Joint Design of Power Allocation and Amplitude Coefficients for Ergodic Rate Optimization in STAR-RIS-Aided NOMA System

In this article, the rate performance of simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided nonorthogonal multiple access (NOMA) system is investigated, and joint optimization designs of power allocation (PA) of users and amplitude coefficients of RIS elements are presented based on statistical channel information for maximizing the ergodic rate. According to the performance analysis, the ergodic rate of STAR-RIS-aided NOMA system is derived for theoretical evaluation and optimization, and resultant tightly approximate expression is attained. Also, an upper bound of ergodic rate is derived for simplifying the tight approximation and the rate optimization. Then, we formulate the joint optimization problem of PA and amplitude coefficients for ergodic rate maximization under the constraints of maximum power, minimal rate, and maximum sum amplitude. It is shown that this multidimensional optimization problem can be simplified as 2-D optimization problem, and thus, we present an optimal scheme based on 2-D search method to obtain the optimal solution. To simplify the optimal scheme, by maximizing the upper bound of ergodic rate, a suboptimal scheme and its improved scheme based on 1-D search method are, respectively, proposed, and they can obtain the performance close to the optimal scheme with lower complexity. Besides, three algorithms are presented for solving the design problems of optimal scheme, suboptimal scheme, and improved scheme, respectively. Simulation results show that the derived theoretical expressions match the simulations well. Moreover, the proposed schemes can achieve higher rate than the conventional fixed PA scheme and fixed amplitude allocation scheme.