Joint power allocation and IRS phase shift optimization for ergodic sum rate in RSMA-OFDM networks with statistical CSI

Rate splitting multiple access (RSMA) serves as the foundational multiple-access scheme for the future wireless networks. Splitting user data into common and private streams enhances the data rate and creates efficient interference management. To augment RSMA’s performance, Intelligent Reflecting Surface (IRS) is currently establishing itself as a viable solution for such networks to dynamically control the environment and create constructive signal paths and suppress unwanted interference. However, the efficiency of IRS-assisted RSMA networks can be critically degraded by frequency-selective fading. Orthogonal Frequency Division Multiplexing (OFDM) directly addresses this challenge by dividing the channel into orthogonal subcarriers, ensuring robust and high-capacity delivery. This paper investigates the ergodic sum rate performance of an IRS-assisted downlink RSMA-OFDM network. Unlike conventional works that assume perfect channel state information (CSI), we consider a more practical scenario where only statistical CSI is available at the base station. In this setting, user messages are split into common and private streams, and the system operates over frequency-selective Rayleigh fading channels. We derive closed-form ergodic rate expressions for both private and common streams and formulate an ergodic sum rate maximization problem by jointly optimizing the power allocation coefficients at the transmitter and the phase shifts at the IRS. To solve this non-convex problem, we propose an efficient alternating optimization (AO) algorithm based on Sample Average Approximation (SAA), with projected gradient ascent for power allocation and Riemannian gradient ascent for IRS phase optimization. Simulation results demonstrate that the proposed IRS-assisted RSMA-OFDM framework significantly enhances the performance of RSMA without IRS, even under frequency-selective fading channels. Moreover, the proposed framework consistently outperforms the traditional NOMA scheme in terms of ergodic sum rate and outage probability.