Kristopher Buchanan

Examination of the near field response of circular antenna arrays

A uniformly distributed family of circular topology is analyzed using probabilistic methods to find mean valued radiation characteristics in the near field (Fresnel zone). Linear arrays with circular and spherical distributions of one, two and three dimensional spaces are compared using this analysis to obtain benchmark performance metrics. This novel method also determines the statistical effects of converging pattern behavior at the hyperfocal distance of each topology. Closed form expressions from this method provide ease in statistical analysis. As a result, this work presents a comparison of data for each respective circularly bounded distribution with its respective hyperfocal distance. Results of each dimensional topology also maintain the same aperture size in comparison to each respective distribution range resolution capability.

Investigation of beamforming patterns from volumetrically distributed phased arrays

This work presents distributed beamforming using three dimensional randomly distributed volumetric arrays. This work examines a statistical ensemble (mean-valued) of average beampattern behavior for canonical and non-canonical volumetrically bound distributed (random) antenna arrays. Cubical, cylindrical, and spherical topologies of isotropic elements are analyzed to show beamforming and scanning from zenith to meridian for canonical topologies. In addition, small amounts of work have previously been investigated and therefore this work helps to enlighten with illustrations of the beampattern phenomena of a select few non-conically bound distributed and volumetric structures. To validate the distributed array pattern behavior, the manifold is composed of one million isotropic radiators densely populated amongst geometrical bounds to examine characteristic pattern behavior. This provides faithful convergence of numerical beampatterns to their expected (mean) patterns. Last of all, results show an increasing complexity of pattern behavior for use in many spatial advancements in distributed beamforming.

Synchronization considerations using circularly distributed arrays

This work statistically examines the receiver capabilities for circularly distributed ad-hoc array topologies of independently controlled element radiators. Performance metrics observed in this study include maximum SNR, tolerance on receiver amplitude variations, phase shifter accuracy and received signal strength variations in the presence of noise and fading.

A computer vision-based framework for the synthesis and analysis of beamforming behavior in swarming intelligent systems

This work proposes a computer vision-based framework for analyzing and synthesizing the collaborative radiation behavior from swarming clusters of intelligent systems. Radiating sensor nodes with inertial measurement units and optical identification features represent the networked cluster of radiators. These create a set of object-distinguishable nodes on a reticulating platform capable of arbitrary spatial distributions. Node discovery and tracking algorithms based on open-source computer vision libraries use image and depth-of-field information from multi-spectral cameras. These locate nodes and their volumetric distribution within the cluster. An automated system then derives the weighted phases for collaborative beamforming from the resulting nodal distribution. Measured and simulated radiation patterns are gathered and compared to demonstrate the capability and accuracy of the proposed framework and to explore its usability in swarm applications.

Transmit beamforming for radar applications using circularly tapered random arrays

This work examines the even and odd characteristic modes of circularly distributed ad hoc array topologies with independently controlled element radiators. Fourier and Laplacian probabilistic methods are applied to derive the associated n-th order characteristic functions governing the radiation patterns of their circular topological family. Ultraspherical harmonics are then used to derive the m-th order even and odd characteristic modes for each respective topological family. Additionally, we derive a means of generating orthogonal radiation excitations using complete basis functions.

Experimental transmit beamforming using a circular canonical family bound to a locus of quadric roots

This work examines the array behavior of a quadric circular canonical family bound to the locus of zeros of n-sphere and n-ball geometry. This topological family is investigated for its total variability suitable for a wide variety of mobile autonomous systems. The generation of sum and difference beam radiation patterns is of particular interest in this work, and is explored in detail along with simulated and measured scan behavior for further developments.

Investigation of a novel subarray nullsteering technique for distributed random arrays

This paper presents a new approach to phased array null-steering using randomly distributed antenna arrays. Classically, null-steering is done by applying adaptive amplitude tapers along individual phased array elements; however, this can be difficult and cumbersome to apply in a distributed system. To achieve the same effect, we propose a novel method which employs parasitic subarrays of circular topologies to precisely place nulls in specified directions of interest. Unlike typical adaptive beamforming algorithms, this process does not require the estimation of second order statistical metrics or knowledge of precise element placement; rather, it utilizes a shared aperture approach to generate null beams simultaneously. The analysis that proceeds examines the mean radiation pattern and mean distributions from finite element models to demonstrate the steering capability. The results show that shell annular and circular annular subarrays of the spherical random array composed of monopole elements steer deep nulls in precise increments.

Investigation of sidelobe behavior for canonical polygon and fractal random array topologies

This work examines the sidelobe behavior of canonical polygons and associated fractal topologies for planar random arrays. The array manifolds are composed of uniformly distributed isotropic radiators densely populated to examine the limiting behaviors of each shape. A stochastic mathematical analysis is used to derive the mean radiation pattern. Numerical experiments are run to demonstrate scanning and to compare the patterns between the canonical shapes and their associated fractal forms. The results show that increasing the number of sharp edges either by additional sides or fractalization leads to higher sidelobe levels.

Sum-difference beamforming for radar applications using circularly tapered random arrays

This work examines a variety of canonical, randomly distributed phased arrays in linear, planar, and volumetric topologies. We investigate their distributed beamforming capabilities in modern mobile autonomous systems. Sum-difference radiation patterns are generated and analyzed for suitability in applications such as amplitude monopulse scanning, direction of arrival estimation, and target tracking. We observe that the inherent randomness of the antenna array distribution alleviates typical half wavelength spacing requirements for grating-lobe free scanning, and tapering of the pattern is accomplished by confining the distribution to quadric topologies. Lastly, comparisons of simulated and measured scanning behavior for conclude the work.

Modal beam generation from circularly bound random array topologies

This work examines the characteristic modes and measurement of a circular canonical family (CCF) of ad-hoc array topologies in which element radiators are used independently to deliver both sum and difference beams. We present a mathematical framework for the analysis of radiation characteristics from randomly distributed antenna arrays of the generalized circular topologies. Fourier probabilistic methods (i.e. characteristic function analyses) are applied to derive associated n-th order characteristic functions governing the radiation pattern. Sum and difference pattern behavior is generated using even and odd element distributions. Numerical simulations are performed using both ANSYS HFSS and MATLAB to demonstrate beam steering and examine the modal pattern characteristics. To validate our analytical approach, we include measured results of uniformly distributed array topologies, geometrically constrained to a set of 32 elements. Scanned patterns are provided for the sum-difference modes in both the E and H planes under lossless conditions. These are compared to theoretically-derived pattern behavior. The results demonstrate the utility of the CCF topology in generating radiation modes; because of this, applying the CCF in radar and electronic warfare technology will lead to greater performance such as enhanced target resolution and increased range capabilities.