  With the aim of integrating over-the-air federated learning (AirFL) and
non-orthogonal multiple access (NOMA) into an on-demand universal framework,
this paper proposes a novel reconfigurable intelligent surface (RIS)-aided
hybrid network by leveraging the RIS to flexibly adjust the signal processing
order of heterogeneous data. The objective of this work is to maximize the
achievable hybrid rate by jointly optimizing the transmit power, controlling
the receive scalar, and designing the phase shifts. Since the concurrent
transmissions of all computation and communication signals are aided by the
discrete phase shifts at the RIS, the considered problem (P0) is a challenging
mixed integer programming problem. To tackle this intractable issue, we
decompose the original problem (P0) into a non-convex problem (P1) and a
combinatorial problem (P2), which are characterized by the continuous and
discrete variables, respectively. For the transceiver design problem (P1), the
power allocation subproblem is first solved by invoking the
difference-of-convex programming, and then the receive control subproblem is
addressed by using the successive convex approximation, where the closed-form
expressions of simplified cases are derived to obtain deep insights. For the
reflection design problem (P2), the relaxation-then-quantization method is
adopted to find a suboptimal solution for striking a trade-off between
complexity and performance. Afterwards, an alternating optimization algorithm
is developed to solve the non-linear and non-convex problem (P0) iteratively.
Finally, simulation results reveal that 1) the proposed RIS-aided hybrid
network can support the on-demand communication and computation efficiently, 2)
the performance gains can be improved by properly selecting the location of the
RIS, and 3) the designed algorithms are also applicable to conventional
networks with only AirFL or NOMA users.
