Learning to Optimize Satellite Flexible Payloads Miguel ´ Angel V´ azquez, Senior Member, IEEE, Pol Henarejos, Senior Member, IEEE and Ana P´ erez-Neira, Fellow Member, IEEE. Abstract—This paper proposes an optimization technique for satellite systems with flexible payloads. Unlike current satellites whose per-beam capacity is fixed, forthcoming payloads will have bandwidth and power allocation reconfiguration capabilities allowing the operators to modify the offered capacity. Assuming a generic flexible payload architecture, this paper introduces an op- timization technique that is able to provide an efficient bandwidth and power allocation that fulfil the user terminals rate requests. Furthermore, we introduce a deep learning regression algorithm able to reproduce the mapping of the proposed optimization tech- nique with a very reduced computational complexity. By using the output of the optimization technique as ground truth, we design a deep neural network that behaves very similar to the optimization problem yet with a dramatically reduced computational time. Numerical results show the benefits of the proposed technique and in particular, we observe two order of magnitude computational time decrease when using the deep learning approach compared to the classical optimization technique yet preserving almost the same performance. Keywords—Satellite communications, deep learning, power con- trol. I. I NTRODUCTION Current commercial multibeam satellite systems present a fixed data-rate capacity at each beam. This fact strongly limits the operator exploitation margin as regional user data rate demands over a certain geographical area shall be predicted when the satellite is built and maintained over the satellite life which is generally about 15 years. Furthermore, mobile user terminals (UTs) such as vessels and airplanes lead to spatial temporal variations of the data-rate demands which might cause certain beams to saturate over a certain period. In order to solve this problem, future satellite payloads will have reconfiguration capabilities. In particular, the on- board analogue infrastructure will allow modular spectrum channelization of each beam, providing a bandwidth and power control over the coverage area. Examples of future flexible payloads are Eutelsat Quantum and Inmarsat-6. Although commercial flexible payloads are currently start- ing to be launched, academia has investigated them in the last fifteen years [1]–[4]. On the one hand, the works [1], [2] introduced the on board technology advances required for the creation of flexible payloads such as preliminary heuristic optimization methods. On the other hand, in [3] the authors assume an arbitrary payload architecture able to increase the flexibility of the allocation of power and bandwidth over the different beams and additional heuristic optimization methods. Finally, the work in [4] introduces a simulated annealing technique for solving a mixed integer linear program that models a particular flexible payload allocation optimization problem. In contrast to the mentioned works, in this paper we introduce a new optimization approach that provides efficient solutions considering a generic flexible payload. In particular, we focus on minimizing the sum the users service level agree- ments (SLAs) violations, defined as the difference between the requested data rate and the offered one by the satellite operator. To the best of authors knowledge, the proposed approach is novel, and it certainly collapses the real problem of flexible satellite payload optimization. The resulting optimization prob- lem is observed to be non-convex and, in order to solve it, we use the concave-convex procedure (CCP) [5]. Although CCP iterative method is able to yield an efficient solution, it requires solving a large number of convex problems, limiting its applicability in very short time-to-react events such as sudden requests of traffic demands. Remarkably, the CCP approach is ideal for large scale variations such as hourly data rate demands or planned new customers deployment. Inspired by the recent results on deep learning for power allocation in different scenarios [6], [7], here we aim at using a deep neural network (DNN) for mimicking the CCP implemen- tation over the conceived optimization problem. Concretely, we train a DNN with a plethora of channel realizations, data- rate user demands, and their corresponding efficient power allocation and we use this dataset as ground truth for designing a DNN. The numerical simulations show that the proposed DNN architecture can reproduce the power allocation efficient solutions of the CCP method. The conceived DNN is very attractive to the satellite industry as it is able to provide efficient power allocations with a dramatically low number of operations. A similar approach was carried out for satellite communications in [8], [9] considering other optimization problem and DNN approximation. The rest of this work is organized as follows. Section 2 presents the power allocation problem for flexible payloads and introduces the use of the CCP method for solving it. The use of DNNs for power allocation is introduced in Section 3, showing how the training can be performed. Numerical results in Section 4 show the performance of the conceived DNNs for this optimization framework. Section 5 concludes. II. SYSTEM MODEL AND PROBLEM STATEMENT The system under consideration is a satellite forward link transmission with frequency-division multiple access. Perfect channel state information is assumed both at the transmitter (i.e. the satellite gateway) and the receivers (the satellite UTs). This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 101004215 (ATRIA) and by the Spanish ministry of science and innovation under project IRENE (PID2020-115323RB-C31 / AEI / 10.13039/501100011033) and grant from the Spanish ministry of economic affairs and digital transformation and of the European union – NextGenerationEU [UNICO-5G I+D/AROMA3D- Space (TSI-063000-2021-70).