A comparison between basis functions for the efficient invasive weed optimization‐based optimization of phase‐only linear array patterns

Abstract

Synthesis of phased array antennas generating shaped patterns by exploiting phase tapering only is a challenging problem. A phase-only tapering permits maximizing the DC to RF power efficiency and results to be particularly useful in satellite applications with stringent constraints on the available power. Such a synthesis is a highly nonlinear problem most effectively addressed via stochastic optimization techniques. In this paper several basis functions to represent the phase distribution are traded-off and compared, within an invasive weed optimization paradigm.

Phase-Only Synthesis for Large Planar Arrays via Zernike Polynomials and Invasive Weed Optimization

“…Details on the algorithm can be found also in [35], [37], [38]. It is worth mentioning that in [30] an accurate comparison between different optimization techniques was carried out on the problem of the phase-only synthesis of linear arrays and IWO over-performed the competitors. Hence it is used here.…”

“…While in the linear case [30] a symmetrical mask would call for symmetrical phases and hence the number of basis functions at a given order could be reduced by selecting only even basis, in the planar case, we must distinguish patterns with a rotational symmetry, which would call for the same symmetry in the phases and hence only Z 0 n functions and nonrotationally symmetrical masks which will need, in principle, all Z m n . In practice, if the beam is rotationally symmetric but not pointing broadside, just the two Z m 1 functions, can be added since they allow for a linear phase and hence for the beam scanning to a generic (u 0 , v 0 ).…”

“…For what concerns the maximum radial degree n to be chosen, preliminary studies in [30] showed that the key issue is allowing enough variation for the phase, as a rule of thumb one full variation (from maximum to minimum or vice versa) in a 4λ radial direction, as the following example will show. Variation of α k coefficients is constrained within an allowable range [U B k , LB k ], which, also according to the previous experience [30], are decreasing with the square of the radial order of the considered Zernike polynomials:…”

“…Previous studies in electromagnetics [26], applications to reflector antennas [27], [28] or to arrays given fixed amplitude tapering and optimizing for phase [29] proved IWO validity in electromagnetics. A more recent paper [30] on phase-only synthesis of linear arrays, showed that with phase distribution expressed in terms of a reduced set of full-domain basis functions in order to decrease the variables to be optimized, IWO outperformed other state-of-the-art evolutionary algorithms like particle swarm or grey wolf optimizer.…”