Variance of the Bearing Angle of a Discrete Linear-Difference Array in a Random Transmission Medium

Abstract

An approximate expression has been derived for the variance of the bearing angle, about the central null point, of a discrete linear-difference array. The Chernov formulation for plane-wave propagation in a random medium, restricted to small absolute values of the phase and amplitude fluctuations, is used as a basis for the derivation. It is further assumed that the phase and amplitude fluctuations are zero-mean normal random variables. A special case is considered in detail for large values of the wave parameter D = 4R/ka2, where R is the range, k is the wavenumber, and a is a characteristic correlation distance. For this case, the variance of bearing angle with range is linear and is nearly independent of the frequency.