Wavefield modeling and array processing .I. Spatial sampling

Transformations for nonideal uniform circular arrays operating in correlated signal environments

“…Indeed, the whole issue of lack of robustness can be related to the phenomenon of "resonance" in classical wave mechanics [19]. Resonance is an inherent limitation of array processing and will arise for certain array geometries, that is, the placement of the antenna elements relative to the operating wavelength of the array.…”

“…It is worthwhile pointing out here that, mathematically, the output signals of the antenna array can also be modeled as being the result of applying a sampling matrix to a representation of the propagating signal wavefield [19]. Resonance manifests itself as a loss of rank in the sampling matrix thus lowering the number of signals the UCA can resolve.…”

“…We first compute and then check its row norms. We retain as many rows as possible since gives the best approximation of the UCA steering vector in mode space [19]. We replace only those rows whose norm is excessively large with rows found by solving the corresponding subproblems of .…”

“…An appropriate choice for , and hence by (6), for some predetermined , is given by [2] and (8) where the first inequality relates to the spatial sampling condition [15], [19], and the second inequality determines the accuracy of the approximation in (7). To facilitate our subsequent discussions, we define the vector (9)…”

“…Denote by the array response (or steering) vector of the UCA in response to a narrow-band signal of wavelength arriving from angle in the azimuth plane. The th component of is given by (1) where is the complex gain pattern of the th element, is the wavenumber, is the angular position of the th array element (2) and to circumvent spatial aliasing, it is necessary that the interelement spacing 2 is less than [15], [19], or alternatively, . Suppose the array elements are identical and omnidirectional such that .…”