Use of a Two-Dimensional Array to Receive an Unknown Signal in a Dispersive Waveguide

Abstract

A relatively simple method is discussed for estimating the phase velocity and direction of an unknown plane-wave signal, propagating across two-dimensional array in a dispersive waveguide. The finite Fourier transform is applied to the output signal of each sensor, and the phases of the smoothed frequency components calculated. The phases of the components are linearly regressed on sensor positions to produce estimates of the wave slowness components. Neither the phase nor group velocity dispersion curves need to be known, except for upper and lower estimates of the range. By smoothing over frequency and transforming, estimates are obtained of the direction and phase velocity of the signal. The precision of estimates depends on the signal-to-noise ratio, the square root of the number of sensors, and the number of wavelengths that fall in the array. Each frequency is treated separately, so that the direction and phase velocity are obtained as a function of frequency. Since the individual frequency components of the signal are separated, the signals observed on a large array can be combined, even though the dispersion is appreciable over the array. For good signal-to-noise power ratios, the dispersion curves are a direct result from the analysis.