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Theory of mutual coupling among minimum-scattering antennas

A novel and rigorou formulation for mutual impedance among a class of idealized but realizable antennas is presented. Unlike past treatments of mutual coupling, which have proceeded from structurally specified antennas, the present treatment deals with a class of antennas, all the electromagnetic properties of which are rigorously expressed explicitly in terms of their radiation patterns alone. Employing a network formulation based on a scattering representation of electromagnetic fields in terms of spherical (or cylindrical) modes, the mutual impedances between such antennas are computed exactly. Several alternate representations for the mutual impedance are derived, one of which is an integral representation involving the power pattern function for both real and complex angles. In special cases, these exact results agree with published results obtained by applying well-known approximate techniques to structurally specified antennas. An important and illuminating example is provided by an infinite planar array of antennas radiating into a half-space for which the present formulation yields the well-known grating-lobe series representation of the active impedance without an explicit reference to structural properties of the radiating elements.

A numerical technique for calculating mutual impedance and element patterns of antenna arrays based on the characteristics of an isolated element

A numerical technique for calculating mutual impedance and element patterns of antenna arrays based on the characteristics of an isolated element is presented. The basis for this technique is the theory of minimum-scattering (MS) antennas and, in particular, the interpretation of the mutual impedance between two canonical minimum-scattering (CMS) antennas as the first term in a perturbation series of the mutual impedance of arbitrary antennas. For the computation of the mutual impedance via the CMS approximation this pattern must be continued analytically into the complex domain. However, numerical codes provide radiation patterns only for real observation angles. To overcome this problem, the numerically calculated patterns are expanded in terms of spherical modes and the computation over complex angles is carried out analytically. Numerical results for collinear and linear arrays of parallel electric dipole antennas and rectangular probe-fed patch antennas are presented and a comparison is made with direct calculations using the WIPL-D code. Results presented show the good agreement between the CMS approximation and the WIPL-D code.

A new root‐based direction‐finding algorithm

[1] Polynomial rooting direction-finding (DF) algorithms are a computationally efficient alternative to search-based DF algorithms and are particularly suitable for uniform linear arrays of physically identical elements provided that mutual interaction among the array elements can be either neglected or compensated for. A popular algorithm in such situations is Root Multiple Signal Classification (Root MUSIC (RM)), wherein the estimation of the directions of arrivals (DOA) requires the computation of the roots of a( 2N � 2) -order polynomial, where N represents number of array elements. The DOA are estimated from the L pairs of roots closest to the unit circle, where L represents number of sources. In this paper we derive a modified root polynomial (MRP) algorithm requiring the calculation of only L roots in order to estimate the L DOA. We evaluate the performance of the MRP algorithm numerically and show that it is as accurate as the RM algorithm but with a significantly simpler algebraic structure. In order to demonstrate that the theoretically predicted performance can be achieved in an experimental setting, a decoupled array is emulated in hardware using phase shifters. The results are in excellent agreement with theory.

Poisson-Spot Intensity Reduction with a Partially-Transparent Petal-Shaped Optical Mask

The presence of a Poisson spot inside a shadow region can best be described as the consequence of constructive interference of light waves diffracted on the edge of the obstruction where its central position can be determined by the symmetry of the object. More recently, the elimination of this spot has received attention in the fields of particle physics, high-energy lasers, astronomy, and lithography. The desired level of intensity suppression is dependent on the type of light source and the field of application. In this paper, we introduce a novel, partially transparent petaled mask shape that suppresses the bright spot by up to ten orders of magnitude in intensity at optical ranges, with potential powerful applications in many of the above fields. The optimization technique formulated in this design can identify mask shapes having partial transparency only near the petal tips.

Response of an antenna to arbitrary incident fields

In a variety of situations it is necessary to determine the response of an antenna to incident fields other than pure plane waves. Usually this is accomplished by the application of the principle of superposition to the antenna reciprocity relation for plane wave incidence. An alternative approach is to represent the incident field as a superposition of an infinite set of spherical free space modes and find the response with the aid of the corresponding antenna scattering matrix representation. Although the two formulations must necessarily be equivalent an explicit connection between them does not appear to have been previously established. This is done in this paper.

Estimating number of sub-Gaussian emitters in a narrowband DOA estimation problem by using independent component analysis

Accurate determination of the number of emitters is an important and nontrivial problem in direction of arrival (DOA) estimation. The energy criterion based on singular values of the sampled data covariance matrix requires either a-priori knowledge of the signal-to-noise ratio (SNR) or the noise energy itself. More refined approaches, such as the Akaike information criterion (AIC) and the minimum description length (MDL) criterion fail when the signals are non-Gaussian. Thus, they are inapplicable to DOA estimation of communication signals, which generally tend to be non-Gaussian. The presented approach is based on independent component analysis (ICA). The information bearing source signals, obtained by blind source separation (BSS), are identified through measuring their distance from Gaussianity. A fixed threshold parameter in the kurtosis domain is used which can be set to accommodate a wide range of SNRs and data sample sizes.

Second and fourth order statistics-based reduced polynomial rooting direction finding algorithms

Polynomial rooting direction finding (DF) algorithms are a computationally efficient alternative to search-based DF algorithms and are particularly suitable for uniform linear arrays (ULA) of physically identical elements provided mutual interaction among the array elements can be either neglected or compensated for. A popular polynomial rooting algorithm is Root-MUSIC (RM) wherein, for an N-element array, the estimation of the directions of arrivals (DOA) requires the computation of the roots of a 2N-2-order polynomial for a second order (SO) statistics- and a 4N-4-order polynomial for a fourth order (FO) statistics-based approach, wherein the DOA are estimated from L pairs of roots closest to the unit circle, when L signals are incident on the array. We derive SO- and FO statistics reduced polynomial rooting (RPR) algorithms capable to estimate L DOA from L roots only. We demonstrate numerically that the RPR algorithms are at least as accurate as the RM algorithms. Simplified algebraic structure of RPR algorithms leads to better performance than afforded by RM algorithms in saturated array environment, especially in the case of FO methods when number of incident signals exceeds number of elements and under low SNR and/or small sample size conditions.

Two-dimensional model of electromagnetic wave propagation in the volume holographic recording using photorefractive polymer

The photorefractive polymer based holographic memories provide the alternative of achieving terabytes of digital data storage with gigabits per seconds of transfer. The stored information in the medium is in the form of electromagnetic distribution and it is governed by the second order inhomogeneous Helmholtz equations with no known exact solution. A numerical approximation using finite element method is employed to model the wave propagation in the polymer. The model is used to approximate the Helmholtz equation for a spatially varying index of refraction medium subject to input of polarized planar waves. The initial results from the mathematical formulation conform to the theoretical expectation of wave propagation on the non-conducting and non-magnetic materials. In addition, assuming periodicity of the inhomogeneous material, the reflective waves are computed and conservation of energy on the medium is verified. The model is used to simulate electromagnetic wave propagation through a two- dimensionally varying index of refraction poly (N- vynilcarbazol) (PVK) polymer. The transmitive waves are computed at various angles of incidents. The stored hologram represented as transmitive wave is reconstructed in reading process.

Performance of an L-Band antenna for radiometric measurements

The objective of this paper is to discuss the performance of a new L-Band, truck-mounted radiometer antenna. This new low loss antenna has been designed to increase the calibration stability of the ComRAD radiometer system. ComRAD is a dual polarized combined radar radiometer system operating as a radar at 1.3 GHz and as a radiometer at 1.413 GHz. It utilizes the same antenna for both frequencies. ComRAD is used to develop algorithms for the sensing of soil moisture in the presence of vegetation. The system is presently being employed to monitor agricultural crops over the growing cycle in preparation for the upcoming SMAP (Soil Moisture Active Passive) satellite mission.

Small Cassegrain antenna for passive remote sensing at L-band

Summary form only given. This paper presents the design, construction and results of measurements of a dual polarized L- band antenna for the NASA Combined Radiometer and Radar System. The radiometer band covers 1.400 -1.427 GHz. and the radar band 1.250 to 1.350 GHz. The focus of this paper is on the radiometer band. The antenna is designed to replace the 48 inch diameter truck-mounted paraboloidal dish used in NASA remote sensing applications because of its excessive loss. It was found that changes of the ambient temperature produced fluctuations in the antenna noise temperature which reduced the accuracy of the radiometer calibration. These fluctuations are caused by the temperature dependent Ohmic loss in the antenna structure, the externally mounted cable connecting the Newtonian feed to the radiometer and in the patch used for the feed. Therefore the principal design goal for the new antenna was to eliminate the need for the cable and the patch and to reduce any additional loss without a degradation of its electrical performance and without increasing its size and weight. A configuration that obviates the need for an external feed-to-radiometer cable connection is a Cassegrain antenna. Its additional advantage is that the feed structure can be designed to have a lower loss than the patch used in the Newtonian feed of the old antenna. Since classic Cassegrain antennas generally require reflectors with diameters of at least 30 wavelengths designing an antenna in a Cassegrain configuration incorporating a reflector with a diameter of only 5 to 6 wavelength represented a real challenge. This challenge was met with the design that employs a novel low loss dielectric (Rexolite) conical support structure for the subreflector. The cone diameter decreases linearly from its base at the apex to the subreflector. The novel feature in this design is that in addition to supporting the subreflector the cone also serves as a dielectric waveguide that illuminates the subreflector. The mechanism for this is the wave within the cone that travels from the apex of the paraboloid toward the subreflector and illuminates it by a partial leakage into the surrounding space. The resulting efficiency is appropriate for a truckmounted antenna system. The input at the apex of the paraboloid employs a circular waveguide that supports two orthogonal TE11 modes thus providing the necessary dual polarization. As confirmed by simulations and measurements the gain and side lobe levels of the new low loss antenna are comparable to those of the old antenna.