This work presents an investigation and analysis of collaborative beamforming for a swarm-enabled distributed sensing project. It investigates the use of a three-dimensional, randomly-populated, and uniformly-distributed cylindrical array. This topology uniquely acts like a practical bound to contain the elements in swarm-type applications. In addition, a cylindrical bound provides mathematical simplicity toward understanding the fundamental research problem of swarm-based UUV sensor networks (both on surface and underwater) and their constraints to implementing a physical system in a volumetric setting. Therefore, statistical, ensemble, mean-valued average beampatterns scanned at the meridian elevation plane are analyzed in closed form and compared side-by-side to the corresponding numerical solution with a large population of one million elements densely populated amongst geometrical bounds. This large density profile applies the law of large numbers of which numerical beampatterns converge to their expected (mean) patterns. Faithful agreement of the solution is shown to validate the distributed array pattern behavior. Additionally, a Chebyshev amplitude taper is investigated for its ability to taper sidelobe levels for traditional linear arrays, and observed in this study for its ability to orthogonalize circular distributions and provide multiple beams. Finally, additional simulations are provided in this work using a manifold that comprises ten, fifty and one hundred isotropic radiators to determine the feasibility of a small element population.

The Swarm-enabled Distributed Sensing (SDS) project was funded to provide a feasibility study to analyze using a swarm as a distributed sensor array to enhance large data collection. This study will detail the steps necessary to address the problem of insufficient undersea sensor coverage in large areas. In addition, this study aims to characterize and understand the fundamental research problem of swarm-based UUV sensor networks (surfaced and underwater) and their constraints to implementation on a physical system. Finally, the results will provide engineering specifications for element positioning and sensor error, enabling low-cost, low-logistic array deployments more flexibly employable than arrays with sizeable installation logistics and budget. Therefore, the outcomes of this study have determined some of the performance parameters that will be required to implement the distributed sensing system that will be constructed with a minimum number of elements to validate the predictions of this work.

This work investigates the three-dimensional radar cross sections (RCS) of a variety of canonical three-dimensional shapes, which differ from traditional two-dimensional studies. Each topology is uniformly distributed, filled with a large quantity of isotropic elements, and the overall distribution is generated as a random filling of the topology. The large quantity of isotropic radiators is used so the radiative response converges to the expected value of the topology. Last, comparisons are made to the nominal radar cross section, three-dimensional patterns generated by MATLAB, to verify that the simulated results of this work match the MATLAB-generated patterns with decent agreement.

This work investigates the direction-finding performance of a ring of various radius sizes and compares the performance for both a periodic and a random assortment of sensors. The topologies are filled with isotropic radiators, and the overall distribution is generated as a random filling of the topology or a periodic filling along the perimeter. Last, the direction-finding capabilities of circular arrays of different size radii are simulated in this work using MATLAB with comparisons of the periodic and randomly distributed sensor arrays using three different direction finding algorithms.

This work examines and compares the radiative behavior of the quadratic U and vertically-inverted quadratic U distribution, both unique convex quadratic functions for the application of distributed antenna arrays. The comparison of the two analogous distributions demonstrated that the beamwidth of the random array relies on how the element population is either clustered or dispersed. Furthermore, this behavior occurs for both characteristic modal solutions in which element radiators are used independently to deliver both sum and difference beams. The quadratic U distribution raises sidelobe levels, and its inverse lowers sidelobe levels. By the same token this applies to a tapered aperture distribution where energy is seen to be removed by the mainbeam, increasing sidelobe levels or oppositely lowering sidelobe levels, but increasing mainbeam width. Thus, a trade-off applies to mainbeam width and its corresponding sidelobe levels. Simulated results for the quadratic U and inverted quadratic U with comparison on beamwidth and sidelobe levels conclude this paper.

This work examines the quadratic U distribution, a unique convex quadratic function for the application of distributed antenna arrays. The analysis applies a fitting phase coefficient for the elements, such that the radiated signal power of each element is coherently added in the far-field region of a specified target direction with net destructive interference occurring in all other regions to suppress sidelobe behavior. The analysis also applies characteristic modal solutions in which element radiators are used independently to deliver both sum and difference beams. Sum-difference radiation patterns are generated and analyzed for suitability in applications such as amplitude monopulse scanning, the 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. Tapering of the pattern is accomplished by confining the distribution to a quadratic U or convex probability topology.

This work examines the characteristic modes and measurement of various circularly distributed array topologies in which element radiators are used independently to deliver both sum and difference beams under lossy conditions. An associated moment generating function is derived, such that analytical patterns use even-odd symmetries for sum difference beam behavior. This approach generalizes the Fourier probabilistic methods by using the Laplace transform to analyze statistical averages catering to the degenerating effects of pattern behavior that is influenced by the environment.

This work investigates Babinet's Principle as applied to distributed arrays such that solving for one characteristic function is tantamount to solving its complement. Simulated results using triangular and complementary triangular distributions end this paper.

In this work, a novel technique using closed-form expressions is rigorously surveyed to collaboratively nullsteer uniformly distributed, planar ring, and volumetric shell distributions. To assess the radiation behavior of these geometries circular tapers is of interest for their attractiveness in derivation, design, application, and mathematical simplicity. A rigorous mathematical derivation is used for the generation of closed-form expressions of the mean-valued radiation characteristics. The numerical simulations are performed using both ANSYS HFSS and MATLAB using a finite-element distribution. To validate the analytical models, we include the measured results of a uniformly distributed ring array topology, constrained to a set of 18 elements and a uniformly distributed shell array topology constrained to 16 elements. The results of all methods are compared to demonstrate exceptional agreement in the recommended theoretical analysis. This process follows differently from traditional phased array nulling methods, which apply the unique amplitude tapers along individual phased array elements. Unlike typical adaptive beamforming algorithms, this process does not require the estimation of second-order statistical metrics and avoids expansions of large polynomial equations. It uses shared aperture characteristics in order to generate null beams simultaneously. This can also be extended to widen null widths from the compounding of these shared aperture distributions, which is shown in simulation.

This work investigates circularly distributed antenna arrays of even and odd characteristic modal superpositions as it applies to a Hardy space. Examples are provided using a family of even (Sinc) and odd (Cosinc) modal tapers of the L-2 norm. Furthermore, this space has unique properties as it causes the negative spatial Fourier coefficients to vanish. This paper concludes with simulated results of newly defined modes within a Hardy space utilizing Sinc and Cosinc modes with and without amplitude tapering.

The radiation performance of circularly bound random arrays with uniform and Gaussian distributions are analyzed statistically to identify metrics of radiation pattern performance. Isotropic radiators are preferred in this analysis since they provide relevant information on the fundamental beamforming behavior, which can be applied to provide reasonable estimates and ideal limitations on the performance gain, peaking sidelobe, and average sidelobe behavior. Numerical results illustrate scanning from zenith to meridian elevation angles to evaluate the theory and compare the behavior of linear, planar circular, and volumetric spherical arrays against the traditional linear periodic array.

We investigate new mean valued solutions of the point spread function of uniformly distributed circular apertures. Our work analyzes approximations with the use of statistical characterization of routine optical techniques. In doing so, we provide a greater understanding of what is to be expected of the imaged data. A final comparison of the mean valued point spread function over a linear aperture is also provided in closed form for the first time in this work.

The radiation performance of circularly bound random arrays with uniform and Gaussian distributions is analyzed statistically to identify regions of deterministic, transitional, and random behavior. Isotropic radiators are preferred in this analysis as they provide relevant information on fundamental beamforming behavior. This can be applied to provide practical estimates and ideal limitations on the maximum peaking sidelobe located in the stochastically described 3dB region with non-deterministic behavior. The mathematical process required for this analysis includes a statistical formulation of the array factor, including the mean, or expected value, and the variance. Analysis from prior work on random arrays provides the framework for this work, but the intuitive and streamlined analytical approach developed here forms an accurate estimate for the maximum peaking sidelobe behavior in a volumetric scan region.

High-frequency (HF) noise measurements are analyzed to investigate temporal noise characteristics measured over an eleven-day period off the coast of Southern California. The investigation employs cross-correlation techniques to distinguish unique signature properties of hourly noise. Correlation techniques provide the ability to accurately identify and characterize normal and temporal noise characteristics.

Turntable inverse synthetic aperture radar (ISAR) has a rich history with many significant connections recognized in antenna theory, Fourier analysis, sampling theory, remote sensing inverse problems, medical tomography, imaging, synthetic apertures, radar signals, range and doppler and signal processing. In fact, most ISAR and synthetic aperture radar (SAR) theory has been derived from perspectives of approximations imposed upon the signal models. Consequently, most literature focuses upon overcoming these artificial limitations that are inherently due to imposed approximations. Our work analyzes these approximations differently with the use of statistical characterization. In doing so we create expected patterns of the ISAR data.

Ensemble progressions for the sophisticated array factors of range-Doppler routines and radar cross sections of simulated scan behavior are investigated and compared against theoretical derivations for a circularly planar distributed array. This topology distribution is attractive because of its mathematical ease of analysis and is bound to a maximum aperture radius A.

This paper presents a survey of mean-valued HF external noise figures of mean day and night noise levels and amplitude probability distributions of noise regions for four-, eleven- and twenty-seven-day - collection periods off the southern California coast. Extraction of the quasi-minimum noise (QMN) power [1] used the "median of minimums" algorithm. Results are then compared to established CCIR [2] noise categories (atmospheric, galactic, man-made/residential, rural, quiet rural) and QMN FA estimates. These empirically-derived models provide a general understanding of the reported noise levels compared to historical measurements under referenced conditions.

This work investigates beam pattern behavior of an isotropic point source and a collection of sources distributed amongst a spherical volume. Pattern behavior is also compared to the tapering of a plane wave expansion of spherical waves demonstrating self-adjoint characteristics. Beampatterns of atomic like orbitals and Zernike polynomials are provided as connections to common applications.

This paper presents high-frequency band noise characteristics, measured over a fourteen-day period while underway off the coast of Southern California. The investigation uses k-means clustering to identify spatial noise variations. Local domains provide insight on regions where high noise HF communications are expected.

This work investigates a far-field quantity, known as the effective length, of one, two and three-dimensional arrays bound within circular constraints and its relation to the Fraunhofer region. Maximum gain is achieved for a volumetric array only when compared using the same effective length of linear and planar arrays.