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

Abbas Mohammed ILA 32, 3-5 November 2003 2

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


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”


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


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


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.


Skywave Estimation Technique

This paper revisits the IFFT Technique

Eigen-decomposition approach for skywave delay estimation, such as MUSIC and ESPRIT algorithm


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


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


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


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


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


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


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


Even at this low SNR value, the groundwave and skywave signals are

isolated and identified

Simulations Results 1


Simulation Results Using Off-air Data 1

0 100 200 300 400 500 600-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

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

0.7

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


Simulation Results Using Off-air Data 2


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


Questions

Questions

You could also email questions to:[email protected],[email protected]

eigen-decomposition techniques for skywave interference detection in loran-c receivers

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