Semitransparent concave screens are viewed as means of reducing radiation in nonworking angular area of an antenna (shadow domain). An analytical procedure for synthesis of screen impedance in the geometrical optics (GO) approximation has been developed. Beyond the limits of the GO approximation, the numerical synthesis procedure has been applied. It has been shown that it is the radii of the screen that defines the achievable cutoff of the fields. To achieve a cutoff on the order of −20 dB in the angular sector of + - 10 degrees with respect to the desired boundary of the shadow domain, the radii of the concave screen is shown to be 2 wavelengths. An example of a compact antenna system for high precision satellite positioning is also presented.