independent wirelesspropagation channels could be achieved by equipping mul-tiple antennas at both transmitter and receiver ends withan appropriate separation distance. The advantage of usingmultiple-input multiple-output (MIMO) [3, 4, 5] architec-ture is to provide more opportunities to transmit and re-ceive replicas of same signals for ensuring high bit error rate(BER) performance, that is, achieving high linkage qual-ity of service (QoS). It is exactly the concept of spatial di-versity (SD) techniques. Here, Alamouti’s space-time blockcoding (STBC) [6, 7] SD criterion is utilized for combiningwith OFDM schemes to construct the so-called STBC-basedwireless MIMO-OFDM systems which are expected to ob-tain twofold beneﬁts.Pilot-symbol-assisted channel estimation (PSACE) tech-niques have been successfully applied to OFDM systems forobtaining a remarkable enhancement. In [8] and [9], theyhad provided the performance comparison among variousdesigns of pilot assignments using diﬀerent kinds of mod-ulation schemes and interpolation techniques. For MIMO-OFDM systems, PSACE methods based on least squares(LS) and minimum mean-squared error (MMSE) algorithmshad been investigated in [10, 11, 12]. In [10], the advan-tages of adopting MIMO-conﬁgured structures for OFDMhad been demonstrated. In [11], the diﬀerence between zero-form and nonzero-form pilot assignments was analyzed forthe design criterion. Another investigation for adopting dif-ferent antenna conﬁgurations had been illustrated in [12] forgeneral extension cases.In addition, the arrangement and properties of pilots formulti-antenna structures are certainly diﬀerent from that of single-antenna cases. Therefore, some modiﬁcations mustbe considered for extending PSACE techniques in MIMO-
DataDataSourceSinkQPSKQPSKMOD.DeMod.2
×
2STBCSTBCENC.DEC.PilotPilotInsertionExtractionIFFTIFFTChannel1Channel2
Σ
AWGNFFTChannel
Estimation
Pilots on Tx.1Pilots on Tx.2L.I.L.I.ML
Detection
Figure 1: The system model of STBC-based wireless2ISO-OFDM transceivers.
OFDM schemes [13, 14]. However, the importance of or-thogonality of pilots between multiple transmitters did notbe veriﬁed, and the detail for recovery of combined signals inthe receiver end was also absent in the previous studies. Inthis paper, this gap is ﬁlled while an eﬃcient channel estima-tion algorithm for MIMO-OFDM is proposed for achievingsuperior results. The remainder of this paper is organized asfollows: The adopted system and channel models in MIMO-OFDM systems are concisely described in Section 2. Theassignment pattern of pilot symbols and proposed channelestimation algorithm are completely presented in Section 3.The comparative simulation results for performance demon-stration under COST 207 mobile wireless environments areanalyzed in Section 4. Some concluding remarks are ﬁnallygiven in Section 5.
2. MIMO-OFDM SYSTEM MODEL
Based on OFDM transmission schemes, two transmittingantennas and one receiving antenna are conﬁgured to formthe 2ISO transmit diversity as [6]. The adopted systemmodel of STBC-based wireless 2ISO-OFDM transceivers hasbeen established and illustrated in Fig. 1 completely. Thesignaling procedureis described as follows: The single QPSK-modulated symbol stream is ﬁrst separated into two STBC-coded symbol streams by Alamouti’s 2
×
2 STBC SD cri-terion for forwarding coded replicas of same data blocksin space and time. Throughout this paper, one block isconsisted of two consecutive symbols for the convenienceof expression. After inserting known pilot symbols accord-ing to speciﬁc pilot patterns, the transmitted signals oneach branch are modulated and multiplexed through in-verse FFT (IFFT) by the unit of an OFDM symbol. TheOFDM frames including the extension of cyclic preﬁx (CP)are then launched into two wireless channels for data trans-mission. The STBC-coded signals with pilots of the
n
-thOFDM symbol carried on the
k
-th OFDM subcarrier whichare forwarded through the
β
-th transmitting antenna can beexpressed in the following:
X
(
β
)
[
n, k
] =
Pilot:
X
(
β
)
[
n, k
p
]
, k
p
= 0
,
1
,
· · ·
, N
p
−
1
,
Data:
X
(
β
)
[
n, k
]
,
otherwise
.
(1)
β
= 1
,
2;
k
= 0
,
1
,
···
, N
s
−
1;
k
p
= 0
,
1
,
···
, N
p
−
1
.
¯
x
(1)
(
t
)¯
x
(2)
(
t
)
N
CP
N
CP
N
s
N
s
N
s
T
s
N
s
T
s
0011
Q
−
1
Q
−
1
τ τ τ τ τ τ
······
α
(1)0
(
t
)
α
(1)1
(
t
)
α
(1)
Q
−
1
(
t
)
Σ
α
(2)0
(
t
)
α
(2)1
(
t
)
α
(2)
Q
−
1
(
t
)
Σ
Σ
¯
r
(
t
)
w
(
t
)
Figure 2: Uncorrelated tapped-delay line transver-sal ﬁlters for two channels.
where the
k
p
-th inserted pilot symbol is presented by index
k
p
;
N
s
and
N
p
represent the total number of OFDM subcar-riers and used pilots, respectively. Note that the assignmentof pilot symbols is according to orthogonal comb-type pilotpatterns. Except the part of “pilot”, the total number of available data symbols is equal to (
N
s
−
N
p
) shown as the“data” portion.In Fig. 2, the two uncorrelated wireless channels could bemodeled by two tapped-delay line transversal ﬁlters with2
Q
mutually independent time-varying Rayleigh faders re-ferring to certain power delay proﬁles. Due to the uncor-related channel conditions, the total eﬀect caused by twopropagation channels reﬂecting on the received signals is ac-tually a summation result [15]. Therefore, channel impulseresponses of the
β
-th wireless channel
h
(
β
)
(
t
;
τ
) can be de-scribed as:
h
(
β
)
(
t
;
τ
) =
Q
−
1
q
=0
α
(
β
)
q
(
t
)
δ
(
t
−
qτ
)
, β
= 1
,
2
,
(2)and the continuous-time received signals at time instance
t
can be represented as follows:¯
r
(
t
)=
N
t
β
=1
h
(
β
)
(
t
;
τ
)
∗
¯
x
(
β
)
(
t
)+
w
(
t
)=
N
t
β
=1
Q
−
1
q
=0
α
(
β
)
q
(
t
) ¯
x
(
β
)
(
t
−
qτ
) +
w
(
t
)
, N
t
= 2
.
(3)where the total path number of a single wireless channel isequal to
Q
, the corresponding tap gains are
α
(
β
)
q
(
t
), the de-lay spread interval of the
q
-th tap is
qτ
as well as the totalnumber of transmitting branches is represented by
N
t
. Af-ter undergoing wireless channel eﬀect, the continuous-timereceived signals ¯
r
(
t
) could be expressed as the combinationcontributed from two transmitted signals ¯
x
(1)
(
t
) and ¯
x
(2)
(
t
)simultaneously with corresponding noise terms
w
(
t
).At the receiver end, the signals’ recovery procedure is ex-plained as Fig. 1: The equivalent baseband received signalsare ﬁrstly removing the CP portion and passing throughFFT for demultiplexing and demodulating as the result ex-pressed as follows. The part of received pilot symbols
R
[
n, k
p
]are extracted according to speciﬁed pilot patterns block byblock. Then the received pilot blocks are operated withthe uncorrupted pilot blocks for estimating the channel fre-
Tx.1Tx.2
nnkk
2
N
r
2
N
r
························
D DDDDDDD
DDDDDDDDDDDDD
DDDDDDD
n
: OFDM symbol index
k
: subcarrier indexD: data symbols: orthogonal pilot blocks
N
r
=
N
s
/N
p
Figure 3: The assignment of comb-type pilot patternwith orthogonal property.
quency responses (CFR’s) on all pilot positions.
R
[
n, k
] =
Pilot:
R
[
n, k
p
]
, k
p
= 0
,
1
,
· · ·
, N
p
−
1
,
Data:
R
[
n, k
]
,
otherwise
.
(4)After linear interpolation, the estimated CFR’s on all datapositions are gotten. The mixed data blocks now can be sep-arated completely by a liner combination procedure, that isactually for STBC decoding, after removing the part of pi-lot symbols. Finally, the most likely results are chosen bymaximum-likelihood detection (MLD) and the QPSK de-modulator would recover the bit streams from the detectedresults.
3. CHANNELESTIMATIONALGORITHM
In order to utilize the advantages of PSACE techniques for2ISO-OFDM systems, some modiﬁcations must be consid-ered in the following: First of all, the amount of total pilotsymbols will be multiplied by the number of transmitting an-tennas, it means that more pilots are necessary for MIMOarchitecture. Secondly, pilot blocks transmitted on diﬀerentantennas must be orthogonal to each other to facilitate thedecoupling of multiple mixed data blocks by utilizing theestimated CFR’s after STBC decoding, then the separatedsymbols could be correctly detected by MLD individually torecover the srcinal transmitted signals. Thirdly, how to as-sign the pilot blocks on two transmitting branches while theinter-transmitter-antenna-interference (ITAI) between eachother could be completely avoided is also discussed in detailhere.In this paper, comb-type pilot patterns are adopted forchannel estimation in STBC-based wireless 2ISO-OFDMsys-tems to provide good QoS in high-speed mobile communi-cation environments. For achieving the purpose, pilot as-signment fashions would be adjusted to satisfy the follow-ing criterions: The allocation of pilot symbols should beequal-spaced and equal-powered with orthogonality prop-erty, moreover, the minimal number of used pilot symbolsmust be greater than or at least equal to the total tap num-ber of channel models [11, 12, 13, 14]. The proper pilot as-signment between two transmitting branches has been welldesigned in Fig. 3.The orthogonal comb-type pilot pattern on two transmit-ting antennas is fully assigned at all OFDM symbol index
n
with a repeated period 2
N
r
between OFDM subcarrierindex
k
. Two successive pilot symbols are assigned togetherto form a pilot block and the spacing between blocks is dis-tributed equally in frequency grids. Due to the unity trans-mission power constraint, halved-power for each pilot sym-bol in 2ISO conﬁgurations is very suitable. In addition, theorthogonality property is indeed essential to facilitate sepa-rating of the mixed transmitted pilot symbols from diﬀerentbranches. With the assignment, the CFR’s on pilot posi-tions of two uncorrelated wireless channels could be able toestimate correctly.The mathematical deﬁnition of orthogonality between pi-lot blocks is given as follows. For instance, if the receivedpilot block transmitted from branch one is operated with theconjugate version of itself, the result will be the power sum of these two pilot symbols which is called block power
P
(
β
)
block
.However, the result will be always zero while pilot blocksfrom diﬀerent transmitting antennas are operated crosswiseto each other. The operations of pilot blocks at indices
k
p
and
k
p
+ 1 on the
β
-th antenna are presented as follows:
P
(
β
)
block
≡
X
(
β
)
∗
[
n, k
p
]
X
(
β
)
[
n, k
p
]+
X
(
β
)
∗
[
n, k
p
+ 1]
X
(
β
)
[
n, k
p
+ 1]; (5)
X
(1)
∗
[
n, k
p
]
X
(2)
[
n, k
p
]+
X
(1)
∗
[
n, k
p
+ 1]
X
(2)
[
n, k
p
+ 1] = 0
,X
(2)
∗
[
n, k
p
]
X
(1)
[
n, k
p
]+
X
(2)
∗
[
n, k
p
+ 1]
X
(1)
[
n, k
p
+ 1] = 0
.
(6)There are two groups of pilot assignment both can satisfythe previous orthogonal property. They are called“nonzero”and “zero” pilot forms [11], respectively, as well as the ma- jor diﬀerence between them is also analyzed as follows: Fornonzero-form cases, the pilot symbols are simultaneouslytransmitted from two branches during every symbol inter-val. For zero-form cases, the speciﬁc pilot blocks are al-ternatively sent through two transmitting antennas, that is,antenna one is consecutively transmitting two pilots at ﬁrstblock while antenna two keeps silence, and the situation willbe contrary during next block period.Due to the alternately transmitted pilot symbols, the fash-ion of zero-form assignment can utilize full unity power fortransmission while the ITAI terms would never be occurred.However, less channel information of CFR’s is collected thanthat of nonzero-form cases because half the chances of chan-nel estimation are performed. In other words, the pilot spac-ing here is enlarged equal to 4
N
r
and the degraded estima-tion performance could be expected at the same time.Although both of them can hold the orthogonality prop-erty shown as (5) and (6), we still should not waste all theavailable pilot tones for achieving superior channel estima-tion results. On the contrary, the patterns of pilot assign-ment without orthogonal properties are deﬁnitely unable tobe adopted. In addition, the performance resulting fromthe pilot assignments which own same properties is almostidentical in spite of the setting of complex pilot values. Fi-nally, the orthogonal nonzero-form pilot assignments will beadopted in this paper.After accomplishing thepilot assignments on two branches,
channel estimation techniques for STBC-based 2ISO-OFDMsystems are then developed. At the receiver end, the portionof pilot blocks are ﬁrstly extracted from the FFT-processedbaseband received signals
R
[
n, k
] according to speciﬁc pi-lot patterns block by block. The pilot blocks,
R
[
n, k
p
] and
R
[
n, k
p
+1], can be expressed as the combination of two pairsknown pilots which are transmitted from diﬀerent anten-nas passing through two uncorrelated channels, then addingwith the corresponding noise terms:
R
[
n, k
p
]=
X
(1)
[
n, k
p
]
H
(1)
[
n, k
p
]+
X
(2)
[
n, k
p
]
H
(2)
[
n, k
p
] +
W
[
n, k
p
]
,R
[
n, k
p
+ 1]=
X
(1)
[
n, k
p
+ 1]
H
(1)
[
n, k
p
+ 1]+
X
(2)
[
n, k
p
+ 1]
H
(2)
[
n, k
p
+ 1]+
W
[
n, k
p
+ 1]
.
(7)The principal notion of the proposed channel estimationalgorithm is to manipulate the orthogonality between pilotblocks for performing channel estimation in 2ISO-OFDMsystems while the mixed transmission signals could be re-covered correctly. Therefore, the extracted pilot blocks areoperated with the conjugate version of uncorrupted pilotblocks which are assigned for transmitting antenna one andantenna two sequentially. The algorithm is now illustratedas follows:ˆ
H
(
β
)
[
n, k
p
] =
X
(
β
)
∗
[
n, k
p
]
R
[
n, k
p
]+
X
(
β
)
∗
[
n, k
p
+ 1]
R
[
n, k
p
+ 1]
.
(8)For the sake of obtaining the estimation results, the CFR’sare assumed identical between two successive subcarriersand vary from block to block in frequency direction. Af-terwards, the actual and estimated CFR’s are presented asfollows, respectively:
H
(
β
)
[
n, k
p
]=
H
(
β
)
[
n, k
p
+ 1] =
H
(
β
)
[
n,
2
k
b
]
,
(9)ˆ
H
(
β
)
[
n, k
p
]=ˆ
H
(
β
)
[
n, k
p
+ 1] =ˆ
H
(
β
)
[
n,
2
k
b
]
,
(10)
k
b
= 0
,
1
,
···
,N
p
2
−
1;
β
= 1
,
2
.
This kind of channel condition is called“block ﬂat-fading”and its physical meaning indicates that the channel envi-ronments are tending to light multipath eﬀect, that is, lessdelay path number and short rms delay spread interval. Un-der this important assumption, the CFR’s at block index
k
b
,that is at pilot index
k
p
= 2
k
b
, of the
β
-th channel could beestimated due to the orthogonality property in (5) and (6).After expanding (8) by using the pilot blocks from transmit-ting antenna one, the estimation results of the 1st channelcan be performed in the following:ˆ
H
(1)
[
n, k
p
]=
X
(1)
[
n, k
p
]
2
+
X
(1)
[
n, k
p
+ 1]
2
H
(1)
[
n, k
p
] +
X
(1)
∗
[
n, k
p
]
X
(2)
[
n, k
p
]+
X
(1)
∗
[
n, k
p
+ 1]
X
(2)
[
n, k
p
+ 1]
H
(2)
[
n, k
p
] +
X
(1)
∗
[
n, k
p
]
W
[
n, k
p
] +
X
(1)
∗
[
n, k
p
+ 1]
W
[
n, k
p
+ 1]
.
(11)
Table 1: Model of
4
-path RA,
σ
rms
≃
0
.
093
µ
sPath Delay (
µ
s) Power (dB)
0 0
.
0 0
.
001 0
.
2
−
7
.
992 0
.
4
−
15
.
983 0
.
6
−
23
.
97After reformulating (11) using (5) and (6), the ﬁnal estima-tion results can be simpliﬁed expressed as follows:ˆ
H
(1)
[
n, k
p
] =
P
(1)
block
H
(1)
[
n, k
p
] +¯
W
(1)
[
n, k
p
]
,
(12)similar results of CFR’s for the 2nd channel can be obtainedthrough performing the same procedure repeatedly by usingthe pilot blocks from transmitting branch two:ˆ
H
(2)
[
n, k
p
] =
P
(2)
block
H
(2)
[
n, k
p
] +¯
W
(2)
[
n, k
p
]
,
(13)where the total transmission power of pilot blocks is unity,
P
(1)
block
=
P
(2)
block
= 1, as well as¯
W
(1)
[
n, k
p
] and¯
W
(2)
[
n, k
p
]both represent the noise and interference terms. Throughthe proposed channel estimation algorithm, the CFR’s of two uncorrelated channels on all pilot positions,ˆ
H
(1)
[
n, k
p
]andˆ
H
(2)
[
n, k
p
], could be estimated accurately and sepa-rately while high signal-to-noise ratio (SNR) conditions areachieved under frequency-ﬂat fast fading channel environ-ments.Finally, all the CFR’s on data positions,ˆ
H
(1)
e
[
n, k
] andˆ
H
(2)
e
[
n, k
], could be completely acquired through ﬁrst-orderlinear interpolation techniques. The available data symbolsthen could be reconstructed individually after performingthe procedures of STBC decoding and MLD detection.
4. COMPARATIVE SIMULATIONS
The simulation parameters for STBC-based wireless 2ISO-OFDM transmission systems are now listed in the following:A QPSK-modulated OFDM scheme with 2ISO structures of using two transmitting antennas and one receiving antennais adopted. Alamouti’s 2
×
2 STBC SD criterion is manipu-lated for achieving transmitter diversity. The total numberof subcarriers
N
s
is 1024 with
N
CP
= 128, and the durationof an OFDM symbol
T
and cyclic extension
T
CP
is 204
.
8
µ
sand 25
.
6
µ
s, respectively. The central frequency
f
c
is set tobe 1
.
9GHz, transmission data rate
R
bit
could be achieved10Mbps and bandwidth
W
of 5
.
625MHz is used. The pi-lot symbols are assigned according to comb-type pilot pat-terns as well as the orthogonal and nonzero pilot propertiesare considered. Furthermore, the total transmission poweris constrained to unity. The simulated channel models arespeciﬁed according to COST 207 4-path rural area (RA), 6-path typical urban (TU) and 6-path bad urban (BU), whoseenvironment parameters are presented in Table 1, Table 2and Table 3, respectively.In order to investigate the limitation of the proposed chan-nel estimation algorithm, BER performance is now sequen-tially observed in 4-path RA, 6-path TU and 6-path BURayleigh fading channel models. In Fig. 4, BER perfor-mance under 4-path RA with pilot-to-data ration (PDR)equal to 1
/
32, that is using 32 pilot tones for channel estima-tion of total 1024 subcarriers, is very excellent at low mobilespeed. In expectation, the performance is degraded whilethe vehicle velocity is increased. Even though the speed is

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