Beamforming and Waveform Optimization for RF Wireless Power Transfer with Beyond Diagonal Reconfigurable Intelligent Surfaces

Radio frequency (RF) wireless power transfer (WPT) is a promising technology to seamlessly charge low-power devices, but its low end-to-end power transfer efficiency remains a critical challenge. To address the latter, low-cost transmit/radiating architectures, e.g., based on reconfigurable intelligent surfaces (RISs), have shown great potential. Beyond diagonal (BD) RIS is a novel branch of RIS offering enhanced performance over traditional diagonal RIS (D-RIS) in wireless communications, but its potential gains in RF-WPT remain unexplored. Motivated by this, we analyze a BD-RIS-assisted single-antenna RF-WPT system to charge a single rectifier, and formulate a joint beamforming and multi-carrier waveform optimization problem aiming to maximize the harvested power. We propose two solutions relying on semi-definite programming for fully connected BD-RIS and an efficient low-complexity iterative method relying on successive convex approximation. Numerical results show that the proposed algorithms converge to a local optimum and that adding transmit sub-carriers or RIS elements improves the harvesting performance. We show that the transmit power budget impacts the relative power allocation among different sub-carriers depending on the rectifier's operating regime, while BD-RIS shapes the cascade channel differently for frequency-selective and flat scenarios. Finally, we verify by simulation that BD-RIS and D-RIS achieve the same performance under pure far-field line-of-sight conditions (in the absence of mutual coupling). Meanwhile, BD-RIS outperforms D-RIS as the non-line-of-sight components of the channel become dominant.

Beyond Diagonal RIS in Multiuser MIMO: Graph Theoretic Modeling and Optimal Architectures with Low Complexity

Reconfigurable intelligent surfaces (RIS) is regarded as a key enabler of wave/analog-domain beamforming, processing, and computing in future wireless communication systems. Recently, Beyond Diagonal RIS (BD-RIS) has been proposed as a generalization of conventional RIS, offering enhanced design flexibility thanks to the presence of tunable impedances that connect RIS elements. However, increased interconnections lead to high circuit complexity, which poses a significant practical challenge. In this paper, we address the fundamental open question: What is the class of BD-RIS architectures that achieves the optimal performance in a RIS-aided multiuser multi-input multi-output (MIMO) system? By modeling BD-RIS architectures using graph theory, we identify a class of BD-RIS architectures that achieves the optimal performance--matching that of fully-connected RIS--while maintaining low circuit complexity. Our result holds for a broad class of performance metrics, including the commonly used sum channel gain/sum-rate/energy efficiency maximization, transmit power minimization, and the information-theoretic capacity region. The number of tunable impedances in the proposed class is ${O}(N\min\{D,N/2\})$, where $N$ denotes the number of RIS elements and $D$ is the degree of freedom of the multiuser MIMO channel, i.e., the minimum between the number of transmit antennas and the total number of received antennas across all users. Since $D$ is much smaller than $N$ in practice, the complexity scales as ${O}(ND)$, which is substantially lower than the ${O}(N^2)$ complexity of fully-connected RIS. We further introduce two novel BD-RIS architectures--band-connected RIS and stem-connected RIS--and show that they belong to the optimal architecture class under certain conditions. Simulation results validate the optimality and enhanced performance-complexity tradeoff of our proposed architecture.

Uplink Rate-Splitting Multiple Access for Mobile Edge Computing with Short-Packet Communications

In this paper, a Rate-Splitting Multiple Access (RSMA) scheme is proposed to assist a Mobile Edge Computing (MEC) system where local computation tasks from two users are offloaded to the MEC server, facilitated by uplink RSMA for processing. The efficiency of the MEC service is hence primarily influenced by the RSMA-aided task offloading phase and the subsequent task computation phase, where reliable and low-latency communication is required. For this practical consideration, short-packet communication in the Finite Blocklength (FBL) regime is introduced. In this context, we propose a novel uplink RSMA-aided MEC framework and derive the overall Successful Computation Probability (SCP) with FBL consideration. To maximize the SCP of our proposed RSMA-aided MEC, we strategically optimize: (1) the task offloading factor which determines the number of tasks to be offloaded and processed by the MEC server; (2) the transmit power allocation between different RSMA streams; and (3) the task-splitting factor which decides how many tasks are allocated to splitting streams, while adhering to FBL constraints. To address the strong coupling between these variables in the SCP expression, we apply the Alternative Optimization method, which formulates tractable subproblems to optimize each variable iteratively. The resultant non-convex subproblems are then tackled by Successive Convex Approximation. Numerical results demonstrate that applying uplink RSMA in the MEC system with FBL constraints can not only improve the SCP performance but also provide lower latency in comparison to conventional transmission scheme such as Non-orthogonal Multiple Access (NOMA).

Uplink Rate Splitting Multiple Access with Imperfect Channel State Information and Interference Cancellation

This article investigates the performance of uplink rate splitting multiple access (RSMA) in a two-user scenario, addressing an under-explored domain compared to its downlink counterpart. With the increasing demand for uplink communication in applications like the Internet-of-Things, it is essential to account for practical imperfections, such as inaccuracies in channel state information at the receiver (CSIR) and limitations in successive interference cancellation (SIC), to provide realistic assessments of system performance. Specifically, we derive closed-form expressions for the outage probability, throughput, and asymptotic outage behavior of uplink users, considering imperfect CSIR and SIC. We validate the accuracy of these derived expressions using Monte Carlo simulations. Our findings reveal that at low transmit power levels, imperfect CSIR significantly affects system performance more severely than SIC imperfections. However, as the transmit power increases, the impact of imperfect CSIR diminishes, while the influence of SIC imperfections becomes more pronounced. Moreover, we highlight the impact of the rate allocation factor on user performance. Finally, our comparison with non-orthogonal multiple access (NOMA) highlights the outage performance trade-offs between RSMA and NOMA. RSMA proves to be more effective in managing imperfect CSIR and enhances performance through strategic message splitting, resulting in more robust communication.

Optimization of Beyond Diagonal RIS: A Universal Framework Applicable to Arbitrary Architectures

Reconfigurable intelligent surfaces (RISs) are envisioned as a promising technology for future wireless communication systems due to their ability to control the propagation environment in a hardware- and energy-efficient way. Recently, the concept of RISs has been extended to beyond diagonal RISs (BD-RISs), which unlock the full potential of RISs thanks to the presence of tunable interconnections between RIS elements. While various algorithms have been proposed for specific BD-RIS architectures, a universal optimization framework applicable to arbitrary architectures is still lacking. In this paper, we bridge this research gap by proposing an architecture-independent framework for BD-RIS optimization, with the main focus on sum-rate maximization and transmit power minimization in multiuser multi-input single-output (MU-MISO) systems. Specifically, we first incorporate BD-RIS architectures into the models by connecting the scattering matrix with the admittance matrix and introducing appropriate constraints to the admittance matrix. The formulated problems are then solved by our custom-designed partially proximal alternating direction method of multipliers (pp-ADMM) algorithms. The pp-ADMM algorithms are computationally efficient, with each subproblem either admitting a closed-form solution or being easily solvable. We further explore the extension of the proposed framework to general utility functions and multiuser multi-input multi-output (MU-MIMO) systems. Simulation results demonstrate that the proposed approaches achieve a better trade-off between performance and computational efficiency compared to existing methods. We also compare the performance of various BD-RIS architectures in MU-MISO systems using the proposed approach, which has not been explored before due to the lack of an architecture-independent framework.

Dual-Polarized Beyond Diagonal RIS

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a family of RIS architectures more flexible than conventional RIS. While BD-RIS has been primarily analyzed assuming uni-polarized systems, modern wireless deployments are dual-polarized. To address this gap, this paper investigates the fundamental limits of dual-polarized BD-RIS-aided systems. We derive the scaling laws governing the performance of BD-RIS and the Pareto frontier of the trade-off between performance and circuit complexity enabled by BD-RIS. Theoretical results show that the group-connected RIS with group size 2 provides remarkable gains over conventional RIS in both Rayleigh and line-of-sight (LoS) channels, while maintaining a reduced circuit complexity.

Rate-Splitting Multiple Access for Integrated Sensing and Communications: A First Experimental Study

A canonical use case of Integrated Sensing and Communications (ISAC) in multiple-input multiple-output (MIMO) systems involves a multi-antenna transmitter communicating with $K$ users and sensing targets in its vicinity. For this setup, precoder and multiple access designs are of utmost importance, as the limited transmit power budget must be efficiently directed towards the desired directions (users and targets) to maximize both communications and sensing performance. This problem has been widely investigated analytically under various design choices, in particular (a) whether or not a dedicated sensing signal is needed, and (b) for different MIMO multiple access techniques, such as Space Division Multiple Access (SDMA) and Rate-Splitting Multiple Access (RSMA). However, a conclusive answer on which design choice achieves the best ISAC performance, backed by experimental results, remains elusive. We address this vacuum by experimentally evaluating and comparing RSMA and SDMA for communicating with two users $(K = 2)$ and sensing (ranging) one target. Over three scenarios that are representative of \emph{vehicular} ISAC, covering different levels of inter-user interference and separation/integration between sensing and communications, we show that RSMA without a dedicated sensing signal achieves better ISAC performance -- i.e., higher sum throughput (upto $50\%$ peak throughput gain) for similar radar SNR (between $20$ to $24{\rm dB}$) -- than SDMA with a dedicated sensing signal. This first-ever experimental study of RSMA ISAC demonstrates the feasibility and the superiority of RSMA for future multi-functional wireless systems.

A Decoupled Channel Estimation Method for Beyond Diagonal RIS

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a new architecture for RIS where elements are interconnected to provide more wave manipulation flexibility than traditional single connected RIS, enhancing data rate and coverage. However, channel estimation for BD-RIS is challenging due to the more complex multiple-connection structure involving their scattering elements. To address this issue, this paper proposes a decoupled channel estimation method for BD-RIS that yields separate estimates of the involved channels to enhance the accuracy of the overall combined channel by capitalizing on its Kronecker structure. Starting from a least squares estimate of the combined channel and by properly reshaping the resulting filtered signal, the proposed algorithm resorts to a Khatri-Rao Factorization (KRF) method that teases out the individual channels based on simple rank-one matrix approximation steps. Numerical results show that the proposed decoupled channel estimation yields more accurate channel estimates than the classical least squares scheme.

Non-reciprocal Beyond Diagonal RIS: Sum-Rate Maximization in Full-Duplex Communications

Reconfigurable intelligent surface (RIS) has been envisioned as a key technology in future wireless communication networks to enable smart radio environment. To further enhance the passive beamforming capability of RIS, beyond diagonal (BD)-RIS has been proposed considering reconfigurable interconnections among different RIS elements. BD-RIS has a unique feature that cannot be enabled by conventional diagonal RIS; it can be realized by non-reciprocal circuits and thus enables an asymmetric scattering matrix. This feature provides the capability to break the wireless channel reciprocity, and has the potential to benefit full-duplex (FD) systems. In this paper, we model the BD RIS-assisted FD systems, where the impact of BD-RIS non-reciprocity and that of structural scattering, which refers to the specular reflection generated by RIS when the RIS is turned OFF, are explicitly captured. To assess the benefits of non-reciprocal BD-RIS, we optimise the scattering matrix, precoder and combiner to maximize the DL and UL sum-rates in the FD system. To tackle this optimization problem, we propose an iterative algorithm based on block coordination descent (BCD) and penalty dual decomposition (PDD). Numerical results demonstrate surprising benefits of non-reciprocal BD-RIS that it can achieve much higher DL and UL sum-rates in the FD scenario than reciprocal BD-RIS and conventional diagonal RIS.

Non-reciprocal BD-RIS in Full-duplex Communications: A Perspective on Sum-rate Maximization

Reconfigurable intelligent surface (RIS) has been envisioned as a key technology in future wireless communication networks to enable smart radio environment. To further enhance the passive beamforming capability of RIS, beyond diagonal (BD)-RIS has been proposed considering interconnections among different RIS elements. BD-RIS has a unique feature that cannot be enabled by conventional diagonal RIS; it can be realized by non-reciprocal circuits and thus has asymmetric scattering matrix. This feature provides probability to break the wireless channel reciprocity, and thus has potential to benefit the full-duplex (FD) system. In this paper, we model the BD RIS-assisted FD systems, where the impact of BD-RIS non-reciprocity and that of structural scattering, which refers to the virtual direct channel constructed by RIS when the RIS is turned OFF, are explicitly captured. To visualize the analysis, we propose to design the scattering matrix, precoder and combiner to maximize the DL and UL sum-rates in the FD system. To tackle this optimization problem, we propose an iterative algorithm based on block coordination descent (BCD) and penalty dual decomposition (PDD). Numerical results demonstrate surprising benefits of non-reciprocal BD-RIS that it can achieve higher DL and UL sum-rates in the FD scenario than reciprocal BD-RIS and conventional diagonal RIS.