Eigen-decomposition Techniques for Skywave Interference Detection in Loran-C Receivers

1. Eigen-decomposition Techniques for Skywave Interference Detection in Loran-C Receivers Abbas Mohammed, Fernand Le Rouxand 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. 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 ILA 32, 3-5 November 2003

3. The Choice of the sampling Point ?Before bandpass filtering 5 standard zero-crossing 4 3 2 1 Signal Amplitude 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” ILA 32, 3-5 November 2003

4. Bandpass filtering effects Figure shows a 5th order Butterworth filter of 20 kHz bandwidth Bandpass filtering reduces out of band noise and interference, thereby improving SNR of the received Loran signals ILA 32, 3-5 November 2003

5. The Choice of the sampling Point ?After bandpass filtering 5 4 typical later zero-crossing selected 3 2 1 Signal Amplitude 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 ILA 32, 3-5 November 2003

6. Objective of Skywave Delay Estimation Techniques Design a receiver whichadjusts thesamplingpointadaptively 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. ILA 32, 3-5 November 2003

7. Skywave Estimation Technique • This paper revisits the IFFT Technique • Eigen-decomposition approach for skywave delay estimation, such as MUSIC and ESPRIT algorithm ILA 32, 3-5 November 2003

8. 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 ILA 32, 3-5 November 2003

9. 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 ILA 32, 3-5 November 2003

10. 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 ILA 32, 3-5 November 2003

11. Simulation Setup ILA 32, 3-5 November 2003

12. Signal Models • Time-domain received signal = groundwave + skywave(s) + noise desired signal unwanted signals • Frequency-domain Take FFT of the time-domain received signal ILA 32, 3-5 November 2003

13. 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 ILA 32, 3-5 November 2003

14. Simulation Parameters • SNR = 24 dB (-13 dB antenna) • Skywave-to-Groundwave Ratio (SGR) = 12 dB • Hanning window bandwidth = 50 kHz • Autocorrelation Matrix, , , M = 4 ILA 32, 3-5 November 2003

15. Simulations Results 1 Even at this low SNR value, the groundwave and skywave signals are isolated and identified ILA 32, 3-5 November 2003

16. Simulations Results 2 ILA 32, 3-5 November 2003

17. Simulations Results 3 ILA 32, 3-5 November 2003

18. Simulation Results Using Off-air Data 1 1 1 0.8 0.9 groundwave component 0.6 0.8 0.4 0.7 0.2 0.6 skywave component Signal Amplitude Normalized Amplitude 0 0.5 -0.2 0.4 -0.4 0.3 -0.6 0.2 -0.8 0.1 -1 0 0 100 200 300 400 500 600 0 50 100 150 200 250 300 350 400 450 500 Time (microseconds) Time (microseconds) Hanning window bandwidth of 50 kHz is used Data Supplied by Van Nee of Delft University ILA 32, 3-5 November 2003

19. Simulation Results Using Off-air Data 2 ILA 32, 3-5 November 2003

20. 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 ILA 32, 3-5 November 2003

21. Questions Questions You could also email questions to: Abbas.Mohammed@bth.se, Fernand.le_roux@bth.se ILA 32, 3-5 November 2003