The beyond-diagonal reconfigurable intelligent surface (BD-RIS) represents the next advancement in reconfigurable intelligent surfaces (RIS), offering enhanced flexibility by supporting multiple modes and architectures. This study examines the spectral efficiency (SE) of a single-cell RSMA-based multi-user MIMO system assisted by two sector BD-RIS. The scattering matrix of BD-RIS and the power allocation between common and private precoders primarily determine the SE. We employ a two-step optimization process to determine these parameters. First, the scattering matrix is optimized by maximizing the total channel gain of the user equipment (UEs). Using the optimized scattering matrix, the power allocation for the common and private streams is then calculated by maximizing the SE of the system through a fractional programming technique, which gives a closed-form solution. The SE is computed using the optimized parameters and is numerically plotted to evaluate the performance of the system. The system is extensively analyzed across various precoding techniques, numbers of UEs, and BD-RIS elements, and is also compared to space division multiple access (SDMA). Numerical results show that BD-RIS outperforms both the traditional RIS and the scenario without RIS.

We propose distributed scheduling algorithms that guarantee a constant fraction of the maximum throughput for typical wireless topologies, and have O(1) delay and complexity in the network size. Our algorithms resolve collisions among pairs of conflicting nodes by assigning a master-slave hierarchy. When the master-slave hierarchy is chosen randomly, our algorithm matches the throughput performance of the maximal scheduling policies, with a complexity and delay that do not scale with network size. When the master-slave hierarchy is chosen based on the network topology, the throughput performance of our algorithm is characterized by a parameter of the conflict graph called the master-interference degree. For commonly used conflict graph topologies, our results lead to the best known throughput guarantees among the algorithms that have O(1) delay and complexity. Numerical results indicate that our algorithms out-perform the existing O(1) complexity algorithms like Q-CSMA.

We consider a carrier sense multiple access (CSMA)-based scheduling algorithm for a single-hop wireless network under a realistic signal-to-interference-plus-noise ratio model for the interference. We propose two local optimization-based approximation algorithms to efficiently estimate certain attempt rate parameters of CSMA called fugacities. It is known that adaptive CSMA can achieve throughput optimality by sampling feasible schedules from a Gibbs distribution, with appropriate fugacities. Unfortunately, obtaining these optimal fugacities is an NP-hard problem. Furthermore, the existing adaptive CSMA algorithms use a stochastic gradient descent-based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. To address this issue, we first propose an algorithm to estimate the fugacities, that can support a given set of desired service rates. The convergence rate and the complexity of this algorithm are independent of the network size, and depend only on the neighborhood size of a link. Furthermore, we show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. Then, we propose another local algorithm to estimate the optimal fugacities under a utility maximization framework, and characterize its accuracy. Numerical results indicate that the proposed methods have a good degree of accuracy, and achieve extremely fast convergence to near-optimal fugacities, and often outperform the convergence rate of the stochastic gradient descent by a few orders of magnitude.