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Several synthesis techniques are available to optimize amplitude and phase excitations of periodic linear arrays to generate flat-top beams. Clearly, the optimal tapering depends on design parameters such as the array length, the number of array elements, the beam flatness, the beam width, the side lobe levels, and others. In this paper, in order to derive useful guidelines and rule of thumb for the synthesis of periodic array antennas, relations between these parameters are derived employing linear programming techniques, which guarantee optimality of the solutions. Such relations are then plotted and used in some design examples.

Over the last decade, more than one hundred CubeSats have been launched, and this number will double very soon. However, the increasing number of launched satellites is not yet followed by an improvement in the communication technology they use: to date, the majority of orbiting CubeSats transmits their data using frequencies allocated in the radio amateur service. If this trend does not change in favor of more advanced technologies, this class of satellites will not be considered a viable solution for commercial purposes, and thus relegated to the role of educational tool or technology demonstrator. The transition to higher frequencies, like those in the Ka band, will enable the design of small and directive antennas, and will make faster data rates attainable. In the nanosatellites development, an antenna can be very demanding in terms of mass and real estate; efficient radiators such as horn antennas or parabolic reflectors in most cases are not viable solutions because of their mass and surface requirements. An ideal antenna should be thin, flat, small, light and designed to be mounted on the outer surface of the spacecraft. In this context, a microstrip array antenna is a convenient solution in terms of size, mass, mounting and cost. In this paper we design a circularly polarized antenna array, with uniform polarization over a wider bandwidth with respect to the bandwidth of the basic array element. In the design of the proposed array, many parameters are subject to optimization: specifically, gain and bandwidth shall be maximized, while the axial ratio and insertion losses shall be minimized. These parameters can be optimized at every stage of the design: for the single patch, the subarray, and the final array. In order to identify the best compromise possible between physical parameters and electromagnetic performances, a multi-objective optimization approach will be adopted. Finally, also the excitations of the elements are optimized following a deterministic algorithm which allows to improve the electromagnetic performances of the uniform array. Numerical results of the consecutive optimization steps will be illustrated.

Two new approaches to the optimal synthesis of difference patterns are proposed that can deal in an effective fashion with arbitrary sidelobe bounds. The first approach, which amounts to solving a convex programming problem, can be applied to completely arbitrary (fixed geometry) arrays and it is capable of taking into account additional constraints. The second approach, which amounts to solving a simpler linear programming problem, can be applied to uniformly spaced linear or planar arrays, and allows results about the uniqueness of the solution to be inferred. Numerical examples show the flexibility and effectiveness of the proposed procedures.

A hybrid approach to the synthesis of the excitations and locations of non-uniformly spaced arrays, in order to achieve optimal focusing in any given direction, is proposed and discussed. The approach takes definite advantage from the convexity of the problem with respect to the excitation variables, and exploits a simulated annealing procedure as far as the location variables are concerned. The corresponding synthesized patterns outperform previously known results in standard benchmark problems.