Why do we call it Mean Square Error beamformer? Study in the unicast and multicast satellite scenarios

Low-complexity suboptimal solutions are widely accepted to design spatial precoders that mitigate the resulting co-channel interference in multibeam high throughput satellites, which is caused by the aggressive frequency reuse. The most widely accepted solution, due to its simplicity and robustness to different channel conditions, is the so-called minimum Mean Square Error (MMSE) precoder. This work reviews the different rationals that support this technique and presents an alternative that maximizes the directivity. With this new point of view we propose a solution that is suitable for both the unicast and the multicast scenario. The latter is quite unexplored in the existing literature, partly explained by its loss of performance with respect to the unicast case. The proposed technique presents a practical and more clear design than the MSE, and the numerical simulations proof its gains compared to the benchmark.