Efficient Planar Near-Field Measurements for Radiation Pattern Evaluation by a Warping Strategy

Abstract

The sampling of the near-field radiated by a planar source observed over a finite planar aperture is addressed. To this end, we employ the warping method that amounts to properly change the observation variables and finding the sampling points as those that allow to approximate the singular values of the radiation operator up to the so-called number of degrees of freedom. In particular, the warping transformations allow to approximate the kernel function of the relevant operator as a band-limited function and hence the sampling theorem is adopted to devise the discretization scheme. Here, we generalize the warping method to the full vector case and introduce a spatially varying oversampling strategy that allows to deal with measurement apertures which are larger than the source. It is shown that the sampling points need to be non-uniformly arranged across the measurement aperture but their number is generally much lower than classical half-wavelength sampling. A numerical analysis is included to support the theoretical arguments. Finally, numerical experiment-based results concerning the radiation pattern estimation of a planar array antenna are presented. To this end, experimental data collected under a uniform half-wavelength sampling scheme are first interpolated over the required non-uniform grid and then processed to obtain the radiation pattern INDEX TERMS Antenna measurements, Near-field far-field (NFFF) transformation, Sampling methods, Antenna radiation patterns, Non-uniform sampling

Non-Uniform Warping Sampling for Data Reduction in Planar Array Diagnostics

“…This crucial point has been recently successfully pursued in [21], [22]. There, a field sampling strategy, that requires a number of measurements M only slightly greater than the NDF reported in (9), was derived.…”

“…This fact has been indeed exploited in [21], where the so-called warping method was introduced and used to derive a new deterministic near-field sampling strategy. This allowed for a remarkable reduction of data points by keeping accuracy close to the λ/2 sampling while estimating the radiation pattern [22]. This result can be in principle useful for CS as well, since the points it returns actually represent the baseline from which further data reduction can be achieved if unknown sparsity information is available.…”

“…Summarizing, this contribution is based on two main ingredients: the warping sampling strategy developed in [22], which allows to perform diagnostics by a significant reduction of data points as compared to the λ/2 sampling, and the application of a detection strategy to highlight the turned-off elements in the array.…”

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

“…Please note that a scattering operator similar to (1) can be obtained by exploiting the Kirchhoff model to the scattering equation when strong scatterers are considered. Our aim is to design a strategy to collect the data on the rectangular domain Ω o × Ω k by following the same approach proposed in [36][37][38]. This consists of discretizing the data space so that the resulting discrete version of the eigenvalue problem associated with the left singular functions of A shares the first NDF eigenvalues of its continuous counterpart.…”

“…Such an approach has been already exploited in the framework of inverse source problems in [36][37][38], where near-field data were collected but only the spatial variable was considered. Instead, in this paper also the frequency diversity is taken into account.…”