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Incoherent Synthesis of Sparse Broadband Arrays based on a Parameter-Free Subspace Clustering

In this paper, we propose an incoherent design method of sparse broadband arrays that optimizes the number of sensors and their positions simultaneously. We introduce an iterative clustering procedure that merges different groups of sensors with a small distance, in terms of Bhattacharyya distance, between their angle distributions. The iterative clustering procedure is initialized with a large number of groups of sensors, and computes in each iteration a clustering score and a threshold. Then, near groups are merged into joint groups, yielding a new set of groups of sensors. We show that the optimal set of sensors is obtained when the clustering score is larger than the threshold, indicating that the remaining groups are distant. The proposed approach is demonstrated by a design of a superdirective beamformer, and its performance is compared with an existing incoherent approach. Experimental results show improved performance in terms of a more favorable tradeoff between directivity factor and white noise gain.