Accurate Channel Estimation in Low SNR Channel
For WLAN 802.11n System
Wahyul Amien Syafei#1 #2, Grifina Nuzulia#1, Sukiswo#1
#1
Electrical Engineering, Faculty of Engineering,
Information System,Post Graduate Program
Diponegoro University, Jl. Prof. H. Soedharto,S.H. Tembalang, Semarang, 50275. Indonesia
#2
#[email protected]@gmail.com
#[email protected]
#[email protected]
Abstract — WLAN 802.11n promises high throughput
wireless communication for multimedia and data. The demand of
higher data rate forces the use of state of the art technology in
WLAN. The robust WLAN system more verified when information
was transmitted in multipath channel that susceptible from
interference. To reduce the interference it is needed an accurate
channel estimation to repair the received signal particularly in low
SNR channel. Some of the well known channel estimation methods
are zero forcing (ZF) and Minimum Mean Square Error (MMSE).
Both of them are simple but low performance.
This paper presents research in channel estimation
method for WLAN 802.11n. It exploits the truncated singular value
decomposition (TSVD) combined with optimal cyclic shift. This
method further is developed to a hybrid MMSE-TSVD which
requires statistical information of channel. Optimal value for
singular value truncated and cyclic shift significantly increases the
error performance of TSVD and MMSE-TSVD.
Run test under low SNR AWGN channel demonstrates
superiority of the proposed TSVD method compared with ZF and
MMSE.
This paper presents research in channel estimation
method for WLAN 802.11n. It exploits the truncated singular
value decomposition (TSVD) combined with optimal cyclic
shift. This method further is developed to a hybrid MMSETSVD which requires statistical information of channel.
Optimal value for singular value truncated and cyclic shift
significantly increases the error performance of TSVD and
MMSE-TSVD.
I. LITERATURE REVIEW
In format packet sent by WLAN there is an LTF as
training sequence to track the variation of channel or to
estimate the channel response. Our proposed algorithm goes
as follows: Firstly, LTF is optimized by taking its singular
value using SVD of LTF matrices then eliminate the biggest
singular values. Cylic shift is permutated on LTF to minimize
condition number between its singular value. The result of
truncated SVD is used to generate pseudoinverse matrices that
used in receiver to compensate channel’s effects. Bellow are
brief definition of each term used in the proposed algorithm.
Keywords : Wireless LAN, 802.11n, channel estimation, SVD, cylic
shift,
I. INTRODUCTION
A. Condition Number (CN)
CN can be defined as The ratio between the biggest
singular value to the smallest one, written as:
(2.1)
λ 2Δ
CN 
λ1
Development of laptop and mobile phone make
possibility for connecting in everywhere. Connection network
on conference room or when sitting on sofa is two example
from flexibility that we got from wireless LAN[1]. First time
wireless LAN standard introduced on 1997 that recognized as
Wi-Fi with maximal data rate 2 Mbps. Then the standard got
improvement become 802.11a/b (1999), 802.11g (2003), and
802.11n (2009) with maximum throughput of 600 Mbps. This
dramatically higher throughput of 802.11n compared to
802.11a/b/g due to a combination of OFDM and MIMO
techniques.
The robust WLAN system more verified when
information was transmitted in multipath channel that
susceptible from interference. To reduce the interference it is
needed an accurate channel estimation to repair the received
signal particularly in low SNR channel. Some of the well
known channel estimation methods are zero forcing (ZF) and
Minimum Mean Square Error (MMSE). Both of them are
simple but low performance.
B. Truncated Singular Value Decomposition (TSVD)
Channel Estimation Method[2]
A Maksimum Likelihood Estimator (MLE) in receiver jth,
̂𝐡𝑗 can be obtained by minimizing following criterion:
j 2
̂ j−𝐫 |
Jml = |𝐋P 𝐡
lp
1
(2.2)
So the channel estimation derived based on that formula :
̂𝐡𝑗 = 𝐗 + 𝐫 𝑗
(2.3)
𝑙𝑝
With X

D. Minimum Mean Square Error (MMSE)[3]
MMSE method used as development of TSVD method.
That is coming from adding channel statistic information 𝜎𝑛2
and Ch to looking for estimated channel in this below formula
2.12.
can be defined pseudoinverse matrix as :
X   LH
 p
While SVD from X

L

p 
1
LHp
(2.4)

hˆ mmse, j   2Ch1  LHp L p
fulfill this below formula :

X  UΛV
H
(2.5)
Based on 2.5 formula, so A matrices that have contents
singular value from decomposing on formula 2.6 :

0


 N tx 
0  0
0  0
  

0  0
LTF 1
truncater carries out the expression
Λ q  truncating (, q )
(2.7)
where truncation matrix (Λ,q) is a step of picking "q" singular
values in a greater order out of singular values and turn the
picked "q" singular values into zero.
A pseudoinverse matrix has been arranged became :
Fig.3.1 Block diagram of wireless LAN transmitter
(2.8)
Optimizer
Pseudoinverse matrix

 tr[Ch VI qq V H ]
Demux
Channel Estimation
Removi
-ng GI
FFT
Removin
g Pilot
Optimizer
Pseudoinverse matrix
rlp2
(2.10)
with
𝜎𝑛2
is
noise
power
𝜆𝑖 is singular value from diagonal matrix.
J h  tr[C h V Λ q Λ 1  I
rlp1
Demux
i 1
λ2
i
Optimization LTF 2
and
STBC
Decoding
Data Series

GI
Viterbi Decoding
2  q
IFFT
De-interleaving
n
GI
Symbol Remapping
q
IFFT
Multiplexing
LTF 2
and channel estimation after truncating singular value can be
described :
̂ ml,j = 𝐗 q+ 𝐫 j
𝐡
lp
(2.9)
C. Truncating Optimization [2]
Optimization q involve 2 condition. That is noise in
channel its called Jn function and channel as Jh function,
Both of them can be appointed on this below formula:
n
Optimization LTF 1
Adding Pilot
truncating singular values. Specifically, the singular value
STBC Encoding
tx
Then, the singular value truncater carries out the step of
Interleaver
1  2     N
J n  σ 2 tr[ Λ 2 ]  σ 2
(2.12)
Multiplexing
singular value ith and it can be assumed as :
X  q  VΛ q U H
LHp  rlpj
(2.6)
Symbol Mapping
is
0
Data series
where 1
.

1
II. SIMULATION STAGE
Diagram block Transmitter and Receiver Wireless LAN
system shown in figure 3.1 and 3.2.
Convolutional Encoding
1 0
0 
2

 

 0 0

Channel Estimation
Removi
-ng GI
FFT
Removin
g Pilot
H Λ q Λ 1  IV H ]
Fig. 3.2 Block diagram of wireless LAN receiver
(2.11)
And then the parameters of simulation defined on
tabel 3.1.
where Iqq indicates a square matrix in which diagonal factors
arranged before (2 -q)th row and (2 -q)th line in an identity
Tabel 3.1 Simulation Parameters
matrix are all zero and Ch is channel covarian matrix.
2
32 ns
MIMO 2x2
BPSK
450 (octet)
Convolutional Encoding
R = ½,k=7
Ideal
0
128
32
320
-1
10
ZF
MMSE konvensional
TSVD
-2
10
-3
10
BER
Sampling Period
Antenna Configuration
Modulation
Length of packet
Forward Error Correction
(FEC)
Sincronization
Frequency offset
FFT
Cylic prefix ()
G (Length of LTF)
-4
10
-5
10
a) Optimisasi LTF
Optimization of LTF conducted in Transmitter antenna as
described on diagram block 3.3
-6
10
-2
0
2
4
6
SNR (dB)
8
10
12
14
16
Start
Fig. 4.1 Graphic of BER Performance versus SNR in conventional MMSE,
ZF and TSVD
LTF matrix
Making Pseudoinverse
Matrix
In fig.4.4, Increasing BER performance more significant
between conventional method and TSVD. BER performance
on TSVD more greater caused by calculation complexity to
looking for estimated channel like optimization on LTF
matrix with truncate singular value as result of estimated
channel. So it have low noise in channel. The other reason is
BER performance more greater on lower SNR condition like
limited power on user handheld.
Singular Value Decomposer
Truncating
( , q )
Reconstruction
Finish
B. A CS Optimal
CS optimal can be measured with partial condition
number (PCN). It can seen with ratio maximum and minimum
from matrix Λ that already truncated. In this research, there
are 3 CS like cs 35, cs 128 and CS 160 that have significant
value as shown in fig.4.2.
Fig.3.3 Block of Optimization LTF
b) Minimum Mean Square Error (MMSE) TSVD
MMSE-TSVD method have same process with TSVD
method on transmitter but it has different process in receiver
and this method as development of TSVD that shown in figure
3.4.
PCN VS CS

X q
r lpj
ĥ
1j
ĥ
ml, j
ĥ
mmse, j
Interpolate with
zero
FFT
Interpolate with
zero
FFT
10
Ĥ
1j
2
Divider
2j
Ĥ
2j
PCN
ĥ
10
no truncation
truncation = 8
truncation = 15
1
Fig.3.4 Block of MMSE-TSVD channel estimation
III. RESULT AND ANALYSIS
A. Testing of performance conventional MMSE, ZF and
TSVD
10
0
50
100
150
200
Number of Cylic Shift
First time, for testing performance of BER,it used
conventional channel estimation. That is conventional MMSE
and ZF that comparing with TSVD method. TSVD method
that tested with take any CS example 78 and q 5. The result of
testing can be figured on figure 4.1.
Fig 4.2 Figure of CS vs PCN
C. A q optimal (truncated singular value)
3
250
300
A q optimal can be derived with minimize sum of Jn and
Jh function. For each CS value that choosen have q optimal
value on table 4.1
the biggest value than the others as shown on fig.4.2.
Otherwhile,CS 35 give the best BER performance because it
have a number of singular value truncation (q) less than other.
Tabel 4.1 A q optimal value
CS th
Q optimal
35
5
128
6
160
6
2) Minimal Mean Square Error (MMSE) TSVD
Graphic of BER perfomance for MMSE-TSVD based on
table 4.1 it can be seen in fig. 4.5:
Optimization graphic for Jn and Jh in CS 35 like seen on
fig. 4.3.
10
-1
MMSEIDEAL
MMSE35
MMSE128
MMSE160
Combining Jn dan Jh
1
J
Jh
Jn
0.9
10
-2
0.8
0.7
10
0.5
0.4
10
X: 5
Y: 0.2818
0.3
0.2
10
0.1
0
0
10
20
30
40
50
60
10
Fig.4.3 Graphic of combination Jn and Jh function for CS 35
BER
10
10
10
10
-3
-2
-1
0
1
2
3
4
In figure 4.5 , there is various combination from CS and a
q optimal that can give different BER performance to MMSETSVD. CS 35 give the best BER performance because it have
less a number of singular value truncation. Impact this result
is minimizing loss of information. Otherwhile, CS 128 have
the the worst performance because PCN that having more big
value as shown in fig 4.5.
From testing BER performance based optimal value of
CS and q that applied for both of method it show more little
PCN value with less number of singular value truncation give
BER performance more great.
IDEAL
CS35
CS128
CS160
-2
-6
Fig.4.5 BER performance versus SNR for MMSE-TSVD
-1
-3
E. Testing BER performance for TSVD, MMSE SVD
and MMSE-TSVD.
For comparing channel estimation that have optimal BER
performance in lower SNR condition its can be seen on fig.4.6.
-4
-5
-6
-3
-5
SNR (dB)
D. Testing BER Performance based on A CS and q Optimal
1) Truncated Singular Value Decomposition Method
(TSVD)
Graphic of BER performance for TSVD based table 4.1
as shown on 4.4.
10
-4
70
A number of q
10
-3
BER
J,Jn,Jh
0.6
-2
-1
0
SNR (dB)
1
2
3
4
Fig.4.4 BER Performance versus SNR in TSVD
For fig.4.4, in trilateral thick line show the best of BER
performance. It caused by ideal channel estimation no
consider AWGN. CS 128 have the worst performance because
there is truncation on singular value and PCN for CS 128 have
4
-1
10
BIBLIOGRAPHY
[1] Syafei, Wahyul Amien, “Study on System Level Design of
Gigabit Wireless LAN’’, Desseratation, Department of
Computer Science and Electronics Kyushu Institute of
Technology, Japan, 2009
[2] Syafei,Wahyul Amien, Shigenori Kinjo dan
Hiroshi
Ochi, “Optimal CSD and Truncated SVD for Channel
Estimation”, doc.:IEEE 802.11-08/1079r0, 2008.
[3] Kinjo,Shigenori,’’ Time Domain Channel Estimation
Schemes
For
OFDM
System
With
MultipleAntennaTransmission”,ISPACS,2009.
MMSE-SVD
TSVD
MMSE-TSVD
-2
10
-3
BER
10
-4
10
-5
10
-6
10
-3
-2
-1
0
1
2
3
4
SNR (dB)
Fig. 4.6 BER performance versus SNR with TSVD, MMSE-SVD and
MMSE-TSVD
In fig. 4.6, channel estimation with MMSE-TSVD have
the best performance. It caused by combining between LTF
optimization with truncation of singular value. LTF matrix
have little matrices value until can minimze impact of noise
and channel statistic information such as noise power and
channel covariant matrix.
IV. CONCLUSION
Based on testing and analysis so it can be inferred as:
1. Based on testing of TSVD and conventional channel
estimation , to reach BER with treshold 10-6 , TSVD,
MMSE and ZF need SNR ±1,8 dB, ±12,8 dB and 16
dB,respectively.
2. A Partial Condition Number (PCN) more than 1 give
impact to select optimal CS until CS give significant
modification from there are no truncation become its
have in CS 35,128 and 160.
3. Minimizing combination value for Jn and Jh make
optimal number of singular value truncation in CS
35,128 and 160 is 5 ,6 and 6,respectively.
4. Based on testing of optimal CS and q, to reach BER
with treshold 10-6 , CS 35, 160 dan 128 need ±1,6 dB,
±1,9 dB, ±2,7 dB,respectively.
5. Based on testing of optimal CS and q for MMSETSVD, to reach BER with treshold 10-6 , CS 35,128
and 160 need SNR ±1,3 dB, ±1,4 dB dan ±2,4
dB.respectively.
6. Based on testing of channel estimation for low power
in MMSE-TSVD, MMSE-SVD and TSVD to reach
BER with treshold 10-6 , need SNR ±1,4 dB, ±1,5 dB
dan ±1,6 dB,respectively.
5