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The purpose of this report is to show that deep nulls can be imposed at specified locations in planar array antenna using phase-only control of coarsely quantized phase shifters. This is done by using the number of phase shifters available for control in the columns of the array to compensate for the small number of bits of the individual phase shifters. Null synthesis algorithms are derived to calculate phase shifts to impose nulls in the phi equals 0 degrees pattern cut of planar array antenna patterns. Results of calculations are presented in this report. Keywords include: Planar array antennas, Phase quantization, Phase-only weight control, and Null synthesis.

A general and convenient method was provided for determining incremental length diffraction coefficients directly from the conventional two- dimensional diffraction coefficients. This sequel provides a detailed analysis of how the nonuniform incremental diffraction coefficients for the half-plane are integrated around the rim of a reflector. These computed far fields of the nonuniform current, when added to the far fields computed from the physical optics current, produce a more accurate total far field of the reflector. Excellent agreement with the far fields obtained from a method moments solution to the electric field integral equation applied to a 20-wavelength-diameter reflector shows that the cross polarization, further-out sidelobes, and fields near nulls of reflector antennas can be appreciably changed by the fields of the nonuniform currents. Finally, we evaluate the fields of the nonuniform current of the reflector through conventional asymptotic evaluation of the diffraction integrals and compare these approximate results with the far fields obtained by numerically integrating the nonuniform incremental diffraction coefficients. Keywords: Diffraction coefficients; Incremental length; Reflector antenna. (JHD), See also Part 3, ADA207796.

In this report, incremental diffraction coefficients for a narrow slit in an infinite, perfectly conducting plane are used to investigate the effects of cracks in the surface of a focal-fed circular paraboloidal reflector antenna. Such cracks can result from the imperfect fitting together of panels to form a large reflector. The imperfections in fitting together are modeled by narrow slits in a paraboloidal surface. The far fields scattered by the cracks are computed by integrating the slit incremental diffraction coefficients (multiplied by the illuminating field) along the cracks. Two forms of cracks are modeled: azimuthal cracks, the projections of which on the aperture plane are concentric circles, and radial cracks, the projections of which on the aperture plane are radii of the projection of the paraboloid. The feed is assumed to be a Huygens source. It is found that narrow azimuthal cracks hardly change the H-plane pattern, moderately change the further out sidelobes of the E-plane pattern, and moderately change the entire cross-polarization pattern. Depending on their orientation the radial cracks can strongly change the E-plane and cross-polarization patterns. However, like the azimuthal cracks, the radial cracks hardly change the H-plane pattern.

In this report non-uniform current (PTD) high frequency incremental diffraction coefficients are derived for the perfectly conducting strip regarded as a truncated half-plane. An essential feature of the high frequency solution derived is that the diffraction at the trailing edge of the H-wave non-uniform leading edge current, which becomes appreciable near grazing incidence, is taken into account even when the leading and trailing edges of the incremental strips are not parallel. The incremental diffraction coefficients for the strip are then used to calculate bistatic radar cross section patterns of a perfectly conducting disk illuminated by a plane wave. Good agreement in general is obtained between the exact bistatic cross section patterns of the disk and the approximate bistatic cross section patterns obtained by adding the integral of the incremental diffraction coefficients around the edge of the disk to the physical optics scattered field.

The problem of calculating the minimum phase-only weight perturbations required to impose nulls in the pattern of a linear antenna array is nonlinear and cannot be solved analytically. The problem is, however, an example of nonlinear programming problem and can be solved numerically. This report describes the performance of two nonlinear programming computer codes, LPNLP and VMCON, on the minimized weight perturbation phase-only null synthesis problem. Both codes are effective in general, although convergence problems may be encountered if nulls are required to be imposed at closely spaced locations in high sidelobe regions of the pattern.

An iterative numerical method is presented for calculating the minimum phase-only perturbations of the element weights of a linear array to impose pattern nulls at prescribed locations. The method is based on repeated linearizations of the equations for the imposed nulls.

A computationally efficient method is presented for calculating the aperture distribution and the far field pattern of a parabolic reflector with an off-axis array feed. Idealized, uncoupled array elements and realistic, mutually coupled, circular waveguide elements are considered. Ray optics are used to determine the scalar aperture field over a rectangular grid of aperture sampling points. Two alternatively methods for performing the aperture integration required for the pattern evaluation are compared: (a) based on summation of subapertures with constant amplitude/linear phase, and (b) based on the Fast Fourier Transform (FFT) and sampling theory. Patterns obtained with this method are compared with independency computed patterns that use other approaches. The range of validity of the aperture field integration method is discussed.

A review is presented of work performed at RADC on the subject of phase-only null synthesis and adaptive nulling in the sidelobes of linear array antenna patterns. Beam space representations are used in much of this work. Related investigations outside RADC are summarized, and a general bibliography of phase-only pattern control investigations is included. Keywords include: Linear Arrays, Phase-Only Weight Control, Pattern Synthesis, and Adaptive Nulling.

General expressions for the mean and variance of the power at an arbitrary location in the pattern are derived for a linear array of isotronic equispaced elements. The phases of the element excitation coefficients are assumed to be set by digital phase shifters, causing random phase errors uniformly distributed in the interval of plus to minus the least significant bit of the phase command. Approximations valid for small phase errors (N bit 4) are obtained. For large arrays, the variance of the power at a location where the error-free pattern has a null is approximately equal to the square of the mean of the power. The theoretical results are compared with Monte Carlo computer simulations. The Kolmogorov-Smirnov test usually shows close agreement between the simulation and the theoretical results. However, the test also shows that the depths of multiple nulls are not statistically independent when there are multiple nulls in the error-free pattern; the probability distribution of the depth of the least deep null is closer to the distribution predicted for a single null than it is to the distribution for multiple nulls. (Author)

A new computational method is presented for calculating the phases required for minimized weight perturbation, phase-only null synthesis in linear array antenna patterns. The method uses nonlinear programming algorithms to determine the coefficients of a beam space representation of the optimal phase perturbations. The derivatives of the objective and null constraint functions with respect to the beam coefficients, required by the nonlinear programming algorithms, are calculated from analytic expressions. The beam space representation allows the number of unknowns to be reduced from half the number of array elements to the number of imposed null locations, and results in a significant reduction in computation time from that required to calculate the phase perturbations directly.

An analysis is performed of nulling in linear array patterns subject to minimization of the weight perturbation. Both combined amplitude and phase perturbation, and phase-only perturbation are treated. The solutions obtained are interpreted in terms of cancellation beams superimposed on the initial pattern. (Author)

The purpose of this report is to show that deep nulls can be imposed at specified locations in pattern cuts parallel to the principal plane cuts of planar array patterns using phase-only control of coarsely quantized phase shifters. This is done by using the number of phase shifters available for control in the columns of the array to compensate for the small number of bits of the individual phase shifters. A null synthesis algorithm is derived to calculate the phase shifts to impose nulls in the nu = nu1 pattern cut of planar array antenna patterns by matching the pattern of a linear array with nulls imposed at the same locations using continuously variable, combined phase and amplitude control. Results of calculations are presented. Keywords: Planar array antennas, Phase quantization, Phase only weight control, Null synthesis, Antenna radiation patterns. (jhd)

The purpose of this report is to show that deep nulls can be imposed at specified locations in the phi = 0 deg. pattern cut of planar array antenna patterns using phase-only control of coarsely quantized phase shifters. This is done by using the number of phase shifters available for control in the columns of the array to compensate for the small number of bits of the individual phase shifters. A null synthesis algorithm is derived to calculate the phase shifts to impose nulls in the phi = 0 deg. pattern cut of planar array antenna patterns by matching the pattern of a linear array with nulls imposed at the same locations using continuously variable, composed phase and amplitude control. Results of calculations are presented.

Nulls cannot be imposed in ideal linear array antenna patterns with phase-only weight control at locations symmetric with respect to the main beam if the phase perturbations are restricted to be small. If, however, no restriction is placed on the magnitude of the phase perturbations, then phase-only nulling at symmetric pattern locations is possible. Several examples are presented to illustrate symmetric nulling with phase-only control. The phase perturbations are calculated by a nonlinear programming computer algorithm. The cancellation patterns tend to be interferometric in shape and result in significant distortion over much of the pattern. (Author)

A proof is given of the odd-symmetry property of the phase perturbations required to impose nulls in a real linear array antenna pattern using phase-only weight control subject to minimization of the absolute weight perturbations. The perturbed weights are, therefore, conjugate symmetric with respect to a phase reference at the center of the array, and the perturbed pattern is real. (Author)

It is proved that the minimum phase-only weight perturbations required to impose a single null in a real, linear array, antenna pattern are odd-symmetric with respect to a phase reference at the center of the array. Hence the perturbed pattern is likewise real. Additional evidence is given for supporting the hypothesis that the minimum phase-only weight perturbations are odd-symmetric for any number of imposed nulls. (Author)

A solution is presented to the problem of obtaining a least-squares fit of phase-only array weight perturbations to a set of combined phase and amplitude perturbations calculated to impose pattern nulls at prescribed sidelobe directions. It is shown that the desired least-squares fit is accomplished by taking only the phase part of the combined phase and amplitude perturbations. This method of phase-only nulling is compared in effectiveness with other phase-only pattern synthesis methods.

The growing interest in adaptive antennas makes it worthwhile to examine the theoretical limits to what can be achieved with reduction of sidelobe levels of array antenna patterns. In this paper we address the problem of determining the minimum possible power that can be present in a specified sidelobe region subject to certain constraints. We consider three different forms of the minimization problem: (1) minimize the ratio of the power in the sidelobe region to the power in the mainbeam region; (2) minimize the ratio of the power in the sidelobe region to the power density in the mainbeam direction; and (3) minimize the power in the specified sidelobe region subject to the constraint that the array response in the mainbeam direction is held constant. It is shown that forms 2 and 3 of the minimization problem lead to identical results, and that the results obtained with form 1 are numerically close to those obtained with forms 2 and 3.