# HERAS: A Modular Matlab Tool Using Physical Optics for the Analysis of Reflector Antennas
## 1 Introduction  
Satcom systems are increasingly moving from broadcast to broadband services, adapting to fast evolving consumer needs for high-throughput connectivity (e.g., video on demand). This marks the shift from broad-shaped beams providing regional or continental coverage to multiple spot-beam antenna architectures enabling spectrum reuse with a cellular-like coverage [1; 2; 3; 4; 5]. For a given frequency allocation, this approach enables a significant capacity increase. This transition is also accompanied by a shift to higher frequencies (e.g., moving from C-band to Ku and Ka-bands and above), thereby enabling wider untapped bandwidths. These systems are generally referred to as high-throughput satellites (HTSs), which provide a total capacity in the order of hundreds of Gbps. Multi-beam reflector antennas (MBRA) are one of the preferred configurations to achieve the requirements from geostationary orbit (GEO) due to the high gain offered by the system optics. Compared to direct radiating arrays (DRAs), MBRAs offer a favourable compromise between coverage characteristics and demands on the payload resources. Existing HTS systems implement passive MBRA architectures (e.g., ViaSat-1 [6], Eutelsat's Ka-Sat [7], Jupiter-1 [8] etc.). These systems combine a reflector with a set of feeds located at the focal plane of the reflector, which are exploited to generate the multi-beam coverage. Depending on the number of feeds employed to generate each beam, two different configurations can be defined: single feed per beam (SFPB), where each beam is generated with one feed; and multiple feed per beam (MFPB), where several feeds generate each beam with the use of beam-forming networks (BFNs), providing adequate beam overlap. The trade-off between these two architectures relies on the coverage characteristics, the size of the on-board antenna farm, and the feed network complexity [5; 9]. As we move towards the next generation of very high-throughput satellite (VHTS) systems, which target total throughput in the order of 1 Tbps, the number of beams is likely to grow from hundreds to thousands in order to achieve significantly larger spectrum reuse factors compared to existing HTS systems. This requires a careful design of the antenna system to provide a high carrier-to-interferer ratio (\(C/I\)), which has a direct impact on achievable data rates per user. Moreover, flexibility in the coverage characteristics, to account for short, mid and longer-term variations of the traffic demands, is becoming of increasing importance for optimising the satellite's \"sellable\" capacity [10]. In order to meet these requirements, upcoming software-defined satellites mostly employ array-fed reflectors (AFR) in imaging configurations, where the reflector magnifies the gain produced by a primary feed array. AFR antenna architectures combine the high gain offered by reflector-based antenna solutions with the flexibility of active array solutions [11]. In order to maximise the benefits from the flexibility offered by the emerging payload architectures and optimise the system performance, VHTS systems are likely to also deploy more advanced resource (e.g., power, time, frequency, polarisation) allocation policies and interference mitigation techniques (e.g., user scheduling and/or precoding) [12]. Consequently, these systems are becoming increasingly complex, such that optimising and evaluating their performance becomes a multidimensional problem that depends not only on the antenna performance but also on the system architecture and operation, as well as the traffic characteristics, thus benefiting from a model-based design (MBD) approach. When it comes to the antenna development, unlike heritage broadcast missions where shaped antennas could be designed against effective isotropic radiated power (EIRP) and gain-to-noise-temperature (G/T) contours, MBRAs for multi-beam and VHTS missions should thus be considered in the context of end-to-end system performance [13].