The paper discusses Gauss-Kruger projection as a projection consisting of spheroidal and spherical parts. For the spheroidal part distribution of projection deformations has been determined and besides, its impact on the metric structure of the initial Gauss-Kruger projection, as an entirety, has been estimated

A simulation-based optimization approach to design of phase excitation tapers for linear phased antenna arrays is presented. The design optimization process is accelerated by means of Surrogate-Based Optimization (SBO); it uses a coarse-mesh surrogate of the array element for adjusting the array’s active reflection coefficient responses and a fast surrogate of the antenna array radiation pattern. The primary optimization objective is to minimize side-lobes in the principal plane of the radiation pattern while scanning the main beam. The optimization outcome is a set of element phase excitation tapers versus the scan angle. The design objectives are evaluated at the high fidelity level of description using simulations of the discrete electromagnetic model of the entire array so that the effects of element coupling and other possible interaction within the array structure are accounted for. At the same time, the optimization process is fast due to SBO. Performance and numerical cost of the approach are demonstrated by optimizing a 16-element linear array of microstrip antennas. Experimental verification has been carried out for a manufactured prototype of the optimized array. It demonstrates good agreement between the radiation patterns obtained from simulations and from physical measurements (the latter constructed through superposition of the measured element patterns).