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 School of Informatics, University of Wales, Bangor, UK ILA 32, Boulder, Colorado, 3-5 November 2003

Abbas MohammedILA 32, 3-5 November 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

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

Abbas MohammedILA 32, 3-5 November 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

Abbas MohammedILA 32, 3-5 November 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

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

Abbas MohammedILA 32, 3-5 November 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

Abbas MohammedILA 32, 3-5 November 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

Abbas MohammedILA 32, 3-5 November 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

Abbas MohammedILA 32, 3-5 November Simulation Setup

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

Abbas MohammedILA 32, 3-5 November 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

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

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

Abbas MohammedILA 32, 3-5 November Simulations Results 2

Abbas MohammedILA 32, 3-5 November Simulations Results 3

Abbas MohammedILA 32, 3-5 November Simulation Results Using Off-air Data Time (microseconds) Signal Amplitude Time (microseconds) Normalized Amplitude Hanning window bandwidth of 50 kHz is used Data Supplied by Van Nee of Delft University skywave component groundwave component

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

Abbas MohammedILA 32, 3-5 November 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

Abbas MohammedILA 32, 3-5 November Questions You could also questions to: