Optimal DVB-S2 spectral efficiency with hierarchical modulation

We study the design of a DVB-S2 system in order to maximise spectral efficiency. This task is usually challenging due to channel variability. The solution adopted in modern satellite communications systems such as DVB-SH and DVB-S2 relies mainly on a time sharing strategy. Recently, we proposed to combine time sharing with hierarchical modulation to increase the transmission rate of broadcast systems. However, the optimal spectral efficiency remained an open question. In this paper, we show that the optimal transmission rate is the solution of a linear programming problem. We also study the performance of the optimal scheme for a DVB-S2 use case.