  In this paper, we investigate two new candidate transmission schemes,
Non-Orthogonal Frequency Reuse (NOFR) and Beam-Hoping (BH). They operate in
different domains (frequency and time/space, respectively), and we want to know
which domain shows overall best performance. We propose a novel formulation of
the Signal-to-Interference plus Noise Ratio (SINR) which allows us to prove the
frequency/time duality of these schemes. Further, we propose two novel capacity
optimization approaches assuming per-beam SINR constraints in order to use the
satellite resources (e.g. power and bandwidth) more efficiently. Moreover, we
develop a general methodology to include technological constraints due to
realistic implementations, and obtain the main factors that prevent the two
technologies dual of each other in practice, and formulate the technological
gap between them. The Shannon capacity (upper bound) and current
state-of-the-art coding and modulations are analyzed in order to quantify the
gap and to evaluate the performance of the two candidate schemes. Simulation
results show significant improvements in terms of power gain, spectral
efficiency and traffic matching ratio when comparing with conventional systems,
which are designed based on uniform bandwidth and power allocation. The results
also show that BH system turns out to show a less complex design and performs
better than NOFR system specially for non-real time services.
