Eigen-decomposition Techniques for Skywave Interference Detection in Loran-C Receivers
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Transcript of Eigen-decomposition Techniques for Skywave Interference Detection in Loran-C Receivers
Eigen-decomposition Techniques for Skywave
Interference Detection in Loran-C Receivers
Abbas Mohammed, Fernand Le Roux and David Last
Dept. of Telecommunications and Signal ProcessingBlekinge Institute of Technology, Ronneby, Sweden
[email protected],[email protected]
School of Informatics, University of Wales, Bangor, UK
ILA 32, Boulder, Colorado, 3-5 November 2003
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Table of Contents First Skywave Interference Detection sampling
point Choice of the sampling point, before bandpass
filtering Bandpass filtering effects Choice of the sampling point, after bandpass filtering Criterium design of the receiver
Previous Skywave Estimation Techniques Eigen-decomposition Technique
MUSIC Algorithm ESPRIT Algorithm
Simulation Setup Simulation Results
Simulation Results Using Off-air Data Conclusions Questions
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The Choice of the sampling Point ?Before bandpass filtering
0 20 40 60 80 100 120 140 160 180 200-5
-4
-3
-2
-1
0
1
2
3
4
5
Time (microseconds)
Sig
nal A
mplit
ude
standard zero-crossing
groundwave
skywave
The time reference point at 30 sec is marked the ”standard zero-crossing”
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Bandpass filtering effects Figure shows a 5th order Butterworth filter of 20 kHz bandwidth
50 60 70 80 90 100 110 120 130 140 150-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (kHz)
Am
plitu
de
Sp
ec
tru
m
(dB
)
Bandpass filtering reduces out of band noise and interference, thereby
improving SNR of the received Loran signals
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0 20 40 60 80 100 120 140 160 180 200-5
-4
-3
-2
-1
0
1
2
3
4
5Sig
nal A
mplit
ude
Time (microseconds)
typical later zero-crossing selected
groundwave
skywave
The amplitude 30 sec after the start of pulse is greatly reduced. A much later zero-crossing must be selected skywave errors
The Choice of the sampling Point ?After bandpass filtering
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Objective of Skywave Delay Estimation Techniques
Design a receiver which adjusts the sampling point adaptively to the optimum value as the delay of the first skywave component varies. Previous skywave estimation techniques were evaluated such as, AR, ARMA, MUSIC by Abbas Mohammed and David Last.
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Skywave Estimation Technique
This paper revisits the IFFT Technique
Eigen-decomposition approach for skywave delay estimation, such as MUSIC and ESPRIT algorithm
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Eigen-decomposition Technique
Autocorrelation matrix , of the received signal , Eigenvector matrix U, where and related eigenvalues ordered in
Signal- and noise eigenvector matrixes and related eigenvalues
IAPAnxnxER wHH
x2)()(ˆ
MM )(nx
wsx RRR ˆˆˆ
HHsss APAUUR ˆ
IUUR wHwww
2ˆ
021 M
21 M
xR
21 wMn
MuuuU ,,, 21
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MUSIC Algorithm
Use the eigen-decomposition technique on the data autocorrelation matrix,
Estimate of the noise variance
The frequencies can be estimated by finding the roots of the polynomial, closest to the unit circle.
Find the power of each complex exponential
xR
M
Pmmw PM 1
2 1ˆ
M
Pmmm zUzUzD
1
** )/1()()(
1
0
)()(M
m
mmm zmuzU
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ESPRIT Algorithm, (Estimation of Signal Parameters Via Rotational Invariance Techniques) Compute eigen-decomposition of the data auto-
correlation matrix,
Make a signal matrix, formed by the eigenvalues and related largest eigenvalues
Partition into and by deleting the last row and the first row, and
Compute where
Estimate the frequencies from eigenvalues of
xR
ˆ12 ss UU
sU
sU
1sU
2sU
sMs UIU 011 sMs UIU 102
2/)arg( iif
i
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Simulation Setup
FFT FFT
Hanning window
Xc()
Xg()
w(t)xg(t)
xg(t)
Xg
h(t)
H()
Xc()
xc(t) = xs(t) + w(t)
1 2
h(t)
g(t)*
xs(t)
xsk(t)
LORAN-C pulseGenerator
Spectrum Divisionwith Windowing
Skywave DelayEstimation
h(-t)
Frequency EstimationAlgorithm
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Signal Models
Time-domainreceived signal = groundwave + skywave(s)
+ noise
desired signal
unwantedsignals
Frequency-domain Take FFT of the time-domain received signal
(t)xc
} { (t)xF(f)X cc
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IFFT Analysis for Skywave Delay Estimation
Perform a spectral-division operation
Spectrum of {received pulse / standard Loran pulse}
Take IFFT of the spectral-division =
Result: estimated arrival times of groundwave and
skywave pulses skywave delay estimate
(f)X
(f)X c
0
(f)X
(f)XF c
0
1
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SNR = 24 dB (-13 dB antenna) Skywave-to-Groundwave Ratio
(SGR) = 12 dB Hanning window bandwidth = 50
kHz Autocorrelation Matrix, , , M
= 4
Simulation Parameters
MM xR
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Even at this low SNR value, the groundwave and skywave signals are
isolated and identified
Simulations Results 1
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Simulations Results 2
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Simulations Results 3
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Simulation Results Using Off-air Data 1
0 100 200 300 400 500 600-1
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0
0.2
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0.6
0.8
1
Time (microseconds)
Sig
nal A
mplit
ude
0 50 100 150 200 250 300 350 400 450 5000
0.1
0.2
0.3
0.4
0.5
0.6
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0.8
0.9
1
Time (microseconds)
Norm
aliz
ed
Am
plit
ude
Hanning window bandwidth of 50 kHz is used
Data Supplied by Van Nee of Delft University
skywave component
groundwave component
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Simulation Results Using Off-air Data 2
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Conclusions
ESPRIT has potentially beter computational and numerical advantage compared to MUSIC
Gives beter estimation results compared to the MUSIC algorithm
We have demonstrated for the first time skywave delay estimates with ESPRIT by using off-air signals
Frequency estimation techniques has critical issues, like , window bandwidth, autocorrelation matrix size which we have to define more closely in future work
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Questions
Questions
You could also email questions to:[email protected],[email protected]