This document summarizes two channel estimation methods for MIMO-OFDM systems: blind channel estimation and QRD-M/Kalman filter based detection. Blind channel estimation works by identifying the channel based on knowledge of the channel and data symbols using noise subspace approach and linear precoding. It has fast convergence, requires few OFDM symbols, and can be used with any number of transmit/receive antennas. QRD-M/Kalman filter based detection uses an adaptive complexity QRD-M algorithm and Kalman filters to track individual channels with lower complexity and good tracking ability. It decomposes the received signal into an upper triangular matrix and uses maximum likelihood detection on individual subcarriers. Both methods are analyzed and their advantages/dis

1. Channel Estimation Methods For MIMO-OFDM Systems
Suleiman Adams [asa69@njit.edu]
New Jersey Institute of Technology
Prof. Alexander Haimovich
1 INTRODUCTION
The future wireless communication systems are
envisioned to be equipped with multiple
antennas because multiple input multiple output
(MIMO) technology can provide significant
increase in channel capacity and link reliability.
To obtain that advantage, channel knowledge is
required at the receiver side but accurate channel
estimation in MIMO systems is difficult.
Conventional pilot aided channel estimation
schemes send orthogonal pilot sequences on
different transmit antennas which wastes the
system resources when number of transmit
antennas is large. Therefore choice of most
efficient channel estimation method is important
for coherent detection and decoding. [1]
Channel estimates for Multiple Input Multiple
Output-Orthogonal Frequency Division
Multiplexing (MIMO-OFDM) systems can be
obtained by transmitting a training sequence
from one antenna at a time while the remaining
transmit antennas are idle. This method,
however, becomes inefficient when the number
of transmit antennas are large.
1.1 Problem being addressed
There are two main problems in designing
channel estimators for wireless MIMO OFDM
systems. The first problem is the arrangement of
pilot information, where pilot means the
reference signal used by both transmitters and
receivers. The second problem is the design of
an estimator with both low complexity and good
channel tracking ability. [2]
Also Intersymbol symbol interference(ISI)
caused due to “N” number of subcarriers
carrying the data over parallel paths modifies the
signal observed at the receiver resulting in
inaccurate channel estimation.
1.2 Methods proposed to overcome above
problem
Two important methods are put forward to
overcome the above stated problems -
a) Blind Channel Estimation method for
channel estimation.
b) QRD-M/ Kalman filter based detection
for channel estimation.
Generally channel estimation methods are used
with either Cyclic Prefix (CP) or Virtual Carriers
(VC). Virtual Carriers are subcarriers which are
set to zero without any information on it. Both
above stated methods are analyzed and
compared to explain which of them provides
more accurate results for channel estimation and
how it can be improved by using no or
insufficient cyclic prefixes.
Figure 1 Basic Channel Estimation method

2. 1
2 BLIND CHANNEL ESTIMATION
2.1 Concept of the estimation method
Blind channel estimation algorithm works on the
principle of identifying the channel based on the
knowledge of channel and data symbols. It uses
“noise subspace approach” & “linear precoding”
because of its simple architecture and good
performance. It develops a condition and
estimation method to be used for any number of
transmitter and receiver antennas to improve the
channel utilization and speed of convergence.
The method works with or without presence of
any Virtual Carriers (VC’s). It can use
minimum of 1 OFDM symbol for filtering
matrix used at transmitter. [1]
2.2 Assumptions for this method
Following are the assumptions being made when
using this method for channel estimation :
a) System consists of multiple transmitter
and receiver antennas
b) Spatial Multiplexing is utilized at
Transmitter
c) Signal is transmitted through continuous
channel
2.3 Signal Model -
The system used has “Mt” number of transmit
antennas and Mr number of receiving antennas.
It is considered that there are “N” numbers of
subcarriers being numbered from “Ko to
(Ko+D-1)” for information data to be
transmitted. [3] To use this system without the
virtual carriers, it is assumed that Ko=0 and
hence total number of subcarriers becomes (N-1)
and total number of virtual carriers becomes 0.
Therefore it is easy to use this method with or
without the presence of VC’s.
Figure 2 System Model for Blind Channel Estimation
2.4 Procedure for channel estimation
Information data to be sent over channel on nth
block of transmitting antenna which is one out
of Mt transmit antennas can be illustrated as
below –
Figure 3 Information Data to be sent over channel at Tx
This information data ready to be sent at the
transmitting antenna is represented as a time
domain sample vector and to make it continuous
time signal so that it can be sent over channel,
pulse shaping by VC is needed through transmit
filter. [1] After generating this pulse shaped
output we sample the information data

3. 2
embedded on an OFDM block and further
transmit each samples one by one through the
channel. This procedure can be represented by
following diagram –
Figure 4 Sampled information transmitted through channel
The received signal is modified by the channel
impulse response along with addition of existing
additive white Gaussian noise. The channel
impulse responses are of finite duration and
current signal is not interfered by previous
signal.
The noise subspace channel estimation can be
used when number of Tx antennas are greater
than number of Rx antennas and vice-versa. At
the receiver after collecting “J” consecutive
OFDM symbols IFFT operation is performed
along with OFDM modulation. [3] The
generated symbol is sampled at each Rx antenna
with rate as (1/T) where T is duration of
complete information symbol. The system for
which channel estimation is to be performed
should satisfy following criteria in order to use
Noise subspace method are-
a) Transfer function of channel impulse
response matrix generated for the
channel should have full column rank
b) Pulse shaping being used should be
“Nyquist Pulse shaping”
c) Upper bound for MIMO channel should
be present rather than its knowledge
d) Additive noise should be uncorrelated
with the Tx signal and autocorrelation
matrix which is generated by Eigen
Value decomposition of the received
signal.
However when the length of CP is greater than
delay spread then length of CP is considered as
upper bound for MIMO channel. Also when
sampling rate is greater than Nyquist rate then
the additive white Gaussian noise might not be
uncorrelated. In such case we need to design a
front end receiver filter with wide bandwidth
which whitens the oversampled noise.
Author has emphasized that when Lemma 1(if
Mt<Mr; j <=2 & transfer function generated for
channel impulse response matrix has full column
rank) is satisfied by MIMO-OFDM channel then
there is no constraint of number of CP’s and
hence the MIMO channel can be estimated with
or without CP too which increases the overall
bandwidth efficiency. Normalized mean square
root (NRMSE) has been used to measure the
performance of the MIMO-OFDM system
considering 2 Tx and 2 Rx antennas, number of
subcarriers N=64. By performing the channel
estimation with 500 trials it is shown that
estimated NRMSE decreases by increasing the
Signal to Noise ratio and OFDM symbol record
length. This also shows that CP is most useful
for noise subspace method than VC’s. As the
subspace dimension increases by increasing the
number of CP’s, the computational complexity
of the estimation method increases but improves
the performance of subspace method. [3]

4. 3
2.5 Advantages
Advantages of this method can be listed -
a) It has fast convergence property for
small data record, hence this method is
most useful for increasing the bandwidth
efficiency with MIMO-OFDM systems
without CP’s.
b) Generates accurate channel estimation
by using less number of OFDM
symbols(J).
c) It does not have any limitation on
number of transmitters and receivers
that MIMO-OFDM system can have.
d) All the resources occupied by pilot
sequences can be released.
2.6 Disadvantages
There are following disadvantages with this
method –
a) On increasing the number of CP’s
increases the complexity of the system
to great extent.
b) This method has “Ambiguity problem”
in which channel and data cannot be
uniquely identified without transmitting
additional pilots.
3 QRD-M/ KALAMAN FILTER BASED
DETECTION
3.1 Concept of detection method
QR decomposition-M/Kalman filter based
channel estimation technique uses “Adaptive
Complexity QRD-M” algorithm and Kalman
filters for tracking indivisual channels. [1] The
QRD-M alogorithm is based on joint detection
& channel estimation for DS-CDMA. The rule
used for choosing M for each subcarrier is
obtained using Kernel Density estimation along
with Lloyd-Max algorithm. In this method
detection is done on individual OFDM
subcarriers which reduces the complexity by tree
search approximate maximum likelihood
detector. Serial stream of information is
converted into parallel and sent over “K”
subcarriers N number of transmit antennas.
QRD-M algorithm works as following – The
signal from all the transmit antennas are passed
through FFT filters and after QR decomposition
data detection is done on each “K” OFDM
subcarriers.
3.2 Assumptions for this method
Following assumptions for the system and
channel are made in order to use this method –
a) MIMO-OFDM system should be
spatially uncoded system.
b) Number of receiving antennas are
greater than number of transmit
antennas (mandatory condition for
decomposition to form upper triangular
matrix and implementing M-algo).
c) All subcarriers and antennas should
have same signal constellation.
d) Coarse OFDM symbol synchronization
should be achieved and set of
information symbols should be IID(
independent & identically distributed).
3.3 Signal Model
A low pass signal model for received MIMO-
OFDM is used. Channel used is considered to be
quasi-static multipath fading channel and is time
varying. The number of receiving antennas are
considered greater then number of transmit
antennas and channels are formed by FIR filters
followed by Kalman filter. [4] Using Kalman
Filters leads to a faster convergence in terms of
iterations compared to other methods, though the
cost of each iteration is higher. The signal
model can be represented as below –

5. 4
Figure 5: Signal Model for QRD-M/Kalman filter based detection.
Transmitter and receiver filters are modeled as
ideal low pass with pass band as [0, 1/Ts] where
Ts is symbol time. Transmitted pulse is
considered as ideal rectangular as bandwidth is
smaller than 1/Ts Hz.
3.4 Procedure for channel estimation
The QRD-M algorithm uses channel estimate
calculated in previous step and Adaptive QRD-
M is used where weaker subcarriers are assigned
larger values of M during tree search. The KDE
(empirical density) is computed of subcarrier
estimated powers and is optimized in M regions
using the Lloyd-Max algo where M is set as
maximum number of paths to search in tree. The
look up table hence formed is used to assign
appropriate values of M based on subsequent
power estimates. QRD-M is used to estimate
channel matrix. [2] A “K”-point IFFT is
calculated using QPSK/QAM data symbols and
the IFFT sequence formed is then transmitted by
one out of many transmit antennas. After
receiving one step channel prediction, received
signal power of particular data symbol is
calculated. The channel estimates are then
rearranged using order stastics of estimated
powers. In this system the timing error is
generated by receiving antenna. Also the
additive white noise which is added after
transmitting signal through channel is circular
white Gaussian noise. At the receiver, received
signal is sampled and Max likelihood detection
is performed using channel one-step predictions
which are obtained from Kalman filter. The
estimated channel matrix is rearranged to
calculate data being transmitted. The Maximum
Likelihood detector can be represented by tree
search and it has levels equal to number of
transmit antennas. [4]
3.5 Advantages
Using QRD-M/ Kalman filter based detection
algorithm for MIMO-OFDM systems has
following advantages over other methods –
a) The method is robust to large Doppler
spreads to improve overall performance
of the system.
b) This method should be preferred as the
QRD-M algorithm with M=1 works as
an interference canceler and permits
closed form Bit error rate computation
for QPSK and has better performance.
c) Due to frequency selective fading,
subcarriers in MIMO-OFDM system
have higher values of Signal to Noise
ratios and since a separate QRD- M
algorithm is run independently on each
subcarrier therefore this method is most
useful for channel estimation with
subcarriers having low values of signal
to noise ratios.
3.6 Disadvantages
The complexity of the whole system grows with
increasing the number of transmit antennas. To
overcome this suboptimal M algorithm can also
be used.

6. 5
4 MATLAB SIMULATION RESULTS
FOR BLIND CHANNEL ESTIMATION
A MATLAB code simulation [2] is shown
below that generates a MIMO communication
with noise space time encoding and channel is
estimated by subspace approach using the
knowledge of the Space time codes. The code
extracts the space time block coding
information, generates a symbol sequence
randomly where symbols belong to set of
integers, modulate the symbols, performs space
time coding, creates a random channel matrix,
applies AWGN and performs channel
estimation.
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Quadrature
In-Phase
Extracted signal nb 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Quadrature
In-Phase
Extracted signal nb 2
Figure 6 Signals Extracted at receiver 1, 2 and 3
5 CONCLUSION
After analyzing and comparing both above
approaches in my opinion Blind Channel
Estimation is best suitable for MIMO-OFDM
systems as it overcomes the intersymbol
interference issue faced during channel
estimation, can be used with systems having any
number of transmitters and receivers. It
increases the bandwidth efficiency as it can be
used with or withut CP’s which further saves on
resources and provides accurate results.
6 BIBLIOGRAPHY
[1] J. Zhao, Analysis and Design of
Communication Techniques in Spectrally
Efficient wireless relaying systems, Berlin:
Logos Verlag Berlin GmbH, 2010.
[2] N. Ammar and Z. Ding, "Blind Channel
Identifiability for Generic linear space time
block codes," IEEE Transactions on Signal
Processing, vol. 55, no. 1, pp. 202-217,
2007.
[3] J. Y. A. I. J. D. G. Kyeong Jin Kim, "A
QRD-M/Kalman Filter-Based Detection &
channel estimation algorithm for MIMO-
OFDM systems," EEE TRANSACTIONS ON
WIRELESS COMMUNICATIONS, vol. 4, no.
2, 2005.
[4] R. W. H. E. J. P. Changyong Shin, "Blind
Channel Estimation for MIMO-OFDM
systems," IEEE TRANSACTIONS ON
VEHICULAR TECHNOLOGY, vol. 56, no.
2, 2007.
[5] Y. S. a. E. Martinez, "Channel Estimation in
OFDM Systems," Freescale Semiconductor,
vol. AN3059, no. Rev 0, 2006.

7. 6
7 APPENDIX
N=512; %Number of symbols to be
transmitted
code_name='OSTBC3'; %Space time code
(see file space_time_coding to obtain the list of
supported STBC)
rate='3/4'; %Space time code (see file
space_time_coding to obtain the list of
supported STBC)
num_code=1; %Space time code (see file
space_time_coding to obtain the list of
supported STBC)
modulation='PSK'; %supported modulation
PSK, QAM,
state_nb=4; %modulation with 4 states
(4-PSK -> QPSK)
nb_receivers=4; %Number of 4 receivers
snr=20; %Signal to noise ratio (dB)
close all;
code_rate=str2num(rate);
[nb_emitters,code_length]=size(space_time_cod
ing(0,code_name,rate,num_code,1));
Nb_symbole_code=code_length*str2num(rate);
%% Generate a symbol sequence randomly and
modulates the symbols
fprintf('- Generate %d random symbols: ',N);
symbols=randint(1,code_rate*N,state_nb);
fprintf('tttOKn');
fprintf('- Apply %d-%s constellation:
',state_nb,modulation);
switch modulation
case 'PSK'
modulator=modem.pskmod(state_nb);
case 'QAM'
modulator=modem.qammod(state_nb);
end
modulated_symbols=modulate(modulator,symb
ols);
fprintf('tttOKn');
%% perform space time encoding and creates a
random channel matrix
fprintf('- Perform %s-%s STBC
encoding:',rate,code_name);
[STBC_blocs]=space_time_coding(modulated_s
ymbols,code_name,rate,num_code);
fprintf('ttOKn');
fprintf('- Generate a %d * %d Random Channel:
',nb_receivers,nb_emitters);
channel_matrix=sqrt(0.5)*(randn(nb_receivers,n
b_emitters)+i*randn(nb_receivers,nb_emitters));
received_signal=channel_matrix*STBC_blocs;
fprintf('ttOKn');
%% Apply AWGN noise and performs channel
estimation
fprintf('- Apply %d dB additive noise: ',snr);
noise_variance=1/(10^(snr/10));
bruit=(sqrt(noise_variance/2))*(randn(nb_receiv
ers,size(STBC_blocs,2))+...
i*randn(nb_receivers,size(STBC_blocs,2)));
received_signal=received_signal+bruit;
fprintf('tttOK (noise
variance=%f)n',noise_variance);
fprintf('- Perform Subspace Channel Estimation:
');
estimated_channel_matrix=subspace_channel_e
stimation_STBC(received_signal,code_name,rat
e,num_code);
fprintf('tOKn');
fprintf('- Compute pinv(H_est)*H:n');
pinv_H_est_H=pinv(estimated_channel_matrix)
*channel_matrix %close to a diagonal matrix
for correct estimation
fprintf