Int. J. Communications, Network and System Sciences, 2011, 4, 578-584
doi:10.4236/ijcns.2011.49069 Published Online September 2011 (http://www.SciRP.org/journal/ijcns)
Novel Semi-Blind Channel Estimation Schemes for
Rayleigh Flat Fading MIMO Channels
Jaymin Bhalani1, Dharmendra Chauhan1, Y. P. Kosta2, A. I. Trivedi3
1Department of Electronics Engineering, Charotar University of Science and
Technology, Changa, India
2Marvadi Education Institute, Rajkot, India
3Department of Electrical Engineering, Faculty of Technology, M.S.University, Baroda, India
Received July 17, 2011; revised August 22, 2011; accepted September 1, 2011
Abstract
In this paper, we propose two novel semi-blind channel estimation techniques based on QR decomposition
for Rayleigh flat fading Multiple Input Multiple output (MIMO) channel using various pilot symbols. In the
first technique, the flat-fading MIMO channel matrix H can be decomposed as an upper triangular matrix R
and a unitary rotation matrix Q as H = RQ. The matrix R is estimated blindly from only received data by us-
ing orthogonal matrix triangularization based house holder QR decomposition, while the optimum rotation
matrix Q is estimated exclusively from pilot based Orthogonal Pilot Maximum Likelihood Estimator (OPML)
algorithm. In the second technique, joint semi-blind channel and data estimation is performed using QR de-
composition based Least Square (LS) algorithm. Simulations have taken under 4-PSK data modulation
scheme for two transmitters and six receiver antennas using various training symbols. Finally, these two new
techniques compare with Whitening Rotation (WR) based semi-blind channel estimation technique and re-
sults shows that those new techniques achieve very nearby performance with low complexity compare to
Whitening rotation based technique. Also first technique with perfect R outperforms Whitening Rotation
based technique.
Keywords: Multiple Input Multiple Output, Orthogonal Pilot ML Estimator, QR Decomposition, Semi Blind
Channel Estimation
1. Introduction
A Multiple Input Multiple Output (MIMO) communica-
tion system uses multiple antennas at the transmitter and
receiver to achieve numerous advantages. Traditionally,
antenna arrays have been used at the transmitter and the
receiver to achieve array gain, which increases the output
SNR of the system. More recently, ways of using multi-
ple antennas has been discovered to achieve diversity
and multiplexing gain by exploiting the once negative
effect of multipath. Under suitable conditions, i.e. a scat-
ter rich environment, the channel paths between the dif-
ferent transmit and receive antennas can be treated as
independent channels due to the multipath effects caused
by the scatterers. Channel state information (CSI) pro-
vides key information for the operation of MIMO wire-
less communication systems and hence need to be esti-
mated accurately. Many channel estimation algorithms
have been developed in recent years. In the literature
[1-4], MIMO channel estimation methods can be classi-
fied into three classes: training based, blind and semi-
blind. For pure training based scheme, a long training is
necessary in order to obtain a reliable channel estimate,
which considerably reduces system bandwidth efficiency.
In Blind methods, no training symbols are used and
channel state information is acquired by relaying on the
received Signal statistics [5-8], which achieves high sys-
tem throughput requiring high computational complexity.
Semi-blind channel estimation approaches as a combina-
tion of the two aforementioned procedures [9-11], with
few training symbols along with blind statistical infor-
mation, such techniques can solve the convergence
problems and high complexity associated with blind es-
timators. Extensive work has been done later by Slock et

J. BHALANI ET AL.
579
al. [12,13] where several semi-blind techniques have
been reported. Whitening Rotation (WR) based semi
blind technique with Orthogonal Pilot Maximum Likeli-
hood (OPML) [14-17] has shown very good performance
compare to other sub-optimal techniques and training
based channel estimation techniques. WR technique is
less computationally complex compare to other matrix
inversion based channel estimation techniques, still there
is computational complexity related to SVD calculation
in WR based technique so there is requirement to pro-
posed matrix decomposition based semi-blind channel
estimation technique which is less complex and have
good performance [18-23]. Here we have proposed two
novel semi-blind channel estimation techniques. In the
first technique, MIMO channel matrix H is decomposed
as H = RQ, where R is upper triangular matrix, which is
estimated blindly from only received data using matrix
triangularization based house holder QR decomposition
while Q is estimated using training symbols based Or-
thogonal Pilot Maximum Likelihood algorithm. Second
proposed technique is based on joint semi-blind channel
and data estimation. The main steps of this novel method
are as follows:
Step 1: Initial training based channel estimation is per-
formed using QR decomposition based Least Square (LS)
algorithm with the help of training input and training
output.
Step 2: Given channel knowledge (estimate), perform
data estimation.
Step 3: Given data estimation and received Output,
perform blind channel estimation using Same method.
These two new proposed techniques shows near by
performance compare to WR based techniques with low
computational cost and first technique with perfect
knowledge of R shows better result. The remainder of
this paper is organized as follows. The second section
describes the system model. The estimation algorithms
with proposed techniques are presented in Section 3,
simulation results and discussion provides in Section 4
and Section 5 concludes this paper.
2. System Model
Consider a flat fading MIMO channel matrix rt
H
c


h
where t is the number of transmit antennas and r is the
number of receive antennas in the system, and each ij
represents the flat-fading channel coefficient between the
receiver and transmitter. Denoting the complex
received data by , the equivalent base-band sys-
tem can be modelled as
th
ith
j
Yc1r



Yk HXkk  

(1)
where
11 121
21 222
12
t
t
rr rt
hh h
hh h
H
hh h

















k represents the time instant, 1t
X
c  is the complex
transmitted symbol vector.

is additive white Gaus-
sian noise such that 2
{(,) n kl I)()}(lEk

   where
(,) 1kl


if 1k

and 0 otherwise. Also, the sources
are assumed to be spatially and temporally independent
with identical source power 2
s

i.e. {()EXkX()}l

2
(,)
s
kl I

 . The signal to noise ratio (SNR) of operation
is defined as SNR
2
2
s

Assume that the channel has
n

been used for a total of N symbol transmissions. Out of
these N transmissions, the first L symbols are known
training symbols and reaming N - L is blind data sym-
bols.
3. Channel Estimation Techniques
3.1. Whitening Rotation Based Semi-Blind
Channel Estimation
Now consider a MIMO channel rt
H
c  which has at
least as many receive antennas as transmit antennas i.e.
. Then, the channel matrix H can be decomposed as rt
H
H
WQ where rt Wc


tt
Qc
is also known as the whit-
ening matrix and


H
QQ Q
, termed as the rotation matrix,
that is unitary i.e. H IQ

. As shown in [14],
the matrix can be estimated from the received data
alone. We therefore employ the pilot information to ex-
clusively estimate the rotation matrix Q. This semi-blind
estimation procedure is termed as a Whitening-Rotation
(WR) scheme. Let the Singular Value Decomposition
(SVD) of H be given as
W
H
P
P
Q . A possible choice for
W is given by W

 and we assume this specific
choice in the rest of the work. We present next a list of
potential assumptions which are employed as appropriate
in subsequent parts of the work.
Assumption A. rt
Wc

 is perfectly known at the
output.
Assumption B. tL
X
c

 is orthogonal i.e.
2H
s
tt
X
XL  I


Assumption A is reasonable if we assume the trans-
mission of a long data stream (N→∞) from which W can
be estimated with considerable accuracy and Assumption
B can be easily achieved by using an integer orthogonal
structure such as the Hadamard matrix.
ˆ
Q:, where the constrained ML estima-
tor of is and
S is the manifold of unitary matrices, is
obtained by minimizing the likelihood
rL
c

Q
Sˆ Q

580 J. BHALANI ET AL.
2
H
YWQX Such that (2)
H
QQ I
H
H
M
WYX
ˆ
Q
. We then have the following result for the
constrained estimation of Q. Under both assumption
the constrained OPML estimate of Q that mini-
mizes the cost function in (2) is given by
ˆ
H
M
M
QVU where, (3)

H
MMM
UVSVDM
This technique has been proposed and proved in [14]
since this procedure employs assumption B. (orthogonal
pilot), which termed as the OPML estimator. The above
expression (3) thus yields a closed form expression for
the computation of , the ML estimate of Q. The
channel matrix H is then estimated as
ˆ
Q
ˆ ˆ
H
H
WQ.
3.2. House Holder QR-OPML (Proposed
Method-I)
A novel algorithm is proposed and studied for QR de-
composition-based scheme in the context of semi-blind
Multi-Input Multi-Output (MIMO) channel estimation.
Specifically, the flat-fading MIMO channel matrix H can
be decomposed as a upper triangular matrix R and a uni-
tary rotation matrix Q. The matrix R is estimated blindly
from only received data by using orthogonal matrix tri-
angularization based house holder QR decomposition
while the optimum rotation matrix Q is estimated exclu-
sively from training samples based on OPML (Orthogo-
nal Pilot ML Estimator) technique.
The output Y can be written as
YHXN (4)
Output covariance matrix can be described as

2
H
YY n
RHXHX I


2H
YY n
RHHI

 (5)
Now apply householder transformation to received
output covariance RYY. In the householder approach, a
series of reflection matrix is applied to matrix RYY col-
umn by column to annihilate the lower triangular ele-
ments. The reflection transformations are ortho-normal
matrices that can be written as

H
AI VV  
where V is the Householder vector and 2
2
For the matrix RYY to annihilate the lower elements of
the K-th column the Ak is Constructed as follows:
2V   .
1) Let V equal the k-th column of RYY
2) Update V by 2
YY YY
VR R

 where ψ = [1, 0, 0,
0, 0]T
3) Determine

equal to 2
2
2V  
4) k
A
is calculated as


H
AI VV  
The from the above steps are pre-multiplied by RYY
sequentially as follows
1
,, 0
nYY
R
AAR



 (6)
where, R is an nn

upper triangular matrix, 0 is a null
matrix, and the sequences of reflection matrices form the
complex transpose of the orthogonal matrix QH, where
QH = AnA1. Further unitary rotation matrix Q will be
estimated exclusively using training sequence based on
OPML algorithm which already explained in Section 3.1,
where Whitening matrix W in Equation (2) is replaced by
upper triangular matrix R. Finally estimated channel ma-
trix is ˆ
ˆ
H
H
HQ.
3.3. Joint Semi-Blind Channel and Data
Estimation QR-NEW (Proposed Method-II)
This novel method based on joint channel and data esti-
mation using QR-decomposition algorithm. Let
p
X
is
pilot (training) and their corresponding output is
p
Y, so
initial channel estimation is calculated using pilot (train-
ing) data only using QR decomposition. Minimizing the
norm square error function of Equation (4)
ˆ
p
p
YXh  
To avoid matrix inversion, we can directly apply QR
decomposition to the error function and estimate initial
channel using following steps
1) ˆ
p
p
YXh   and if ˆ
0
p
p
YXh   
2) Decompose
p
X
into, hermitian matrix
p
Q and
upper triangular matrix
p
R using QR decomposition
algorithm.
ˆˆ
0
p
pp p
R
YXhQ h




where H
QQ I

due to hermitian property multiply both
sides by
H
Q therefore,
ˆ
0
p
H
p
p
RhYQ



 (7)
Then is estimated using back-substitution method.
ˆ
h
From that we can find estimated blind data
ˆ
h
ˆH
best b
X
hY where b Y is received output data. Now
perform same procedure to minimize norm square error
function
ˆ
bbest
YXH   , so
ˆ
0bbest
YXH   
Decompose best
X
into, hermitian matrix b and
upper triangular matrix using QR decomposition
algorithm
Q
b
R

J. BHALANI ET AL.
581
ˆ
0
b
bb
R
YQ H



Now , multiplying both side, therefore
H
bb
QQ I
ˆ
0
b
H
bb
R
H
YQ
 

 (8)
Final channel estimation ˆ
H
is performed using back
substitution method.
3.4. Least Square (LS) Training Based Channel
Estimation
Received signal can be expressed in Equation (4). The
channel estimation is to find a solution ˆ
H
for the equa-
tion ˆ
X
HY. What LS mean is to minimize the Euclid-
ean norm squared of the residual ˆ
A
HY, that is,

2
ˆˆˆ
H

X
HYXHY XHY  (9)
 
ˆˆ ˆˆ
H
H
H
H
X
HXHYXHXHYY Y
ˆ
H
Differentiating with respect to H and setting equal to 0
yields
ˆ
220
HH H
X
XHX YXXHX Y 
Finally LS algorithm

1
LS
ˆHH
H
XX XY


The term (XTX)–1XH is called pseudo-inverse of matrix
X, denoted by X†.
4. Simulation Results
Extensive computer simulations have been conducted to
demonstrate and compare the performance of Training
based LS, WR based semi-blind channel estimation and
proposed novel semi-blind channel estimation techniques
for Rayleigh flat fading MIMO channels. We consider
alamouti coded 2 × 6 (two transmitters and six receivers)
MIMO systems with 100 blind data symbols among
20,000 pair transmitted symbols under 4-PSK modula-
tion scheme using 4, 8 and 16 pilot symbols. Result
shows in figures depicts that semi-blind channel estima-
tion techniques have better BER performance than train-
ing based LS channel estimation technique further first
novel technique with perfect R outperforms others.
4.1. BER (Bit Error Rate)
As a performance measure, BER is evaluated for training
based LS channel estimation technique, WR based
semi-blind channel estimation technique, proposed ma-
trix triangularization based Householder QR decomposi-
tion semi-blind channel estimation (first technique) and
proposed QR decomposition based joint semi-blind cha-
nnel and data estimation technique (second technique) in
a Rayleigh flat fading MIMO channel. Simulation results
are related to three cases: MIMO 2 × 6 with 4 pilots, 8
pilots and 16 pilots respectively.
4.1.1. MIMO 2 × 6 wit h 4 Pil ots
Figure 1 indicates the BER Vs SNR for above men-
tioned different channel estimation techniques using 4
pilot symbols and 100 blind symbols for 2 transmitter
and 6 receiver antennas under 4 PSK modulation scheme.
First novel technique with perfect R outperforms WR
technique with 1 dB to 2 dB improvements. Both newly
proposed techniques shows similar performance, with
0.4 dB to 0.5 dB performance losses compare to conven-
tional WR technique. When SNR equals to 2 dB, BER is
0.0320 for TBCE-LS, 0.0243 for QR-NEW (proposed
technique-II), 0.0207 for WR and 0.0153 for HQR-
OPML (proposed technique-I) with perfect R, further at
5 dB SNR , BER goes around 10–3.
4.1.2. MIMO 2 × 6 wit h 8 Pil ots
Figure 2 indicates the BER Vs SNR for same analysis
using 8 pilot symbols .Here when SNR equals to 2 dB,
BER is 0.0154 for TBCE-LS, 0.0127 for QR-NEW
(proposed technique-II), 0.0115 for WR and 0.091 for
HQR-OPML (proposed technique-I) with perfect R.,
further at 5 dB SNR, BER goes slightly greater than 10–4,
So 1 to 1.5 dB performance improvements compared to 4
pilots scheme.
4.1.3. MIMO 2 × 6 wit h 16 Pilots
BER performance for 16 pilots demonstrated in Figure 3
shows further performance improvements compared to
previous cases. Here at 2 dB SNR, BER is 0.0102 for
TBCE-LS, 0.0100 for QR-NEW, 0.081 for WR and
0.042 for HQR-OPML with perfect R. At 5 dB SNR,
BER is 0.0003, which considered as best one. Further it
shows almost 2 dB improvements compared to past
cases.
4.1.4. Complexity Compar isons
Complexity analysis of channel estimation techniques
have been taken for m receiver matrix and n transmitter
MIMO channel matrix, Whitening Rotation based
semi-blind channel estimation technique consists of two
singular value decomposition (SVD) and two matrix
multiplication operations. The SVD and multiplication
process having total O (mn2) and (mn) floating point
operations respectively hence total complexity is O (2
mn2 + 2 mn). Proposed houeholder QR decomposition s

J. BHALANI ET AL.
582
Figure 1. BER Vs SNR for diff. channel estimation techniques using 4 Training and 100 Blind symbols for 2 transmitter and
6 receiver antennas for 4 PSK modulation scheme.
Figure 2. BER Vs SNR for diff. channel estimation techniques using 8 Training and 100 Blind symbols for 2 transmitter and
6 receiver antennas for 4 PSK modulation scheme.
Figure 3. BER Vs SNR for diff. channel estimation techniques using 16 Training and 100 Blind symbols for 2 transmitter and
receiver antennas for 4 PSK modulation scheme. 6

J. BHALANI ET AL.
583
based first technique consists of householder reflection
QR operation, which having O (n3) floating point opera-
tions, further its having one SVD and two multiplication
process so total floating point operations are O (n3 + mn2
+ 2mn). Second novel technique having two QR decom-
position process with three multiplication process, hence
total operations related to this technique are O (2n3 +
3mn). Finally this analysis depicts that novel techniques
having less complexity compare to Whitening Rotation
based semi-blind channel estimation technique.
5. Conclusions
The work investigated for Householder based QR-OPML
and joint channel and data estimation based QR-NEW
semi-blind channel estimation techniques for Rayleigh
flat fading MIMO channel using two transmitter and six
receiver antennas combinations and various pilot sym-
bols. The simulations result shows that BER perform-
ance improves as number pilot symbols increase. Finally
those techniques compare with Whitening rotation (WR)
based semi-blind channel estimation technique and ob-
served House holder QR-OPML based first novel tech-
nique with perfect R outperforms WR based semi-blind
technique with low complexity.
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