Int’l J. of Communications, Network and System Sciences, 2011, 4, 384-387
doi:10.4236/ijcns.2011.46045 Published Online June 2011 (http://www.SciRP.org/journal/ijcns)
PCA Application in Channel Estimation in
MIMO-OFDM System
Mona Nasseri1, Hamidreza Bakhshi2, Sara Sahebdel3, Razieh Falahian4, Maryam Ahmadi3
1Young Researchers Club, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Electrical Engineering, Shahed University, Tehran, Iran
3Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
4Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Received February 18, 20 1 1; revised March 16, 2011; accepted March 31, 2011
Abstract
Initial estimation is a considerable issue in channel estimation techniques, since all of the following proc-
esses depends on it, which in this paper its improvement is discussed. Least Square (LS) method is a com-
mon simple way to estimate a channel initially but its efficiency is not as significant as more complex ap-
proaches. It is possible to enhance channel estimation performance by using some methods such as principal
component analysis (PCA), which is not prevalent in channel estimation, and its adaptation to channel in-
formation can be challenging. PCA method improves initial estimation performance by projecting data onto
direction of eigenvectors by means of using simple algebra. In this paper, channel estimation is examined in
Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system, with
significant advantages such as an acceptable performance in frequency selective fading channel. Moreover
the proposed channel estimation method manipulates the benefits of MIMO channel by using the information,
gained by all channels to estimate the information of each receiver.
Keywords: Channel Estimation, MIMO-OFDM, PCA, Pilot Aided Technique
1. Introduction
Multiple Input Multiple Output system, uses multiple
antennas at both receiver and transmitter, to increase
channel capacity [1] and link reliability. Also OFDM
technique is appropriate for frequency selective envi-
ronments due to its channel conversion to parallel flat
fading subchannels [2] simplifying receiver structure,
additionally it leads to high spectral efficiency. The
combination of OFDM and MIMO system takes benefits
from both techniques.
Channel information is needed at receiver for signal
detection and its accuracy affects on overall system per-
formance. Different channel estimation methods have
been used to gain channel information, one is the blind
method [ 3], which u se s st a t istical information of channel.
The other one is the training based channel estimation [4],
using known training data. The latter method is chosen
as it is applicable in fast time varying channels and mo-
bile wireless systems. In this approach, pilots are inserted
among the data at the transmitter, extracted at receiver to
estimate channel and to compensate channel fading. Ap-
plying an interpolator is necessary, while pilots are sent
through some subcarriers. Interpolator has different types
[5] but for an initial chann el estimation, a linear one, can
be sufficient.
In this paper the initial data aided channel estimation
method, LS [6] is applied, as it is simple and applicable.
In the next step, PCA, a linear mapping method [7], is
used to improve channel estimation, by using the eigen-
vectors with the largest eigenvalues and its objective is to
minimize projection error. Due to the importance of
some of its properties like width and length, PCA can be
a good choice in this research to improve channel esti-
mation.
In this paper the initial channel estimation technique,
proposed in [8] is extended, but at first the method, used
in [8], is described briefly in Section 3.1, and its im-
provement by PCA method is explained in 3.2, finally
results are shown in Section 4, followed by conclusion.

M. NASSERI ET AL.
385
2. MIMO-OFDM System Description
A 2 × 2 MIMO-OFDM system is shown in Figure 1. In
the OFDM system, first binary data is mapped to sym-
bols by modulation and pilots are inserted among sub-
carriers, in equal space according to sampling theory [9],
which are used for channel estimation.
To transform data from frequency domain into time
domain, Inverse Fast Fourier Transform (IFFT) block is
employed
Elimination of Inter Symbol Interference (ISI) [10] is
done by inserting a guard interval, in front of transmitted
symbol, which is the copy of the last Mg samples of each
symbol. Then the signal passes through the frequency
selective fading channels, in 4 paths, and white gaussian
noise is added to the signal.
At receiver all of the procedures are done reversely;
guard interval is removed and signal is sent to FFT block.
But before demodulation, channel is estimated by ex-
tracting pilot tones and applied to received data to extract
output data, also in each antenna the 2 received data
stream is averaged before sending to demodulation
block.
3. Channel Estimation
3.1. Comb Type Pilot Based Initial Channel
Estimation
Two transmitter antennas send data streams, so that K
subcarriers are assigned as pilot tones in M subcarriers
which are known at receiver. They are inserted in each
symbol, in a distance of Sg
At receiver, each antenna receives two data streams, in
the other word four vectors of received data is available.
Channel estimation is performed by LS method to train
sequences, by extracting pilots at receiver which is
shown by YP and pre-known transmitted pilots as XP:
 







1
HH
PP PP
LS
H
mXmXmXmYm


(1)
In comb type pilot arrangement [5], interpolating is
necessary to extend the estimation to other subcarriers.
There are different kinds of interpolators but linear is
adequate one in this research. The channel in (kMK

m

)th subcarrier, 0mMK

, 0obtaining
linear interpolator, is expressed as: kK ,
 




ˆˆ
1
M
Hkm Hpk
K
H
pkH pk
mMK


 




(2)
Channel estimation is app lied in adjacent pilot subcar-
riers to evaluate channel in subcarriers between them. As
the system is 2 × 2, 4 channel estimation vectors will be
gained.
3.2. Improved Channel Estimation, Applying
PCA Method
PCA is a non-parametric method to re-express data, us-
ing basis vectors, applying simple linear algebra. PCA
provides a way to reduce complex data to a lower di-
mension. Selecting Orthogonal directions for principal
components are solutions to predict original data.
M
MM, emerged of
sampling theory. While, MS denotes the distance be-
tween subcarriers. The received signal can be expressed
as Y = XH + W, where X and W show transmitted signal
and additive white gaussian noise respectively. Complex
channel response, including L coefficients, is shown by
H = [h1, , hL]. 
PCA is widely applied in pattern recognition, image
processing, moreover it is a proper classifier, but it isn’t
common in channel estimation. Here, the proposed ap-
proach of using this method in channel estimation is de-
scribed. Generally PCA can be summarized in 3 steps.
Figure 1. Schematic of MIMO-OFDM system.

M. NASSERI ET AL.
386


First Step: Data is arranged in a M × N matrix.
This paper is aiming to improve the estimated data
which is channel info rmation. The mentioned matrix can
be built by them. Therefore a M × 4 matrix is made of 4,
M × 1 channel vector and each column of the channel
matrix is considered as a dimension:
12
ˆˆˆ ˆ
,,..., M hhhh

 (3)
Second Step: Normalizing data by subtracting the
mean of data.
At first the mean is calculated and normalization is
implemented by following equations:
1
1
ˆˆ
M
i
i
h
M
hh






(4)
After the subtracting mean which is the average across
each dimension, the data set will have the mean of zero.
Third Step: The most important step is calculating the
Singular Value Decomposition (SVD) or eigenvectors of
the covariance, which shows the distribution of data.
Covariance matrix is obtained by (5):
ˆˆ
H
Chh (5)
Since the data is 4 dimensional, a 4  4 covariance
matrix is calculated. By determining eigenvalues and
eigenvectors of square covariance matrix, useful infor-
mation about data is gained.
SVD is a way to analyze data and demonstrates co-
variance, using eigenvectors [e1, e2, , eN] and scalar
eigenvalues [λ1, λ2, , λN]. Also the vectors of [he1, he2,
, heN], form an orthogon al basis, so that the vector hek
has the length of



k

.
1
1ˆˆ
NH
ii
i
Ce e
hh ee
N








 (6)
Leads to:

2
1
1ˆ
NH
i
i
eh
N


 (7)
Finally the channel estimation transforming by a pro-
jection operation is expressed by (8):

ˆˆ
p
hh e

 (8)
The eigenvectors with the highest eigenvalues is the
principle component of data set. Therefore the eigenvec-
tors are ordered by eigenvalues, highest to lowest, which
highest vector will be us ed for channel projection. Addi-
tionally the eigenvector with lower standard deviation is
more appropriate for channel projection.
4. Results
Parameters of MIMO-OFDM system, used in simulation,
are summarized in the Table 1 [8]. A 2 × 2 system, in-
cluding 2 transmitter antennas and 2 receiver antennas is
simulated in MATLAB software. Guard interval is cho-
sen greater than delay spread to eliminate ISI. There are
4 multipath fading channels using jakes spectrum type.
Specific channel parameters such as delay spread, Dop-
pler frequency, and tap power, are extracted from Stan-
ford University Interim channel model [11], which were
measured for fixed broadband wireless applications.
Transferred pilots, inserted among data based on comb
type, are used to estimate channel. As previously de-
scribed in section 3, pilots are extracted and channel is
estimated, using LS, then linear interpolation is applied
to indicate channe l in all subcarriers. Finally PCA is used
to project data onto direction of eigenvectors, which
minimizes the projection error and keeps some properties
such as width and length, as they are significantly im-
portant in channel estimation. The channel estimation
improvement, using PCA is shown in Figure 2, in Bit
Error Rate (BER) performance and Figure 3 in Mean
square Error (MSE), compared with ideal channel, while
fading effects were ignored, but the impact of white
noise was considered. These figures show the channel
Table 1. channel parameter, used in simulation [8].
parameter specifications
Number of transmitter 2
Number of receiver 2
FFT size 1024
Guard interval 256
Pilot Interval 5
Bandwidth 1.75 MHz
Data modulation QPSK
Pilots modulation BPSK
Channel type Rayleighy fading, SUI model
Figure 2. BER performance of channel estimation compar-
ing with ideal channel.

M. NASSERI ET AL.
387
Figure 3. MSE performance of channel estimation compar-
ing with ideal channel.
estimation improvement, so that the system works in
lower Signal to Noise Ratio (SNR) by using advantages
of PCA method. Therefore it is unnecessary to use com-
plex algorithms to enhance estimation quality. Addition-
ally, the benefits of MIMO systems are manipulated by-
contributing all channels in estimation.
5. Conclusions
Acquiring accurate information at receiver depends on
channel estimation quality. Therefore in this paper,
channel estimation improvement was considered in a 2 ×
2 MIMO-OFDM system. This kind of system gets ad-
vantages of both MIMO and OFDM techniques. It has
high channel capacity and also ISI and Inter-Channel
Interference (ICI) are removed due to converting fre-
quency selective fading channel to flat fading subchan-
nels. In channel estimation section, channel was esti-
mated initially by LS method, using training sequences
which were sent in some subcarriers with equal distances
emerge of sampling theory. After evaluating channel in
pilot subcarriers, linear interpolator was used to estimate
channel in all subcarriers. In the final step, to improve
channel estimation, PCA method was chosen to project
data onto directions of eigenvalues and reduced complex
data to lower dimension. Simulation results show im-
provement of channel estimation in BER and MSE per-
formance.
6. References
[1] E. Telatar, “Capacity of Multi-Antenna Gaussian Chan-
nels,” European Transactions on Telecommunication,
Vol. 10, No. 6, 1999, pp. 585-595.
doi:10.1002/ett.4460100604
[2] J. G. Proakis, “Digital Communications,” 4th Edition,
McGraw-Hill, New York, 2001, pp. 709-800.
[3] S. Roy and C. Y. Li, “A Subspace Blind Channel Estima-
tion Method for OFDM Systems without Cyclic Prefix,”
IEEE Transactions on Wireless Communications, Vol. 1,
No. 4, 2002, pp. 572-579.
doi:10.1109/TWC.2002.804160
[4] Y. Li, “Simplified Channel Estimation for OFDM Sys-
tems with Multiple Transmit Antennas,” IEEE Transac-
tions on Wireless Communications, Vol. 1, No. 1, 2002,
pp. 67-75. doi:10.1109/7693.975446
[5] M.-H. Hsieh and C.-H. Wei, “Channel Estimation for
OFDM Systems Based on Comb-Type Pilot Arrangement
in Frequency Selective Fading Channels,” IEEE Transac-
tions on Consumer Electronics, Vol. 44, No. 1, 1998, pp.
217-225. doi:10.1109/30.663750
[6] H. Minn and N. Al-Dhahir, “Optimal Training Signals for
MIMO OFDM Channel Estimation,” IEEE Transactions
on Wireless Communications, Vol. 5, No. 5, 2006, pp.
1158-1168. doi:10.1109/TWC.2006.1633369
[7] S. Haykin, “Neural Networks,” Prentice-Hall, Upper
Saddle River, 1994, pp. 363-370.
[8] M. Nasseri and H. Bakhshi, “Iterative Channel Estima-
tion Algorithm in Multiple Input Multiple Output Or-
thogonal Frequency Division Multiplexing Systems,”
Journal of Computer Science, Vol. 6, No. 2, 2010, pp.
224-228. doi:10.3844/jcssp.2010.224.228
[9] A. Oppenheim a nd R. Sc hafer, “Discre te Time Signal,” 2nd
Edition, Prentice-Hall, Upper Saddle River, 1999, p. 146.
[10] R. V. Nee and R. Prasad, “OFDM for Wireless Multime-
dia Communications,” Artech House, London, 2000, pp.
33-50.
[11] V. Erceg, K. V. S. Hari, M. S. Smith and D. S. Baum,
“Channel Models for Fixed Wireless Applications,” IEEE
802.16.3 Task Group Contributions, 2001.