{'fraction_non_alphanumeric': 0.015558698727015558, 'fraction_numerical': 0.0, 'mean_word_length': 5.378378378378378, '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}}
Detection of subspace waveforms in subspace interference and noise

The natural models of multi-access communication and modern radar and sonar systems involve infinite-dimensional waveform spaces. A common problem in these systems is the detection of subspace signals measured in the presence of subspace interference and broadband noise. By and large, the existing theory for such problems has been developed for finite-dimensional measurement spaces rather than the infinite-dimensional waveform spaces needed here. In this paper the log of the generalized likelihood ratio detector for the waveform problem is derived and is shown to have a certain chi-squared distribution, depending on the hypothesis.