{'fraction_non_alphanumeric': 0.019917582417582416, 'fraction_numerical': 0.0027472527472527475, 'mean_word_length': 6.072815533980583, '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}}
Concurrent adaptive beamforming for standard hexagonal array based on dual norm‐constraint correntropy in the presence of alpha stable noise

This article presents dual norm‐constraint correntropy beamforming methods for standard hexagonal array (SHA) to mitigate the effects of alpha stable noise and maintain the sparsity of filter coefficients. Both goals are achieved simultaneously through the use of norm regularization constraint and the novel convex combination technique. Firstly, we construct constrained optimization equations considered the constraints present in the constrained least‐mean‐square (CLMS) algorithm by incorporating the maximum correntropy criterion (MCC). In addition, in order to decrease the number of active elements for limited power supply array system, we introduce an L1‐norm equation to the list of constraints of the adaptive filter that forces the coefficients with small magnitudes to zero. Then, we utilize the convexity and stability of L2‐norm to devise the constrained maximum correntropy gradient L2‐norm (CMCG‐L2) for further reducing the misadjustment caused by alpha noise and improving the directivity performance of the adaptive beamformer. A novel convex combination scheme is also reported to satisfy the conflicting requirements between the sparsity and mean‐square‐error. Our simulation results demonstrate the superiority of the proposed methods over other previously developed beamforming techniques.