{'fraction_non_alphanumeric': 0.02422145328719723, 'fraction_numerical': 0.0, 'mean_word_length': 5.602739726027397, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Two-Stage Decoupled DOA Estimation Based on Real Spherical Harmonics for Spherical Arrays

Spherical arrays have been widely used in direction-of-arrival (DOA) estimation in recent years. In this paper, we develop a unitary matrix to transform the complex spherical harmonics into real ones and obtain a real-valued covariance matrix after forward–backward (FB) averaging. Based on this transformation, a two-stage decoupled approach (TSDA) is proposed to decouple the estimation of the elevation and the azimuth. First, we propose a unitary spherical harmonics estimation of signal parameter via rotational invariance technique using one recurrence relation of real spherical harmonics to obtain the elevation estimation. Because of the limitation of using another recurrence relation to estimate the azimuth; second, we propose a unitary spherical harmonics root multiple signal classification (U-SHRMUSIC) to obtain the azimuth. Moreover, using the phase shift characteristic of real spherical harmonics, we also propose a low-complexity U-SHRMUSIC that can further decrease the computational load in the second stage. The proposed TSDA can not only achieve more accurate DOA estimation via FB averaging and two-stage estimation after decoupling but also reduce the computational complexity by exploiting real operations. Computer simulations, especially simulations of the real environment, validate the effectiveness of the proposed method.