Integrating Over-the-Air Federated Learning and Non-Orthogonal Multiple Access: What Role Can RIS Play?

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 reconfigurable intelligent surface (RIS)-aided hybrid network by leveraging the RIS to flexibly adjust the decoding order of heterogeneous data. A new metric of computation rate is defined to measure the performance of AirFL users. Upon this, 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 reflection coefficients. Since the concurrent transmissions of all computation and communication signals are aided by the discrete phase-shifting elements at the RIS, the formulated 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 difference-of-convex programming, and then the receive control subproblem is addressed by successive convex approximation, where the closed-form expressions of simplified cases are derived to obtain deep insights. For the reflection design problem (P2), a 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 non-convex problem (P0) iteratively. Finally, simulation results reveal that i) the proposed RIS-aided hybrid network can support on-demand communication and computation efficiently, ii) the system performance can be improved by properly selecting the location of the RIS, and iii) the designed algorithms are also applicable to conventional networks with only AirFL or NOMA users.