Refocusing beams of a satellite mirror antenna with moderate deformations of its reflector
Authors: Dardymov A. V. , Choni Yu. I. 
Published: October 2024

Multibeam hybrid reflector antenna (MBHRA) is part of high-performance satellite communication systems. It provides high gain thanks to its large mirror and the use of antenna array to form enough beams covering the working area. Therefore, it is crucial to maintain the needed beams configuration to provide clients with high quality signal. The location of the beams may change because the reflector profile changes under the changeable thermal flux from the Sun, which is not stationary due to orbital motion of the satellite. Although the appearing distortions of the reflector profile are a priori small, but they cause beams to displace from their assigned positions in up to their width of tenth of a degree. Consequently, the level of the signal in coverage areas goes down. Modern MBHRA form their beams with clusters, i.e. groups of elements of the antenna array. Typically, cluster consists out of seven elements: one in the center and others at the vertices of a perfect hexagon. The fact that several antenna elements form a beam opens up the possibility of electronically controlling the beams by adjusting the amplitudes and phases of the exciting distribution, or more precisely, the weighting coefficients of the clusters. To determine which amplitudes and phases to apply, it is necessary to know the current state of the reflector, characterized by either its geometry or its electrodynamic equivalent, such as the best-fit paraboloid (BFP). Laser measurement and photogrammetry are popular solutions for that. A useful alternative to them is reconstruction of the BFP from the signals received by the MBHRA antenna array from a ground-based radio beacon. Emphasizing the dependence of these signals on the state of the reflector, we call them the “signal imprint” of the reflector. The possibility to implement a single ground beacon is due approximation the reflector profile as an equivalent best-fit paraboloid. BFP is uniquely defined by six parameters: change of the focal length, turns in two orthogonal planes and shift of the apex in space {ΔF; αz; αy; Δx; Δy; Δz}. Since some of the parameters are highly correlated in terms of their influence on the signal imprint, the re-construction problem becomes more complicated. So a question whether the set of parameters is overloaded arises reasonably. Maybe it is possible to get rid of some parameters. We considered two options to reduce the number of parameters: focal displacement + turns {ΔF; αz; αy} and apex shift {Δx; Δy; Δz}. Statistical modelling confirms the possibility to reduce the number of sought-for BFP parameters down to the mentioned three instead of six. If the maximum of the focal spot does not shift outside the cluster, then reducing the number of the sought-for BFP parameters to three causes a very small decrease in the gain of beams compared to using the full set of parameters. For the above options, the decrease in gain is 0.03 dB or 0.25 dB. It is interesting to note that in the turns option {ΔF; αz; αy} there is a better correspondence to the reflector surface compared to the displacement option {Δx; Δy; Δz}, but worse matching of the signal imprint, and as a consequence a greater loss in gain. This is due to the higher sensitivity of the beam orientation to the mirror rotations than to the vertex displacement.