  Low Earth orbit (LEO) satellite communications (SATCOM) with ubiquitous
global connectivity is deemed a pivotal catalyst in advancing wireless
communication systems for 5G and beyond. LEO SATCOM excels in delivering
versatile information services across expansive areas, facilitating both
unicast and multicast transmissions via high-speed broadband capability.
Nonetheless, given the broadband coverage of LEO SATCOM, traffic demand
distribution within the service area is non-uniform, and the
time/frequency/power resources available at LEO satellites remain significantly
limited. Motivated by these challenges, we propose a rate-matching framework
for non-orthogonal unicast and multicast (NOUM) transmission. Our approach aims
to minimize the difference between offered rates and traffic demands for both
unicast and multicast messages. By multiplexing unicast and multicast
transmissions over the same radio resource, rate-splitting multiple access
(RSMA) is employed to manage interference between unicast and multicast
streams, as well as inter-user interference under imperfect channel state
information at the LEO satellite. To address the formulated problems
non-smoothness and non-convexity, the common rate is approximated using the
LogSumExp technique. Thereafter, we represent the common rate portion as the
ratio of the approximated function, converting the problem into an
unconstrained form. A generalized power iteration (GPI)-based algorithm, coined
GPI-RS-NOUM, is proposed upon this reformulation. Through comprehensive
numerical analysis across diverse simulation setups, we demonstrate that the
proposed framework outperforms various benchmarks for LEO SATCOM with uneven
traffic demands.
