  Current State-of-the-Art High Throughput Satellite systems provide wide-area
connectivity through multi-beam architectures. However, due to the tremendous
system throughput requirements that next generation Satellite Communications
expect to achieve, traditional 4-colour frequency reuse schemes, i.e., two
frequency bands with two orthogonal polarisations, are not sufficient anymore
and more aggressive solutions as full frequency reuse are gaining momentum.
These approaches require advanced interference management techniques to cope
with the significantly increased inter-beam interference, like multicast
precoding and Multi User Detection. With respect to the former, several
peculiar challenges arise when designed for SatCom systems. In particular, to
maximise resource usage while minimising delay and latency, multiple users are
multiplexed in the same frame, thus imposing to consider multiple channel
matrices when computing the precoding weights. In this paper, we focus on this
aspect by re-formulating it as a clustering problem. After introducing a novel
mathematical framework, we design a k-means-based clustering algorithm to group
users into simultaneously precoded and served clusters. Two similarity metrics
are used to this aim: the users' Euclidean distance and their channel distance,
i.e., distance in the multidimensional channel vector space. Through extensive
numerical simulations, we substantiate the proposed algorithms and identify the
parameters driving the system performance.
