# HERAS: A Modular Matlab Tool Using Physical Optics for the Analysis of Reflector Antennas
## 4 Applications of the Tool
### Efficient Estimation of an Array Fed Reflector Antenna with a Large Number of Feeds  
The fixed coverage characteristics of passive SFPB/MFPB antenna architectures do not allow a favourable match of the satellite capacity to evolving traffic demands. With the technology developments in solid-state power amplification (SSPA) and digital payloads, phased-array active antenna solutions emerge as an attractive candidate to deliver the desired flexibility. Despite the favourable characteristics, the deployment of DRAs at an aperture size suitable to meet stringent link budget requirements for broadband geostationary satellite missions will remain challenging for the foreseeable future. In particular, the limited digital processing capacity of existing and near-future payloads suggests a requirement for extensive implementation of analogue beam-forming networks, which combined with the thermo-mechanical demands associated with distributed SSPA increases the complexity and costs of DRA-based payloads. AFRs in imaging configuration where the feed array assembly is collectively used to generate each beam are gaining attention for future VHTS systems due to their flexibility [11; 57; 58]. In these systems, a beam-forming network is required, and precoding and resource allocation  
Figure 8: Estimated coverage characteristics in an SFPB scenario. (**a**) Aggregate gain. (**b**) \(C/I\). Figure 9: Numerical error resulting from the use of threshold and beam interpolation techniques in an SFPB scenario. An acceleration factor in time of 80 is achieved. can be added in order to increase the overall system performance [12; 14; 59]. Preferably, these will be implemented in the digital domain, providing a fully reconfigurable software-defined payload such as the recently launched Eutelsat Quantum [60] and other planned broadband missions such as Space Inspire of Thales Alenia Space [61] and OneSat of Airbus [62]. This trend calls for a payload design process aided by multidisciplinary optimisation. Considering the increasing number of beams and the size of the feed arrays, an efficient tool to estimate the multi-beam coverage characteristics is again becoming of significant relevance. The analysis method for AFR systems entails multiple steps. These include the calculation of the beam-forming coefficients, which defines the weighted contribution of each feed in the formation of each beam; power normalisation, which ensures that each feed-radiated power is within the capability available at the corresponding amplifier; and PO computation, which transforms the reflector illumination to the associated far-field characteristics. Depending on the ratio between the number of feeds and the number of beams, beam-forming may be considered either at primary or secondary level; in other words, before or after the PO computation. If beam-forming is applied at a primary level, the PO integral is performed for each beam using the equivalent surface currents obtained when the reflector is illuminated with the array field, i.e., the weighted sum of the feed array fields contributing to a particular beam. Primary-level beam-forming could be computationally favourable in cases where the number of beams is lower than the number of feeds, since it requires one PO computation per beam. The acceleration techniques discussed above in the SFPB scenario (e.g., _threshold_ and _interpolation_) can be directly applied. It is noted that in this case, the beam-forming matrix should be defined in advance of the coverage computation. In particular, Equation (4) defines the beam-forming computation applied to the currents at the reflector surface of every feed, \(\overline{f}_{f}\), with the elements excitation matrix, \(W\), to obtain the weighted currents for each beam, \(\overline{f}_{b}\), to which the PO integral is applied to derive the far-field.