Synthesis of Angle Arrays by the NDF of the Radiation Integral

Abstract

Linear arrays have been well studied for their widespread applications. However, they suffer from severe limitations in their scanning capabilities due to the inherent main beam spreading. The combination of two linear arrays, radiating simultaneously, may provide the coverage of a wide angular domain by identical beams. More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its Singular Value Decomposition and the Number of Degrees of Freedom of the source according to its geometry. Then a connection with the known closed form results of the single line case is established. Next, for an angle geometry, the discussion of the Point Spread Function reveals the condition to be achieved for an angle source to radiate identical beams with an angular coverage larger than the one of a single linear source with the same total length. Finally, the approach is applied to linear arrays, arranged in an angle geometry, also including the effect of the element factor. Numerical results about the synthesis of identical focused radiation patterns demonstrate the usefulness of the approach.

Synthesis of High Directivity Beams for Conformal Sources

“…where θ ∈ [−π, π] is the observation variable, ‖ ′( )‖ is the differential element of , β = 2π/λ is the free space wavenumber and λ is the wavelength. As in [10], [14], the weight function ℎ(θ, ) is meant to add a directive behavior to each source element defined by the η parametric variable. In particular, if θ is the direction orthogonal to the η curve element, the function…”

“…The two rectilinear sources support the electric currents 1 and 2 which give rise to the following field is the angle providing the direction orthogonal to each segment. In [10], it has been found that, when dealing with sets of non-overlapping rectilinear sources, an approximation of the NDF is given by the sum of the NDF due to a single rectilinear source. Hence, in this case,…”

“…Such a method would be very useful in an early stage of an antenna synthesis problem to steer the design choice in the trade-off between mechanical and electrical performances. In [9], [10] an inverse problem approach is applied to examine the radiation properties of different conformal sources. It is based on the evaluation of the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF) of the relevant radiation operator.…”

NDF of Scattered Fields for Strip Geometries

“…In References [18][19][20], a different problem is considered, i.e., the inverse source problem when a (2D) source current must be reconstructed from its radiated field. Our investigation focused on estimating the NDF of the source according to its geometry so that a robust imaging algorithm can be set up.…”

“…This can be achieved by the SVD of the relevant radiation operator, analytically, when possible, by asymptotic upper bounds or numerically. For instance, circumference [18], angle [19], and conic [20] sources have been examined. In particular, in [19], theoretical arguments are developed for a collection of linear sources to show the role of their total electrical length to determine their NDF.…”