Generalized broadband beamforming using a modal decomposition

We propose a new broadband beamformer design technique which produces an optimal beampattern for any set of samples in space and time. The modal subspace decomposition (MSD) technique is based on projecting a desired pattern into the subspace of patterns achievable by a particular set of space-time sampling positions. This projection is the optimal achievable pattern, in the sense that it minimizes the mean-squared error (MSE) between the desired and actual patterns. The main advantage of the technique is versatility as it can produce optimal beamformers for both sparse and dense arrays, non-uniform and asynchronous time sampling, and dynamic arrays where sensors can move throughout space. It can also be applied to any beampattern type, including frequency-invariant and spot pattern design.