Low complexity subspace based direction of arrival estimation for large arrays

Large array size real time direction finding systems like phased array radars require very fast processing of signals. With subspace based array signal processing like MUltipleSIgnalClassification (MUSIC) algorithm high accuracy and resolution can be achieved if the data collection time is sufficiently large or the Signal to Noise Ratio (SNR) is adequately high. However high computational complexity of search based MUSIC algorithm prohibits its use for large arrays. Root MUSIC was proposed to reduce the computational complexity of search based MUSIC algorithm. It avoids the search in MUSIC by polynomial rooting to estimate Direction of Arrival (DOA). However the computational complexity of polynomial roots finding is still high for large array size real time systems. For large arrays, we propose to use Discrete Fourier Transform (DFT) based MUSIC algorithm where the polynomial rooting in root MUSIC is replaced with DFT, which can be computed efficiently with Fast Fourier Transforms (FFT). The Hierarchical Pruned FFT (HPFFT) based method in this paper, further reduces the computational complexity for large array size. Adaptive techniques are chosen for subspace estimation which require much lesser computations compared to Eigen Value Decomposition (EVD) based methods. It is proposed that low complexity hierarchical pruned FFT based MUSIC algorithm combined with adaptive subspace estimation, can be used for large array based DOA estimation. Simulation results for rectangular array are presented to compare the complexity and performance of root MUSIC, DFT MUSIC and HPFFT MUSIC.