Reactance domains unitary MUSIC algorithms based on real-valued orthogonal decomposition for electronically steerable parasitic array radiator antennas

This study proposes three algorithms, requiring only real-valued operations, to estimate the directions of arrival (DoAs) of correlated sources impinging onto electronically steerable parasitic array radiator (ESPAR) antennas. The constraints on the proposed algorithms are the same as those imposed onto the reactance domains-MUSIC (RD-MUSIC) algorithm allowing superior high-resolution localisation capabilities even for correlated sources scenarios with reduced computational cost as well as a low processing time compared with existing schemes. The first of the three proposed algorithms is a real-valued formulation of the standard MUSIC algorithm for ESPAR antennas that reduces significantly the computational complexity in the eigen-analysis stage. However, the other two algorithms are based on real-valued orthogonal decompositions (RVOD) techniques to estimate the noise subspace of the covariance matrices. We demonstrate that both the RVOD techniques can efficiently replace the requirement of singular value decomposition or eigenvalue decomposition which reduces further the computational complexity and makes the DoAs estimation faster. The Cramer Rao bound on the variance of DoAs estimated by the three proposed algorithms is analysed. The asymptotic performance of the developed methods is studied and compared with conventional antenna arrays. The simulation results confirm that the developed methods achieve superior precision and accuracy in DoAs estimation compared to RD-MUSIC even for correlated signals and prove the validity of our approach.