  This paper investigates the model aggregation process in an over-the-air
federated learning (AirFL) system, where an intelligent reflecting surface
(IRS) is deployed to assist the transmission from users to the base station
(BS). With the purpose of overcoming the absence of the security examination
against malicious individuals, successive interference cancellation (SIC) is
adopted as a basis to support analyzing statistic characteristics of model
parameters from devices. The objective of this paper is to minimize the
mean-square-error by jointly optimizing the receive beamforming vector at the
BS, transmit power allocation at users, and phase shift matrix of the IRS,
subject to the transmit power constraint for devices, unit-modulus constraint
for reflecting elements, SIC decoding order constraint and quality-of-service
constraint. To address this complicated problem, alternating optimization is
employed to decompose it into three subproblems, where the optimal receive
beamforming vector is obtained by solving the first subproblem with the
Lagrange dual method. Then, the convex relaxation method is applied to the
transmit power allocation subproblem to find a suboptimal solution. Eventually,
the phase shift matrix subproblem is addressed by invoking the semidefinite
relaxation. Simulation results validate the availability of IRS and the
effectiveness of the proposed scheme in improving federated learning
performance.
