International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 - Sep 2014
Channel Estimation in MIMO-OFDM Systems
P. Venkateswarlu#1, R. Nagendra#2
#
Dept. of Electronics and Communication Engineering, Sree Vidyanikethan Engineering College
Tirupati, India - 517102.
Abstract— In this work various channel estimation algorithms
of the Orthogonal Frequency Division Multiplexing (OFDM) and
Multiple Input Multiple Output-Orthogonal Frequency Division
Multiplexing (MIMO-OFDM) are studied. The result of Linear
Minimum Mean Square Error (LMMSE) channel estimation
algorithm was compared with the Least Squares (LS) and
Minimum Mean Square Error (MMSE) for both OFDM and
MIMO-OFDM systems.
Index Terms — OFDM, MIMO-OFDM, LS, MMSE,
LMMSE, Channel estimation.
I INTRODUCTION
There is an increasing demand for the high data rates with
effective utilization of available limited spectrum. To fulfil
these requirements Multiple Input Multiple OutputOrthogonal Frequency Division Multiplexing (MIMO-OFDM)
techniques have been adopted.
MIMO technology is one of the major attracting techniques
in wireless communications, because it offers significant
increases in data throughput and coverage without additional
bandwidth or transmitter power. It also provides high spectral
efficiency and link reliability. Because of these properties,
MIMO is an important part of modern wireless
communication standards such as IEEE 802.11n (Wi-Fi), 4G,
3GPPLTE, WiMAX and HSPA+.
In Mobile communication systems prior to transmit the
information certain characteristics of the radio waves are
changed in accordance with the information bits. At the
receiving end the information bits are retrieved accurately, if
the channel characteristics are known. The channel may vary
instantaneously because of the propagating medium, which
leads to the signal degradation. The Channel State information
(CSI) provides the known channel properties for a wireless
link. It provides the effects of fading and scattering on a signal
propagating through the medium. Normally the CSI estimated
at the receiver fed back to the transmitter. If it is not estimated
accurately at the receiver, leads to system degradation. It can
be estimated by using different channel estimation algorithms.
This estimation can be done with a set of well known
sequence of unique bits for a particular transmitter and the
same can be repeated in every transmission burst. Thus the
channel estimator estimates the channel impulse response for
each burst separately from the well known transmitted bits
and corresponding received samples. This paper describes the
fundamentals of MIMO-OFDM system and study of various
channel estimation techniques and their performance.
The channel can be estimated by using several estimation
algorithms as described in [7]. The various types of pilot
arrangements for the channel estimation are shown in figure
ISSN: 2231-5381
1(a) and 1(b) respectively. The pilot based or training based
channel estimation algorithms are adopted here. The training
based channel estimation can be carried out by either block
type pilots or comb type pilots along with the data symbols. In
block type pilot estimation, one specific symbol full of pilot
subcarriers is transmitted periodically as in Fig 1(a). This
estimation is suitable for slow fading channels. But, in comb
type pilot estimation pilot tones are inserted into each OFDM
symbol with a specific period of frequency bins as shown in
Fig. 1(b). This type of channel estimation is very much
suitable where the changes even in one OFDM block. The
comb type pilot arrangement is used in this work for channel
estimation.
Figure 1(a). Comb Type Pilot
Figure 1(b). Block Type Pilot
This paper organized as follows. Section II provides the
MIMO-OFDM system description; the next section provides
various pilot based channel estimation algorithms for MIMOOFDM systems. The next section presents the results and
discussion on the obtained performance. Finally, the
conclusion is specified in section V.
SYSTEM DESCRIPTION
In MIMO systems multiple antennas are used at both ends
of the transmitter and receiver. Usage of MIMO-OFDM
systems in modern wireless communication systems provides
II
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 - Sep 2014
increased system capacity and coverage with robustness
against multipath fading. Because of the unique properties of
the MIMO and OFDM systems, these systems are used in
high-speed wireless communication systems.
A simple MIMO-OFDM system with NTx transmit
antennas and NRx receive antennas is shown in Figure 2.
B. Minimum Mean Square Error Estimator (MMSE)
The MMSE estimate of the channel can be obtained by
using the following equation


H Mmse
 Fh Mmse
 FR hy R yy1 Y
(5)
Where
 
 EYY   XFR
R hy  E hY H  R hh F H X H
R hy
H
hh
F H X H   n2 I N

H Mmse
 Fh Mmse
 FR hh F H X H ( XFR hh F H X H   n2 I N ) 1 Y
(6)
Where Rhh is the channel auto- correlation matrix given by
Rhh =E[hhH] and
 n2 is noise variance, F=[ WKnk ] is the DFT
1
nk
matrix with WK 
Figure 2. MIMO-OFDM system model
e
 j2 
kn
N
K
C. Linear Minimum Mean Square Error Estimator (LMMSE)
A simple MIMO system can be modelled as
The LMMSE channel estimator minimize the mean square
error between the actual and estimated channels, obtained by
applying the Wiener–Hof equation as follows
y=H x + n
(1)
Where x and y are the transmit vector and receive vectors, H

and n are the channel matrix and the noise vectors respectively.
hLmmse
 R hy R yy1 Y
It is assumed that the signal is transmitted over a multi path The cross correlation matrix is given by
Rayleigh fading channel characterized by
H
H

R hy  E hY
L1
h     i     i 
(2)
i 0
Where  i are the time delays of the different paths and L is
the number of multipaths.
At the receiver, the synchronization is perfect so that
transmitted data can be extracted. So that we make an
assumption that the cyclic prefix is longer than the channel
maximum excess delay.
III
CHANNEL ESTIMATION ALGORITHMS
A. Least Squares Channel Estimator (LSE)

H Ls  arg{min{ Y  XH Ls }H{ Y  XH Ls
} (3)

Where, H Ls is the Least Squares (LS) Estimate of the
channel.
Therefore it can be written as
H Ls 
Y
N
 H
X
X
(4)
This method is simplest among the channel estimation
algorithms. But, it is prone to noise since it doesn’t consider
any statistical parameters. Hence the performance is poor
when compared with the other estimation methods.
ISSN: 2231-5381
 R
hh
(7)
X
(8)
The auto correlation matrix is given by


R yy  E YY H  XR hh X H   n2 I N
(9)
The LMMSE estimator can be rewritten as follows by using
the above relations



h Lmmse
 R hh R hh   n2 XX H
h
 1 1

ls
(10)
Various channel estimation and optimization techniques
have been proposed in [1]-[4].
W Hardjawana, R Li, B Vucetic and Y Li In [1] a novel
pilot- aided iterative receiver with joint ICI cancellation and
decoding, based on pilot symbols and iterative soft-estimate of
data symbols is proposed. This algorithm uses time-domain
interpolation and least-square (LS) methods for estimating the
channel. Soft-estimate for data symbols are obtained by a
maximum-a-posterior (MAP) decoder and improved
subsequently
N Aboutorab,W Hardjawana,B Vucetic In [2] proposed an
Iterative channel estimation and inter carrier interference
(ICI) cancellation method for highly mobile users in longterm evolution (LTE) systems. This a l g o r i t h m estimates
the wireless channel by using pilot symbols, estimates of the
data symbols, and Doppler spread information at the receiver.
The channel estimates are obtained by employing a leastsquare (LS) method and a simplified parallel interference
cancellation (PIC) scheme coupled with decision statistical
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 - Sep 2014
combining (DSC) is used to cancel the ICI and to improve
data symbol detection.
In [3] MM Rana and MK Hosain proposed a normalized
least mean (NLMS) square and recursive least squares (RLS)
adaptive channel estimator for multiple input multiple output
(MIMO) orthogonal frequency division multiplexing (OFDM)
systems. These channel estimation (CE) methods uses adaptive
estimator which are able to update parameters of the estimator
continuously, so that the knowledge of channel and noise
statistics are not necessary. This NLMS/RLS CE algorithm
requires knowledge of the received signal only. The RLS CE
algorithm provides faster convergence rate and good
performance compared to NLMS CE method.
In [4] Channel estimation algorithms and their
implementations for mobile receivers are considered. The
3GPP long term evolution (LTE) based pilot structure is
used as a benchmark in a multiple-input multiple- output
(MIMO) orthogonal frequency division multiplexing (OFDM)
receiver. The decision directed (DD) space- alternating
generalized expectation-maximization (SAGE) algorithm is
used to improve the performance from that of the pilot symbol
based least-squares (LS) channel estimator. The performance is
improved with high user velocities, where the pilot symbol
density is not sufficient. Minimum mean square error
(MMSE) filtering is also used in estimating the channel in
between pilot symbols. The pilot overhead can be reduced to
a third of the LTE pilot overhead with DD channel
estimation, obtaining a ten percent increase in data throughput.
In order to reduce complexity and take advantage of “null”
sub-carriers, MMSE based iterative channel estimation
algorithm is proposed in [4]. A compensation process is
proposed to simplify the traditional iterative MMSE channel
estimator. After this iterative compensated MMSE channel
estimation in frequency domain, a simple “linear interpolation”
in time domain is performed to obtain channel estimates over
all OFDM symbols. Simulation results show that the ICMMSE channel estimation algorithm has good performances
which approach the performance with perfect channel state
information in both SIMO and MIMO transmission modes.
In [6], an improved DCT based channel estimation with
very low complexity is proposed and evaluated in
IEEE802.11n and 3GPP/LTE MIMO-OFDM systems. The
whole DCT window is divided into R small overlapping
blocks where the length of these blocks is a power of 2. The
performance is improved because the noise component is
averaged on a larger number of subcarriers.
Figure 3(a). BER Vs SNR curve for SIMO-OFDM
Figure 3(b). MSE Vs SNR curve for SIMO-OFDM
The MIMO-OFDM system performance is evaluated using
the BER and MSE curves for the various SNR values is
shown in the figures 4(a) and 4(b) respectively. The
performance analyses of the various algorithms for MIMOOFDM were shown in the following diagrams. From this it is
observed that the proposed method is having better
performance when SNR increases.
IV RESULTS AND DISCUSSION
The BER and MSE curves obtained are shown in the
following figures. The performance of the SIMO-OFDM is
evaluated using the BER and MSE plots for the various SNR
values is shown in the figures 3(a) and 3(b) respectively
Figure 4(a). BER Vs SNR curve for MIMO-OFDM
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 - Sep 2014
[6]
[7]
[8]
M Diallo, R Rabineau, L Cariou, and M Hélard. "On Improved DCT
Based Channel Estimation with Very Low Complexity for MIMOOFDM Systems," In VTC spring. 2009.
P. Venkateswarlu, R.Nagendra, “Channel Estimation Techniques in
MIMO-OFDM LTE Systems,” Int. Journal of Engineering Research
and Applications, Vol. 4, Issue 7( Version 1), July 2014, pp.
Vineetha Mathai, K. Martin Sagayam "Comparison And Analysis Of
Channel Estimation Algorithms In OFDM Systems," International
Journal of Scientific & Technology Research, Volume 2, Issue 3,
March 2013,pp 76-80.
Figure 4(b). MSE Vs SNR curve for MIMO-OFDM
From the above performance curves the following
conclusions are derived. The MSE values are almost same for
the LS and MMSE for both SIMO-OFDM and MIMO-OFDM
cases. The proposed method outperforms when compared to
the LS and MMSE estimation algorithms. Similarly, from the
BER curves it is find that the proposed algorithm performance
is superior to the other two techniques.
V
CONCLUSION
The performance of the SIMO-OFDM and MIMO-OFDM
systems performance is evaluated in terms of the BER and
MSE for various SNR values. From this the proposed method
has good performance when compared to the LS and MMSE
techniques in both the cases.
VI FUTURE SCOPE
The proposed method involves complex computations such
as finding the inverse of the matrix in every iteration. These
computations can be avoided by using the methods describes
in [8] for the OFDM systems.
REFERENCES
[1]
[2]
[3]
[4]
[5]
W Hardjawana, R Li, B Vucetic and Y Li, "A New Iterative Channel
Estimation for High Mobility MIMO-OFDM Systems," IEEE Trans.
Vehicular Technology Conference, pp. 1-5, 2010.
N Aboutorab,W Hardjawana,B Vucetic, "A New Iterative DopplerAssisted Channel Estimation Joint With Parallel ICI Cancellation for
High-Mobility MIMO-OFDM Systems," IEEE Transactions on
Vehicular Technology, vol. 61, pp. 1577 - 1589, 2012.
MM Rana, MK Hosain, "Adaptive Channel Estimation Techniques for
MIMO-OFDM Systems," International Journal of Advanced Computer
Science and Applications, Vol. 1, No.6, pp. 134-138, 2010.
J Ketonen, M Juntti, J Ylioinas and J R. Cavallaro, “Decision-Directed
Channel Estimation Implementation for Spectral Efficiency
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