While Cramér-Rao lower bound is an important metric in sensing functions in integrated sensing and communications (ISAC) designs, its optimization usually involves a computationally expensive solution such as semidefinite relaxation. In this paper, we aim to develop a low-complexity yet efficient algorithm for CRLB optimization. We focus on a beamforming design that maximizes the weighted sum between the communications sum rate and the sensing CRLB, subject to a transmit power constraint. Given the non-convexity of this problem, we propose a novel method that combines successive convex approximation (SCA) with a shifted generalized power iteration (SGPI) approach, termed SCA-SGPI. The SCA technique is utilized to approximate the non-convex objective function with convex surrogates, while the SGPI efficiently solves the resulting quadratic subproblems. Simulation results demonstrate that the proposed SCA-SGPI algorithm not only achieves superior tradeoff performance compared to existing method but also significantly reduces computational time, making it a promising solution for practical ISAC applications.

Joint communications and sensing (JCAS) is expected to be a crucial technology for future wireless systems. This paper investigates beamforming design for a multi-user multi-target JCAS system to ensure fairness and balance between communications and sensing performance. We jointly optimize the transmit and receive beamformers to maximize the weighted sum of the minimum communications rate and sensing mutual information. The formulated problem is highly challenging due to its non-smooth and non-convex nature. To overcome the challenges, we reformulate the problem into an equivalent but more tractable form. We first solve this problem by alternating optimization (AO) and then propose a machine learning algorithm based on the AO approach. Numerical results show that our scheme scales effectively with the number of the communications users and provides better performance with shorter run time compared to conventional optimization approaches.

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has garnered significant research interest recently due to its ability to generalize existing reconfigurable intelligent surface (RIS) architectures and provide enhanced performance through flexible inter-connection among RIS elements. However, current BD-RIS designs often face challenges related to high circuit complexity and computational complexity, and there is limited study on the trade-off between system performance and circuit complexity. To address these issues, in this work, we propose a novel BD-RIS architecture named Q-stem connected RIS that integrates the characteristics of existing single connected, tree connected, and fully connected BD-RIS, facilitating an effective trade-off between system performance and circuit complexity. Additionally, we propose two algorithms to design the RIS scattering matrix for a Q-stem connected RIS aided multiuser broadcast channels, namely, a low-complexity least squares (LS) algorithm and a suboptimal LS-based quasi-Newton algorithm. Simulations show that the proposed architecture is capable of attaining the sum channel gain achieved by fully connected RIS while reducing the circuit complexity. Moreover, the proposed LS-based quasi-Newton algorithm significantly outperforms the baselines, while the LS algorithm provides comparable performance with a substantial reduction in computational complexity.

Rate-splitting multiple access (RSMA) is gaining increasing recognition as a pivotal technology for advancing green communication networks, primarily due to its proficiency in boosting energy efficiency (EE) and lowering power consumption at the transmitter. In this article, we commence by offering a concise overview of the latest advancements in RSMA for green communications. Motivated by the limitations identified in existing studies, we then focus on robust beamforming design of RSMA to optimize the ergodic EE with imperfect channel state information at the transmitter (CSIT). We first introduce an enhanced successive convex approximation (ESCA) algorithm, which expands upon the traditional successive convex approximation (SCA) approach for maximizing EE with perfect CSIT and adapts it to the imperfect CSIT scenario. To further reduce the computational complexity, we develop a novel and efficient beamforming optimization algorithm to tackle the ergodic EE problem. A key feature of our proposed approach is the use of the semi-closed-form optimal beamforming structure identified for the ergodic EE problem. Subsequently, we propose a fixed-point-iteration (FPI)-based algorithm to determine the optimal Lagrange dual variables within the optimal beamforming structure. Numerical results show that both proposed algorithms achieve near-optimal solutions and the efficient semi-closed-form optimization algorithm remarkably reduces the computational complexity. Moreover, this study is the first to present an extensive numerical comparison of the ergodic EE between RSMA and other baseline multiple access techniques under imperfect CSIT. These results further highlight the superior EE gains offered by RSMA, reinforcing its potential as a key enabler for green communication networks.

Rate-splitting multiple access (RSMA) emerges as a compelling physical-layer transmission paradigm for effectively managing interference in 6G networks. Within the realm of RSMA transmission frameworks, generalized rate-splitting (GRS) stands out as a versatile strategy that embraces existing multiple access (MA) schemes, including space division multiple access (SDMA), non-orthogonal multiple access (NOMA), and orthogonal multiple access (OMA) as specific instances. Despite its versatility, GRS encounters significant design challenges, particularly in dealing with the resource optimization complexities resulting from the exponential growth in the number of common streams with the number of users. To tackle the issue, in this work, we propose a novel and highly efficient beamforming optimization algorithm for GRS to maximize the ergodic sum rate (ESR) with imperfect channel state information at the transmitter (CSIT). Specifically, the stochastic ESR maximization problem is first transformed into a deterministic one using sampled average approximation (SAA). This transformed problem is further decomposed into a series of convex subproblems by the fraction programming (FP) approach. Based on the Karush-Kuhn-Tucker (KKT) conditions of each subproblem, we derive the optimal beamforming structure (OBS) of GRS. To determine the Lagrange dual variables within the OBS, we then propose a fixed point iteration (FPI)-based method. Through extensive numerical results, we show that the proposed algorithm significantly reduces the computational complexity without sacrificing ESR performance compared to conventional optimization algorithms. Thanks to the efficiency of our algorithm, we illustrate, for the first time, the performance of GRS with more than three users. We draw the conclusion that our proposed algorithm shows promise in advancing the practical application of RSMA in 6G.

In this paper, we aim at maximizing the weighted sum-rate (WSR) of rate splitting multiple access (RSMA) in multi-user multi-antenna transmission networks through the joint optimization of rate allocation and beamforming. Unlike conventional methods like weighted minimum mean square error (WMMSE) and standard fractional programming (FP), which tackle the non-convex WSR problem iteratively using disciplined convex subproblems and optimization toolboxes, our work pioneers a novel toolbox-free approach. For the first time, we identify the optimal beamforming structure and common rate allocation for WSR maximization in RSMA by leveraging FP and Lagrangian duality. Then we propose an algorithm based on FP and fixed point iteration to optimize the beamforming and common rate allocation without the need for optimization toolboxes. Our numerical results demonstrate that the proposed algorithm attains the same performance as standard FP and classical WMMSE methods while significantly reducing computational time.

Joint optimization for common rate allocation and beamforming design have been widely studied in rate splitting multiple access (RSMA) empowered multiuser multi-antenna transmission networks. Due to the highly coupled optimization variables and non-convexity of the joint optimization problems, emerging algorithms such as weighted minimum mean square error (WMMSE) and successive convex approximation (SCA) have been applied to RSMA which typically approximate the original problem with a sequence of disciplined convex subproblems and solve each subproblem by an optimization toolbox. While these approaches are capable of finding a viable solution, they are unable to offer a comprehensive understanding of the solution structure and are burdened by high computational complexity. In this work, for the first time, we identify the optimal beamforming structure and common rate allocation for the weighted sum-rate (WSR) maximization problem of RSMA. We then propose a computationally efficient optimization algorithm that jointly optimizes the beamforming and common rate allocation without relying on any toolbox. Specifically, we first approximate the original WSR maximization problem with a sequence of convex subproblems based on fractional programming (FP). By exploiting the Karush-Kuhn-Tucker (KKT) conditions of each subproblem, the optimal beamforming structure is derived. An efficient hyperplane fixed point iteration method is then proposed to find the optimal Lagrangian dual variables. Numerical results show that the proposed algorithm achieves the same performance but takes only 0.5% or less simulation time compared with the state-of-the-art WMMSE, SCA, and FP algorithms. The proposed algorithms pave the way for the practical and efficient optimization algorithm design for RSMA and its applications in 6G.