Modeling of digital spatial processing under conditions of troposphere propagation of centimeter radio waves for wireless telecommunication

Objectives. A radio beam traveling through the layers of the atmosphere depends on the refractive index and its vertical variation. In this regard, attenuation may occur when radio rays propagate in a waveguide manner at low altitudes. A multipath fading effect may also occur when several rays reflected from different layers of the troposphere and having different spatial coordinates in elevation arrive at the receiver. The aim of the study is to simulate the operational algorithms of digital antenna arrays (DAA) in order to increase the range and reliability of radio communication using a tropospheric waveguide. The main advantage of the DAA consists in the high gain and controllability of the pattern shape. In order to evaluate algorithms for direction-of-arrival estimation with superresolution and beamforming, it is necessary to select an appropriate method for modeling beam propagation in the layers of the troposphere. It is proposed to use DAA to increase the range and reliability of radio communications using a tropospheric waveguide. The performance of algorithms for direction-of-arrival estimation and beamforming in the troposphere can be evaluated using ray tracing simulation. Methods. Parabolic equations are used to estimate the path losses of radio waves in the centimeter range. A ray tracing algorithm referring to a tropospheric waveguide is used to estimate the phases in the aperture of the receiving array. A spatial correlation matrix is reliably generated to form the basis for calculating coordinates using a superresolution multiple signal classification (MUSIC) method and the weighting factor vector (algorithm for maximizing the signal-to-noise + noise ratio). Results. Typical cases of a tropospheric waveguide based on a modified refractive index were considered. The bit error rate curves are obtained as a function of the geometry of the antenna arrays after the signal has passed through the tropospheric waveguide. Circular and spherical antenna arrays composed of directional antenna elements are considered. Conclusions. Numerical studies suggest that the range of communication links using digital antenna arrays increases in the centimeter band. The best geometry for this purpose is circular, since providing the lowest bit error rate for binary phase-shift keyed signals.