# Progress in Canted Sector Antennas and Non-Periodic Arrays

## Sidelobe performance can be improved cost-effectively.

Progress has been made in a continuing effort to develop low-geometric-profile, wide-frequency-band microwave antennas intended for incorporation into wide-band aperiodic arrays for use in high-speed communications. The effort has produced improved designs for canted sector antennas, cost-effective approximations of random arrays of such antennas, and software for simulating the performances of such antennas and arrays.

The effort began with an examination of simple canted sector antennas, which consist mainly of triangular radiating elements canted above ground planes. The limits of the operational frequency bands of these antennas and arrays thereof are determined by limits on acceptable variations in their radiation patterns. Simple canted sector antennas offer advantages of simplicity and wide impedance bandwidths. The disadvantage of simple canted sector antennas is that they exhibit close-to-broadside radiation-pattern depressions that are unacceptable for the purpose of adequate scanning of arrays.

To improve the broadside radiation patterns, departures from the simple canted sector design were sought. The resulting improved design of a radiating antenna element differs from the simple design by including tapers at all three corners and upward bends at two corners (see Figure 1). The bend angle, the cant angle, the dimensions of the tapers, and other angular and linear dimensions are design parameters that can be chosen to optimize performance with respect to the bandwidth and/or the radiation pattern. The improved design of Figure 1 was derived by modifying a corresponding prior simple canted sector design for operation in the nominal frequency band from 2 to 6 GHz. Computational simulations and tests of the real antenna showed that with a bend angle of 20° and a cant angle of 5°, the improved design yields a voltage standing-wave ratio less than about 2.5 to 6 GHz and removes broadside depressions that occur in the radiation pattern of the unmodified antenna at 3.6 and 4.4 GHz. The vertical dimension of the improved antenna is 22.3 mm — only slightly greater than the 22.1 mm of the unmodified antenna. (The improved design does not remove a broadside depression at 2 GHz, but in other respects, the improved antenna performs substantially as required from 2.2 to 6 GHz).

In principle, antennas can be positioned in random arrays to improve sidelobe performances. Because it may prove too costly to fabricate truly random arrays, in some applications it might be cost-effective to construct less-expensive pseudorandom arrays that exhibit acceptable sidelobe performances over specified frequency ranges. The approach taken in this development effort is to use random subarrays as building blocks of larger pseudorandom arrays. This approach admits of variations, including periodic arrays of random subarrays (PARS, depicted in Figure 2), arrays of periodically rotated random subarrays (ARRS-P), and arrays of randomly rotated random subarrays (ARRSR). Computational simulations have shown that for an array of a given aperture size and number of elements, the PARS approach offers the robust wideband performance of a random array in a geometrically simpler design, but with sidelobes somewhat higher than those of a purely random array of the same size. Sidelobe performance can be improved somewhat by progressing from PARS through ARRS-P to ARRS-R.

The software used to perform the computational simulations implements a marching-on-time, method-of-moments algorithm for solving a time-domain electric-field integral equation of an antenna. Given a band-limited excitation, the algorithm solves for surface currents induced on the radiating element and the ground plane. For a geometry modeled by use of N_{s} surface unknowns and N_{t} time steps, the number of arithmetic operations required by the algorithm scales as O(N_{t}N^{2}_{s} {where “O(x)” signifies “of the order of x”}. The algorithm can be augmented by use of a parallel-processing fast-Fourier-transform (FFT)-based accelerator, reducing the number of arithmetic operations to O(N_{t}N_{s}[log(N_{s})]^{2}). The software employs a standard message-passing interface for communication among processors and utilizes the Fastest Fourier Transform in the West (FFTW) library [a publicly available subroutine library for computation of parallel FFTs]. This software makes it possible to analyze the broadband characteristics of antennas characterized by N_{s} >10^{5}, using supercomputers comprising tens of processors, in practical amounts of time.

*This work was done by Jennifer T. Bernhard, Paul E. Mayes, Eric Michielssen, Garvin Cung, and Kiersten Kerby of the University of Illinois for the Army Research Laboratory. For more information, download the Technical Support Package (free white paper) at www.defensetechbriefs.com/tsp under the Electronics/Computers category. ARL-0011*

##### This Brief includes a Technical Support Package (TSP).

###### Progress in Canted Sector Antennas and Non-Periodic Arrays

(reference ARL-0011) is currently available for download from the TSP library.

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