Superdirective Beamforming Based on the Krylov Matrix

Superdirective beamforming has attracted a significant amount of research interest in speech and audio applications, since it can maximize the directivity factor (DF) given an array geometry and, therefore, is efficient in dealing with signal acquisition in diffuse-like noise environments. However, this beamformer is very sensitive to sensor self-noise and mismatch among sensors, which considerably restricts its use in practical systems. This paper develops an approach to superdirective beamforming based on the Krylov matrix. We show that the columns of a proposed Krylov matrix, which span a chosen dimension of the whole space, are interesting beamformers; consequently, all different linear combinations of those columns lead to beamformers that have good properties. In particular, we develop the Krylov maximum white noise gain and Krylov maximum DF beamformers, which are obtained by maximizing the WNG and the DF, respectively. By properly choosing the dimension of the Krylov subspace, the developed beamformers that can make a compromise between reasonable values of the DF and white noise amplification. We also extend the basic idea to the design of the Krylov maximum front-to-back ratio, parametric superdirective, and parametric supercardioid beamformers.