- Direction of arrival (DOA) estimation for speech sources is an important task in audio signal processing. This task becomes a challenge in reverberant environments, which are typical to real scenarios. Several methods of DOA estimation for speech sources have been developed recently, in an attempt to overcome the effect of reverberation. One effective approach aims to identify time-frequency bins in the short time Fourier transform domain, that are dominated by the direct sound. This approach was shown to be particularly adequate for spherical arrays, with processing in the spherical harmonics domain. The direct-path dominance (DPD) test, and a method which is based on the directivity of the sound field are recent examples. While these methods seem to perform well, high reverberation conditions may degrade their performance. In this work, the structure of the spatial correlation matrix is comprehensively studied, showing that under some well-defined conditions, the DOA of the direct sound can be correctly extracted from its dominant eigenvector, even when contaminated by reflections. This new insight leads to the development of a new test, performing an enhanced decomposition of the direct sound (EDS), denoted the DPD-EDS test. The proposed test is compared to previous DPD tests, and to other recently proposed reverberation-robust methods, using computer simulations and an experimental study, demonstrating its potential advantage. The studies include multiple speakers in highly reverberant environments, therefore representing challenging real-life acoustics scenes.