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A three-dimensional antenna array with a spherical surface was investigated. The channels were randomly placed at array points with a vertical and horizontal step equal to 0.45 wavelengths. For uniform filling of the sphere, the minimum allowable distance between the channels was introduced, depending on the number of channels and the sphere size. The maximum side lobe level depends on the number of channels. To calculate the path difference in a given direction, the coordinate system was rotated so that one of the coordinate axes coincided with the selected direction. To find the radiation pattern, the scalar product of the amplitude-phase distribution vector corresponding to the signal emission direction was calculated by the complex-conjugate vector of the amplitude-phase distribution corresponding to all possible directions of signal arrival from an external source.

Analysis of the directional pattern of a non-equidistant antenna array with a random arrangement of radiating elements in three-dimensional space