Transcript Document

Eigen-decomposition Techniques for
Skywave Interference Detection in
Loran-C Receivers
Abbas Mohammed, Fernand Le Roux and David Last
Dept. of Telecommunications and Signal Processing
Blekinge 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
Table of Contents

First Skywave Interference Detection sampling point
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
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Choice of the sampling point, before bandpass filtering
Bandpass filtering effects
Choice of the sampling point, after bandpass filtering
Criterium design of the receiver
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Eigen-decomposition Technique
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
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
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MUSIC Algorithm
ESPRIT Algorithm
Simulation Setup
Simulation Results


Previous Skywave Estimation Techniques
Simulation Results Using Off-air Data
Conclusions
Questions
Abbas Mohammed
ILA 32, 3-5 November 2003
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The Choice of the sampling Point ?
Before bandpass filtering
5
standard zero-crossing
4
Signal Amplitude
3
2
1
0
-1
groundwave
-2
skywave
-3
-4
-5
0
20
40
60
80
100
120
140
160
180
200
Time (microseconds)
The time reference point at 30 msec is
marked the ”standard zero-crossing”
Abbas Mohammed
ILA 32, 3-5 November 2003
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Bandpass filtering effects
Figure shows a 5th order Butterworth filter
of 20 kHz bandwidth
10
0
Amplitude Spectrum (dB)
-10
-20
-30
-40
-50
-60
-70
-80
50
60
70
80
110
100
90
Frequency (kHz)
120
130
140
150
Bandpass filtering reduces out of band noise
and interference, thereby improving SNR of
the received Loran signals
Abbas Mohammed
ILA 32, 3-5 November 2003
4
The Choice of the sampling Point ?
After bandpass filtering
5
4
typical later zero-crossing selected
Signal Amplitude
3
2
1
0
-1
groundwave
-2
skywave
-3
-4
-5
0
20
40
60
80
100
120
140
160
180
200
Time (microseconds)
The amplitude 30 msec after the start of pulse is greatly reduced.
A much later zero-crossing must be selected  skywave errors
Abbas Mohammed
ILA 32, 3-5 November 2003
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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.
Abbas Mohammed
ILA 32, 3-5 November 2003
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Skywave Estimation Technique
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This paper revisits the IFFT Technique
Eigen-decomposition approach for
skywave delay estimation, such as
MUSIC and ESPRIT algorithm
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ILA 32, 3-5 November 2003
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Eigen-decomposition Technique
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ˆ , M M
Autocorrelation matrix R
x
of the received signal x(n) ,
Rˆ x  Rˆ s  Rˆ w
Rˆ x  Ex(n) x H (n) APAH   w2 I
Eigenvector matrix U, where U  u1,u 2 ,, uM 
and related eigenvalues ordered in
1  2    M  0

Signal- and noise eigenvector matrixes and
related eigenvalues
2
H
H
ˆ







Rs  Us Us  APA
1
M
Rˆ  U U H   2 I
     2
w
Abbas Mohammed
w
w
w
n1
ILA 32, 3-5 November 2003
M
w
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MUSIC Algorithm
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Use the eigen-decomposition technique on the data
autocorrelation matrix, Rˆ x
Estimate of the noise variance
The frequencies can be estimated by finding the
roots of the polynomial, closest to the unit circle.
D( z ) 
M 1
M
U
m  P 1

M
1
ˆ 
m

M  P m P 1
2
w
m
*
m
*
( z )U (1 / z )
U m ( z )   um (m) z m
m 0
Find the power of each complex exponential
Abbas Mohammed
ILA 32, 3-5 November 2003
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ESPRIT Algorithm, (Estimation of Signal
Parameters Via Rotational Invariance
Techniques)
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Compute eigen-decomposition of the data autocorrelation matrix, Rˆ x
Make a signal matrix, U s formed by the eigenvalues
and related largest eigenvalues
Partition U s into U s and U s by deleting the last row
1
2
and the first row, U s  I M 1 0U s and U s  0I M 1 U s
2
1
ˆ where U s  U s ˆ
Compute 
2
1
Estimate the frequencies from eigenvalues
fi   arg(i ) / 2
Abbas Mohammed
ILA 32, 3-5 November 2003
i of ˆ
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Simulation Setup
xg(t)
w(t)
h(t)
*
h(-t)
g(t)
xg(t)
LORAN-C pulse
Generator
1
2
xsk(t)


xs(t)
xc(t) = xs(t) + w(t)
FFT
FFT
Xg
Xc()
Xc()
Spectrum Division
with Windowing
Xg()
H()
Hanning window
Frequency Estimation
Algorithm
Skywave Delay
Estimation
h(t)
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ILA 32, 3-5 November 2003
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Signal Models
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Time-domain
received signal = groundwave + skywave(s) + noise
xc (t)

desired signal
unwanted
signals
Frequency-domain
Take FFT of the time-domain received signal
X c (f)  F { xc (t)}
Abbas Mohammed
ILA 32, 3-5 November 2003
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IFFT Analysis for Skywave Delay
Estimation

Perform a spectral-division operation
 X c (f) 


X
(f)
 0 
Spectrum of {received pulse / standard Loran pulse}

Take IFFT of the spectral-division = F
1
 X c (f)


X
(f)
 0 
Result: estimated arrival times of groundwave and
skywave pulses
Abbas Mohammed
skywave delay estimate
ILA 32, 3-5 November 2003
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Simulation Parameters

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SNR = 24 dB (-13 dB antenna)
Skywave-to-Groundwave Ratio (SGR) =
12 dB
Hanning window bandwidth = 50 kHz
Autocorrelation Matrix, Rˆ x , M  M , M = 4
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ILA 32, 3-5 November 2003
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Simulations Results 1
Even at this low SNR value, the groundwave and
skywave signals are isolated and identified
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ILA 32, 3-5 November 2003
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Simulations Results 2
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ILA 32, 3-5 November 2003
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Simulations Results 3
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ILA 32, 3-5 November 2003
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1
1
0.8
0.9
0.6
0.8
Normalized Amplitude
Signal Amplitude
Simulation Results Using Off-air
Data 1
0.4
0.2
0
-0.2
-0.4
0.7
0.6
0.4
0.3
0.2
-0.8
0.1
100
200
300
400
500
600
skywave component
0.5
-0.6
-1
0
groundwave component
0
0
50
100
Time (microseconds)
150
200
250
300
350
400
450
500
Time (microseconds)
Hanning window bandwidth of 50 kHz is used
Data Supplied by Van Nee of Delft University
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ILA 32, 3-5 November 2003
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Simulation Results Using Off-air
Data 2
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ILA 32, 3-5 November 2003
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Conclusions

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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
Abbas Mohammed
ILA 32, 3-5 November 2003
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Questions
Questions
You could also email questions to:
[email protected],
[email protected]
Abbas Mohammed
ILA 32, 3-5 November 2003
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