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Volume 2, Issue 4 MAY 2015
A NOVEL WEIGHTED SUBSPACE FITTING
CFO ESTIMATION IN THE OFDM SYSTEMS
K. LIGI (PG Scholar) 1
Mr. P. GIRIBABU, M.TECH2
1
2
Department of Electronics and Communication Engineering
Associate Professor, Department of Electronics and Communication Engineering
ABSTRACT
Whenever we
INTRODUCTION
are
designing
the
wireless
communication systems that must possess of high
reliability and low latency and also the optimization
when switching is takes place in different circuits. and
in that system it contains of lot of hardware
impairments
regarding power supply . when the
supply load changes in circuit suddenly the carrier
frequency drifts it results in transient carrier frequency
offset(CFO) in cannot be estimated by using of the
traditional estimators and is typically addressed by
inserting or extending guard intervals. In this paper
we are presenting the modeling and estimation of the
transient CFO , which is modeled as the response of an
under damped second order system. To compensate for
the transient CFO, we are proposed a low complexity
parametric estimation algorithm by using of the null
space of Hankel-like matrix. It was constructed from
the phase difference of the two halves of the repetitive
training sequence.
Here a weighted subspace fitting algorithm is derived
with a slight increase in complexity to minimize the
mean squared error of the estimated parameters in
Since cooperation was first projected for wireless
networks,
it's
communications
performance
become
and
gains
a
preferred
networking
for
area
analysis.
cooperation
stem
of
The
from
mitigating long path-loss and shadowing ef fects and
short multipath fading effects. The combined path-loss
of a two-hop transmission is also but direct
transmission, and RF absorbing objects within the
atmosphere are often circumvented to scale back
shadowing. this can be analogous to multi-hop routing
and might be performed at either net work (NET) or
medium access (MAC) layer, with larger potency at the
latter. Relaying also can give a receiver with redundant
messages that travel through spatially distinct ways,
reducing the impact of multipath. This creation of
special diversity, referred to as cooperative diversity,
provides better average performance and might be
achieved at either the mack or physical (PHY) layer,
with larger performance gains at the latter. the tip
results of path-loss and variety gains provided through
cooperation
is
improved
network
performance,
realizable as varied combinations of
noise.
IJOEET
32
Volume 2, Issue 4 MAY 2015
power savings, rate will increase, network coverage
protocols. Experimentation is a chance to get
growth, and interference reduction. A number of realistic quantifications of performance gains for
characteristics
of
cooperative
schemes
make planned cooperative schemes in actual propagation
experimentation essential for transitioning proposed
environments and network topologies.
schemes to practical applications. Information flowing
through a cooperative link visits multiple nodes
Finally, modeling and simulation typically
create idealistic assumptions regarding the capabilities
Within the network, suggesting cooperation of the physical radio platforms on that planned
can have implications for multiple layers of the protocols ar to be run. Common limitations in realprotocol stack, together with at a minimum the PHY,
world radios like a scarcity of frequency and temporal
MAC, and internet layers. Decisions made at one layer
arrangement
can impact the potency of the others, increasing
estimation, and quantization errors have an oversized
protocol
quality
opportunities
however
for
providing
cross-layer
synchronization,
imperfect
channel
several impact on the effectiveness of the many cooperative
improvement.
schemes. though a considerable quantity of the
Performance metrics to guage such cross-layer
literature
addresses
these
problems
directly,
schemes, like output and delay at the mack and
experimentation is that the solely thanks to establish
internet layers, need giant networks to get realistic
alternative impediments and make sure devised
estimates. Modeling and simulation will become
solutions are so solutions.
unwieldy because the variety of nodes at intervals a
network grows, creating experimentation “one of the Proposed method:
factual approaches for benchmarking”. complicated
The Traditional CFO Estimation:
interactions between layers will be not possible to fully
We assume that the receiver estimates the CFO through
predict, creating full implementation necessary to spot
the preamble OFDM symbol, whose first and second
conflicts that will degrade performance.
halves are identical.
Cooperative gains determined by theoretical
work and simulation vary considerably relying upon
Then, we can express the transmitted preamble
signal as
the models chosen for the network topology and
therefore the wireless channel. Real-world propagation
environments area unit notoriously difficult to model;
the
foremost
faithful
models
quickly
become
cross-layer nature of cooperation, and experimentation
becomes the sole sensible thanks to measure full
IJOEET
0≤ ≤
≤ ≤2
(1)
Where T is the time interval between the two halves.
Thus, the received signal impaired by CFO can be
written as
intractable for each theoretical work and simulation.
increase this the multi-layer simulation needed by the
( )
( − )
( )=
( )= ∫
( )
∞
ℎ( ) ( − )
+ ( )
∫
∆ ( )
+
(2)
Where h(t) is the channel response, s(t) is the
33
Volume 2, Issue 4 MAY 2015
transmitted preamble and n(t)andˇ n(t) are the additive , ∆ ( ) =
sin
1−
+
> 0,
Gaussian noise at the receiver before and after RF
0 < < 1 (5)
down-conversion, respectively. Δω(t) is the CFO
Where ζ and
are the damping factor and undamped
between the transmitter and receiver. ˇ n(t)is much less
natural frequency, respectively.0< ζ<1means that the
than n(t). Hence, we drop this noise term thereafter.
second order system is underdamped .φ and α are the
For the traditional CFO estimation, we assume that the
initial phase and gain of the response, respectively.
CFO is constant, then (2) reduces to
To model the transient CFO, we define the
∞
( )=
ℎ( ) ( − )
∆
+ ( )
0
overall CFO in terms of two parts: a transient CFO and
a steady state CFO. We assume that the steady state
CFO, denoted by ΔωS, is constant during the preamble
(3)
≤ ≤2
The first and second halves of the received preamble OFDM symbol. Then, the overall CFO can be written
as Δω(t)=Δ
(t)+Δ . Thus, the received signal
can be written as
( )= ∫
∞
ℎ( ) ( − )
+
∆
( )
0≤
( )=
≤
∫
( )=
∫
become
∞
ℎ( ) ( − )
+
( )
∆ (
)
0≤ ≤
∞
( )
ℎ( ) ( − )
( ) ∆
(∆
∫
+
)
(6)
In this paper, we assume that the steady state
Where n1(t) and n2(t) are the additive noise in CFO is estimated and removed from the baseband
r1(t) and r2(t), respectively. Therefore, the first and signal to simplify the estimation of the transient CFO.
second halves of the received preamble symbol have a This assumption is reasonable in practice since a
fixed phase difference of Δω Tin sample-wise with the terminal first detects the downlink preamble signal to
absence of the additive noise. The traditional CFO obtain the time synchronization, the steady state CFO,
estimation is to compute this fixed phase difference.
and other necessary information to access to the
The maximum likelihood estimation of the CFO, wireless network during the initialization stage. The
terminal stays in RX state during this stage and does
denoted by Δˆω , is
∆
=
∠(∑
∗(
) (
))
not have to be running in TDD mode.
(4)
Let us now consider the received preamble symbol in
Transient CFO Model: Then, we claim that the two halve
transient CFO, denoted by Δω T(t), can be model as
the step response of a second order underdamped
( )= ∫
IJOEET
ℎ( ) ( − )
( )
+
∫
∆
( )
( )=
system, which can be expressed as an exponentially
damped sinusoid, i.e.
∞
∫
∞
ℎ( ) ( − )
+
( )
∫
∆
( )
34
Volume 2, Issue 4 MAY 2015
The phase difference between the first and second
The prediction filter order, L, which is also the number
halves is denoted by ψ(t)
of columns of the Hankel matrix, is chosen to optimize
( )=∠
∗(
) ( )
the estimation performance in the subspace based
linear prediction problems, such as the Kumaresan–
=
( )
∆
+
( )
(7)
( ) is the noise term in the phase difference.
Where
Tuft (KT) method ,and matrix pencil method . the first
order perturbation analysis for the KT method as
(
Note that ψ(t) is just the definite integral of the
)≈
4
3
( − )
1≤
transient CFO over interval[t, t+T]. Then ψ(t)is still an
≤
exponentially damped sinusoid with the same damping
The proposed subspace based algorithm is described
−
factor and frequency, but different initial phase and below.
gain, i.e.,
( )=
We construct the prediction matrix:
∆ ( )
+
=
+
( )
sin
+
( )
1−
(0)
(1)
⋮
( − 2 − 1)
=
( )
( + 1)
⋮
( − − 1)
(2 )
(2 + 1)
⋮
( − 1)
(8)
(9)
Subspace Based Estimation of a and
:
Wr is a Hankel-like matrix composed of noise, i.e.
Estimating the parameters of damped sinusoid
(0)
(1)
⋮
( − 2 − 1)
has been extensively. The existing algorithms are,
⎡
however, rather generic and can be generally put into = ⎢
⎢
⎢
four categories: direct fitting in time domain using
⎣
signal samples, direct fitting in frequency domain with
DFT based algorithms, covariance based linear
prediction, and subspace(SVD) based linear prediction.
Then, the complex roots of the prediction
Assume that the singular value decomposition (SVD)
of
is
=[
]
Performance
=
(0)
(1)
⋮
( − − 2)
IJOEET
(1)
⋯
(2)
⋯
⋮
⋱
( − − 1) ⋯
( − 1)
( )
⋮
( − 1)
( + 1)
⋮
( − − 1)
(2 )
⎤
(2 + 1) ⎥
⎥
⋮
⎥
( − 1) ⎦
(10)
polynomial are found to compute the damping factor
and frequency.
( )
0
0
=
Analysis
and
0
(11)
Weighted
Subspace
Fitting: The WSF algorithm is proposed based on the
perturbation analysis of the subspace based estimator.
We use the first order subspace perturbation analysis
35
Volume 2, Issue 4 MAY 2015
The Hankel-like matrix is
are
=
+
, where
0
=
defined
+
and Where
=
0
( )
⎡
=⎢
⎢
⎣
( )
(12)
is a Vandermonde matrix defined as
1
(
(
1
)
.
.
(
)(
)
(
)
.
.
)(
)
⎤
⎥
⎥
⎦
(20)
a first-order approximation of the perturbation at high
SNR is given by
∆
Estimation of the Initial Phase and Gain :Observe
(13)
≈ −
Assumev0=[
,
,
that the noise of the phase difference vector is not
] T. Defining the
instantaneous SNR as ρ(nTs),we have
Assume the covariance matrix of ψ is R, and the
[ ], =
|
|
(
)
[ ],
positive definite matrix R−1 can be factored as
|
+
|
(
(
(
(
(14)
)
(
covariance matrix of Sψ is an identity matrix. The
(16)
)
estimation of r with prewhitened least squares method
We propose a weighted subspace fitting method in
is
order to reduce the MSE of the estimatedv0. The
weighted subspace fitting can be modeled as
=
=
+
(21)
=
Then S acts as a prewhitening matrix since the
(15)
)
∗
=
|
∗
+
)
|
+
)
∗
=
[ ],
white. We can use a whitening solution as follows.
( )
̂=
( )
( )
(22)
EXPERIMENTAL RESULTS
(17)
4
Estimated
Original
3
2
Selection of Time Lag r : In constructing the matrix
Sigh
1
Hr, it is important to select the time lag r.
0
In this section, we investigate the best strategy to
-1
-2
select r. Let us recall that the mean square error of
-3
0
ΔvD in
‖ ]=
( )
≤
((
)
10
((
( )∑
≤
) )
(
(
The sample covariance matrix of noise free matrix Hr
→∞
=
( )
( )
(19)
40
50
Time
60
70
80
90
100
-3
10
10
-4
-5
is asymptotically equivalent to
lim
30
)
(18)
)
20
Figure: compaison between original And estimated signals
)
--MSE of damping Factor
[‖∆
10
10
Proposed
KT
MP
CRB
-6
5
10
15
20
25
30
---SNR
figure: Comparison of the MSE of the estimated damping
IJOEET
36
Volume 2, Issue 4 MAY 2015
--MSE of Estimated Frequency
10
10
10
10
-3
-4
-5
Proposed
KT
MP
CRB
-6
5
10
15
20
---SNR
between
SNR
to
MSE
Figure: plot
frequencies
estimation
Figure :
no CFO correction
32
26
24
Proposed with WSF
Without WSF
No Compensation
30
28
Proposed with WSF
No Compensation
Without WSF
22
Estimated SNR
Estimated SNR
26
20
18
16
24
22
20
14
18
12
16
10
14
14
16
18
20
22
---Input snr
24
26
28
Figure: Estimated SNR
12
14
16
18
20
22
---Input snr
24
26
28
Figure:
Extension under SUI channel
Figure: after CFO correction without WSF
CONCLUSION:
Here in this paper we are analyzed a unique
problem in the wireless communication system i.e.
CFO (carrier frequency offset).it was mainly observed
in switching systems of transmitter and receiver .to
reduce this problem we are proposed a algorithm based
on the subspace decomposition of the Hankel-like
matrix. And to improve the antenna accuracy a
weighted subspace fitting algorithm is proposed in both
numerical simulations and experimental results The
performance analysis is verified from the tested
collected samples.
REFERENCES
[1] P. O. Murphy, “Design, implementation and
characterization of a cooperative communications
system,” Ph.D thesis, Rice University, Houston,TX,
USA, 2010.
Figure: after CFO correction with WSF
IJOEET
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37
Volume 2, Issue 4 MAY 2015
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