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Estimation of the direction of arrival of signals from nano-satellites using antenna interferometry
Author(s)
Fenni, Magano Tweetheni Shidhika
Date Issued
2014
Type
Thesis
Publisher
Cape Peninsula University of Technology
Abstract
The thesis reports on the evaluation and comparison of various signal processing algorithms
for estimating the direction of arrival (DOA) of a high frequency (HF) beacon signal from a
CubeSat in Low Earth Orbit (LEO). The DOA of the HF beacon signal is expressed in terms
of the two angles, azimuth ( α ) and elevation ( ). The azimuth and elevation angles of the
received HF signal are calculated from the phase differences between signals observed at
three elements of an L-shaped crossed-loop antenna array. The algorithms which were
evaluated are the Zero Crossing (ZC), Cross Correlation (CC), Fast Fourier Transform (FFT)
and Cross Power Spectral Density (CPSD) algorithms. A theoretical analysis was done to
demonstrate that the phase differences at the radio frequency (RF) of the beacon are
propagated to the baseband signals. The algorithms were thus tested using simulated
baseband signals as would be derived from the RF signals intercepted by the three elements
of an L-shaped crossed-loop antenna array. Gaussian noise with a given signal-to-noise ratio
(SNR) was added to the simulated baseband signals. The algorithms were implemented in
MATLAB. The criteria for the selection of the best algorithm were accuracy and speed. The
standard deviation (SD) of the azimuth and elevation errors was used to measure the
performance accuracy of each algorithm, while the computational time for a given number of
samples and runs was used to express the speed of each algorithm.
First the ZC, CC, FFT and CPSD algorithms were evaluated for various SNR values, and
compared with respect to SD of the azimuth and elevation errors. The analysis of the
simulations demonstrate that the FFT and CPSD algorithms outperform the ZC and CC
algorithms by estimating the DOA with a small SD of errors even at the low SNR of 0 dB,
where the noise amplitude is the same as the signal amplitude. The ZC algorithm estimates
the DOA with a large SD of error at low SNR due to multiple ZC points occurring during the
same cycle. The ZC algorithm breaks down when the SNR decreases below 35 dB. The
accuracy of the ZC algorithm depends on the method by which the ZC points are detected.
The CC algorithm breaks down when the SNR decreases below 10 dB. The CPSD and FFT
algorithms break down when the SNR decreases below – 20 dB. However, at a high SNR of
40 dB and above, all the algorithms estimate the DOA with a SD of error smaller than 1˚ for
the azimuth and elevation. Next, the ZC, CC, FFT and CPSD algorithms were compared with
respect to computation time. The FFT was found to be the fastest algorithm. Although the
CPSD and the FFT algorithms reach the same accuracy in the estimation of the DOA, the
FFT was selected as the optimum algorithm due to its better computation time.
Recommendations are made regarding the implementation of the proposed algorithms for
real signals from the HF direction finding (DF) array. At the time of submission of this thesis,
such signals were not yet available.
for estimating the direction of arrival (DOA) of a high frequency (HF) beacon signal from a
CubeSat in Low Earth Orbit (LEO). The DOA of the HF beacon signal is expressed in terms
of the two angles, azimuth ( α ) and elevation ( ). The azimuth and elevation angles of the
received HF signal are calculated from the phase differences between signals observed at
three elements of an L-shaped crossed-loop antenna array. The algorithms which were
evaluated are the Zero Crossing (ZC), Cross Correlation (CC), Fast Fourier Transform (FFT)
and Cross Power Spectral Density (CPSD) algorithms. A theoretical analysis was done to
demonstrate that the phase differences at the radio frequency (RF) of the beacon are
propagated to the baseband signals. The algorithms were thus tested using simulated
baseband signals as would be derived from the RF signals intercepted by the three elements
of an L-shaped crossed-loop antenna array. Gaussian noise with a given signal-to-noise ratio
(SNR) was added to the simulated baseband signals. The algorithms were implemented in
MATLAB. The criteria for the selection of the best algorithm were accuracy and speed. The
standard deviation (SD) of the azimuth and elevation errors was used to measure the
performance accuracy of each algorithm, while the computational time for a given number of
samples and runs was used to express the speed of each algorithm.
First the ZC, CC, FFT and CPSD algorithms were evaluated for various SNR values, and
compared with respect to SD of the azimuth and elevation errors. The analysis of the
simulations demonstrate that the FFT and CPSD algorithms outperform the ZC and CC
algorithms by estimating the DOA with a small SD of errors even at the low SNR of 0 dB,
where the noise amplitude is the same as the signal amplitude. The ZC algorithm estimates
the DOA with a large SD of error at low SNR due to multiple ZC points occurring during the
same cycle. The ZC algorithm breaks down when the SNR decreases below 35 dB. The
accuracy of the ZC algorithm depends on the method by which the ZC points are detected.
The CC algorithm breaks down when the SNR decreases below 10 dB. The CPSD and FFT
algorithms break down when the SNR decreases below – 20 dB. However, at a high SNR of
40 dB and above, all the algorithms estimate the DOA with a SD of error smaller than 1˚ for
the azimuth and elevation. Next, the ZC, CC, FFT and CPSD algorithms were compared with
respect to computation time. The FFT was found to be the fastest algorithm. Although the
CPSD and the FFT algorithms reach the same accuracy in the estimation of the DOA, the
FFT was selected as the optimum algorithm due to its better computation time.
Recommendations are made regarding the implementation of the proposed algorithms for
real signals from the HF direction finding (DF) array. At the time of submission of this thesis,
such signals were not yet available.
Additional information
Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2014
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