1. 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 Abbas.Mohammed@bth.se, Fernand.le_roux@bth.se School of Informatics, University of Wales, Bangor, UK ILA 32, Boulder, Colorado, 3-5 November 2003

2. Abbas MohammedILA 32, 3-5 November 20032 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

3. Abbas MohammedILA 32, 3-5 November 20033 The Choice of the sampling Point ? Before bandpass filtering 020406080100120140160180200 -5 -4 -3 -2 0 1 2 3 4 5 Time (microseconds) Signal Amplitude standard zero-crossing groundwave skywave The time reference point at 30 sec is marked the standard zero-crossing

4. Abbas MohammedILA 32, 3-5 November 20034 Bandpass filtering effects Figure shows a 5 th order Butterworth filter of 20 kHz bandwidth Bandpass filtering reduces out of band noise and interference, thereby improving SNR of the received Loran signals

5. Abbas MohammedILA 32, 3-5 November 20035 020406080100120140160180200 -5 -4 -3 -2 0 1 2 3 4 5 Signal Amplitude 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

6. Abbas MohammedILA 32, 3-5 November 20036 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.

7. Abbas MohammedILA 32, 3-5 November 20037 Skywave Estimation Technique This paper revisits the IFFT Technique Eigen-decomposition approach for skywave delay estimation, such as MUSIC and ESPRIT algorithm

8. Abbas MohammedILA 32, 3-5 November 20038 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

9. Abbas MohammedILA 32, 3-5 November 20039 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

10. Abbas MohammedILA 32, 3-5 November 200310 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

11. Abbas MohammedILA 32, 3-5 November 200311 Simulation Setup

12. Abbas MohammedILA 32, 3-5 November 200312 Signal Models Time-domain received signal = groundwave + skywave(s) + noise desired signalunwanted signals Frequency-domain Take FFT of the time-domain received signal

13. Abbas MohammedILA 32, 3-5 November 200313 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

14. Abbas MohammedILA 32, 3-5 November 200314 SNR = 24 dB (-13 dB antenna) Skywave-to-Groundwave Ratio (SGR) = 12 dB Hanning window bandwidth = 50 kHz Autocorrelation Matrix,,, M = 4 Simulation Parameters

15. Abbas MohammedILA 32, 3-5 November 200315 Even at this low SNR value, the groundwave and skywave signals are isolated and identified Simulations Results 1

16. Abbas MohammedILA 32, 3-5 November 200316 Simulations Results 2

17. Abbas MohammedILA 32, 3-5 November 200317 Simulations Results 3

18. Abbas MohammedILA 32, 3-5 November 200318 Simulation Results Using Off-air Data 1 0100200300400500600 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Time (microseconds) Signal Amplitude 050100150200250300350400450500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (microseconds) Normalized Amplitude Hanning window bandwidth of 50 kHz is used Data Supplied by Van Nee of Delft University skywave component groundwave component

19. Abbas MohammedILA 32, 3-5 November 200319 Simulation Results Using Off-air Data 2

20. Abbas MohammedILA 32, 3-5 November 200320 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

21. Abbas MohammedILA 32, 3-5 November 200321 Questions You could also email questions to: Abbas.Mohammed@bth.se, Fernand.le_roux@bth.se