Coupling criteria for arrays in a channel

Abstract

In this paper, an analogy is made and developed between a linear array of receivers with far-field sources in an unbounded, homogeneous medium and an arbitrary array of receivers with arbitrarily placed sources in a channel. The transfer function of a signal transmitted through a channel is the well-studied transmission loss (TL). The singular value decomposition (SVD) is performed on the transfer function between sources and receivers. The three components of the SVD are related to various factors in the case of the linear array in an unbounded, homogeneous medium. The case of a translationally invariant channel described using modes is considered. This modal description is also related to the three components of the SVD. The sum of the eigenvalues of the SVD is proposed as a single number which quantitatively describes the amount of coupling between an arbitrary array and the sound channel, assuming that the distribution of sources spans the propagating modes. This single number can then be used to assess the ability of various array configurations to sample the sound channel. [Work supported by ONR.]