{"ID":2831334,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08887","arxiv_id":"2512.08887","title":"A Fast Broadband Beamspace Transformation","abstract":"We present a new computationally efficient method for multi-beamforming in the broadband setting. Our \"fast beamspace transformation\" forms $B$ beams from $M$ sensor outputs using a number of operations per sample that scales linearly (to within logarithmic factors) with $M$ when $B\\sim M$. While the narrowband version of this transformation can be performed efficiently with a spatial fast Fourier transform, the broadband setting requires coherent processing of multiple array snapshots simultaneously. Our algorithm works by taking $N$ samples off of each of $M$ sensors and encoding the sensor outputs into a set of coefficients using a special non-uniform spaced Fourier transform. From these coefficients, each beam is formed by solving a small system of equations that has Toeplitz structure. The total runtime complexity is $\\mathcal{O}(M\\log N+B\\log N)$ operations per sample, exhibiting essentially the same scaling as in the narrowband case and vastly outperforming broadband beamformers based on delay and sum whose computations scale as $\\mathcal{O}(MB)$. Alongside a careful mathematical formulation and analysis of our fast broadband beamspace transform, we provide a host of numerical experiments demonstrating the algorithm's favorable computational scaling and high accuracy. Finally, we demonstrate how tasks such as interpolating to ``off-grid\" angles and nulling an interferer are more computationally efficient when performed directly in beamspace.","short_abstract":"We present a new computationally efficient method for multi-beamforming in the broadband setting. Our \"fast beamspace transformation\" forms $B$ beams from $M$ sensor outputs using a number of operations per sample that scales linearly (to within logarithmic factors) with $M$ when $B\\sim M$. While the narrowband version...","url_abs":"https://arxiv.org/abs/2512.08887","url_pdf":"https://arxiv.org/pdf/2512.08887v2","authors":"[\"Nakul Singh\",\"Coleman DeLude\",\"Mark Davenport\",\"Justin Romberg\"]","published":"2025-12-09T18:24:04Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}