Physical layer security is a useful tool to prevent confidential information from wiretapping. In this paper, we consider a generalized model of conventional physical layer security, referred to as hierarchical information accessibility (HIA). A main
feature of the HIA model is that a network has a hierarchy in information accessibility, wherein decoding feasibility is determined by a priority of users. Under this HIA model, we formulate a sum secrecy rate maximization problem with regard to precoding vectors. This problem is challenging since multiple non-smooth functions are involved into the secrecy rate to fulfill the HIA conditions and also the problem is non-convex. To address the challenges, we approximate the minimum function by using the LogSumExp technique, thereafter obtain the first-order optimality condition. One key observation is that the derived condition is cast as a functional eigenvalue problem, where the eigenvalue is equivalent to the approximated objective function of the formulated problem. Accordingly, we show that finding a principal eigenvector is equivalent to finding a local optimal solution. To this end, we develop a novel method called generalized power iteration for HIA (GPI-HIA). Simulations demonstrate that the GPI-HIA significantly outperforms other baseline methods in terms of the secrecy rate.
Rate-splitting multiple access (RSMA) is a general multiple access scheme for downlink multi-antenna systems embracing both classical spatial division multiple access and more recent non-orthogonal multiple access. Finding a linear precoding strategy
that maximizes the sum spectral efficiency of RSMA is a challenging yet significant problem. In this paper, we put forth a novel precoder design framework that jointly finds the linear precoders for the common and private messages for RSMA. Our approach is first to approximate the non-smooth minimum function part in the sum spectral efficiency of RSMA using a LogSumExp technique. Then, we reformulate the sum spectral efficiency maximization problem as a form of the log-sum of Rayleigh quotients to convert it into a tractable non-convex optimization problem. By interpreting the first-order optimality condition of the reformulated problem as an eigenvector-dependent nonlinear eigenvalue problem, we reveal that a leading eigenvector is a local optimal solution. To find the leading eigenvector, we propose a computationally efficient algorithm inspired by a power iteration method. Simulation results show that the proposed RSMA transmission strategy provides significant improvement in the sum spectral efficiency compared to the state-of-the-art RSMA transmission methods, while requiring considerably less computational complexity.
