Wavenumber support regions for arbitrary arrays (Q1077363)

In multidimensional spectral estimation it is common to define spectra using wavenumber as an independent variable. Here, an interesting attempt to define wavenumber support (WS) is presented. This is achieved by introducing the concept of the aliasing frequency \(\Omega\) of an array, so that, for a given array, signals, whose frequencies are outside the interval (-\(\Omega\),\(\Omega)\) are indistinguishable. Linear and planar arrays are considered. The main idea of the theory is that for real arrays the WS must be a compact set of the Euclidean space. This is obtained by postulating that the element positions in the array are inaccurately known, i.e. they are known with an error \(\delta\) significantly smaller than the smallest of the element distances. In this case the aliasing frequency is finite. It is shown that the results could be obtained by assuming an uncertainty in the knowledge of the phase.