Kinematic Properties of Short-Pulsed Sparse Transmitting Arrays

Abstract

Abstract-The kinematic properties of an array of transmitting antennas that are transiently excited by a sequence of modulated pulses, with high repetition rate, are explored.The array's parameterization is carried out via the energy radiation pattern. It is shown that the energy radiation pattern can be decomposed into a set of different types of beam contributions, defined over a beamskeleton, which is determined by the array's physical and excitation parameters. The different types of beams are main beams, gratinglobe beams and cross-pulsed lobe beams, each corresponding to a different pulsed interference mechanism. While grating lobes are timeharmonic phenomena, cross-pulsed lobes are unique for excitation with a pulsed sequence. The different beam types set limits for array sparsity in terms of the array's physical and excitation parameters. The array's directivity is introduced as a figure of merit of its performance and to demonstrate the resulting effect of the time-domain excitation characteristics. The array's parameterization can be used with any type of excitation -from extreme narrow band (time-harmonic) to extreme ultra-wideband (transient/short pulsed) excitation. For timeharmonic excitation, the resulting characterization matches that of the classical frequency domain antenna theory.

Characteristic Basis Functions of the Energy Radiation Pattern of a Sparse True Time Delay Array

“…The choice of r 0 (t), ω 0 , and φ depends on the temporal characteristics of ψ(t). This modeling of ψ(t) does not limit the discussion to a certain type of pulsed excitations, as will be shown below; rather, it allows some of the unique properties attributed to NB, QM and UWB/SP excitation regimes to be quantified (for additional discussion, see, [3]). …”

“…npφ (t), whenevert is greater than the single pulse duration (pulsed-width), see, e.g., [3]. In such a caset is the pulse repetition duration (with PRF =t…”

“…As such, the ERP provides a simpler representation by only one coordinate, i.e., the angular, of the radiation pattern. Nevertheless, in terms of the observability of certain kinematic characteristics of the TD array, it was already shown, see, e.g., [2,3] that they also have an impact on the ERP. Therefore, the ERP is a valid tool for TTD array kinematic analysis.…”

“…In a previous publication [2,3] a kinematic analysis of the TTD array was performed with the radiated field (in the time domain) and via its ERP. This analysis yielded a representation of the radiation pattern by the array's set of radiated beams that are structured on an angular predetermined lattice.…”

“…For an equi-spaced linear array, the decomposition of the ERP into its corresponding CBFs is carried out using an eigendecomposition of Toelplitz and circulant matrixes [4][5][6]. The resulting set of CBFs encapsulates the possible kinematic characteristics of the array and therefore is complementary to [2,3]. In particular it provides a new, and refined, point of view on the TTD array's sparsity and gives additional analysis tools for obtaining some bounds and characteristics of the array's performance upon synthesizing a TTD array.…”