Estimation of the direction of arrival of signals from nano-satellites using antenna interferometry

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.