  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.
