{'fraction_non_alphanumeric': 0.0208105147864184, 'fraction_numerical': 0.004381161007667032, 'mean_word_length': 5.093333333333334, '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}}
3D Coprime Arrays in Sparse Sensing

Coprime arrays are a class of sensor arrays that play a crucial role in various signal processing tasks because of their desirable properties such as sparsity and increased degrees of freedom (DOF) of coarrays. In this contribution, a new class of three-dimensional (3D) arrays is constructed from pure cubic fields. By studying the properties of cubic integers, we convert the problem of finding two coprime 3-by-3 integer matrices to that of two coprime integers in the ring of integers of a cubic field, which significantly reduces the design complexity and expands the design space of these matrices. The proposed construction offers naturally commutative matrices and includes generalized circulant matrices as a special case (under certain restriction of a parameter). The surged DOF is guaranteed by the generalized Chinese Remainder Theorem (CRT) for rings and ideals.