Array gain of a broadside vertical line array in shallow water

Abstract

An analysis is presented of the signal gain and the noise gain of a broadside vertical line array operating in a shallow-water channel with one lossy boundary. The signal gain is derived by representing the signal field as a sum of normal modes, and is shown to lie between N and 2N provided the number of modes in the field is less than (h/2L); and a simple criterion is derived for the maximum useful aperture of the array, beyond which no significant improvement in signal gain can be achieved. The derivation of the noise gain is based on the assumption that, over the aperture of the array, the noise field can be represented as a linear superposition of plane waves. On introducing the high-N approximation it is shown that, for arbitrary anisotropy, the noise gain is the reciprocal of a series of Bernoulli polynomials, the coefficient of each being determined by the directional density function of the noise. A discussion of the noise gain in isotropic noise and in three different anisotropic noise fields illustrates the utility of the approximate method for determining the noise gain.