Low-Overhead Channel Estimation Framework for Beyond Diagonal Reconfigurable Intelligent Surface Assisted Multi-User MIMO Communication

Beyond diagonal reconfigurable intelligent surface (BD-RIS) refers to a family of RIS architectures characterized by scattering matrices not limited to being diagonal and enables higher wave manipulation flexibility and large performance gains over conventional (diagonal) RIS. To achieve those promising gains, accurate channel state information (CSI) needs to be acquired in BD-RIS assisted communication systems. However, the number of coefficients in the cascaded channels to be estimated in BD-RIS assisted systems is significantly larger than that in conventional RIS assisted systems, because the channels associated with the off-diagonal elements of the scattering matrix have to be estimated as well. Surprisingly, for the first time in the literature, this paper rigorously shows that the uplink channel estimation overhead in BD-RIS assisted systems is actually of the same order as that in the conventional RIS assisted systems. This amazing result stems from a key observation: for each user antenna, its cascaded channel matrix associated with one reference BD-RIS element is a scaled version of that associated with any other BD-RIS element due to the common RIS-base station (BS) channel. In other words, the number of independent unknown variables is far less than it would seem at first glance. Building upon this property, this paper manages to characterize the minimum overhead to perfectly estimate all the channels in the ideal case without noise at the BS, and propose a twophase estimation framework for the practical case with noise at the BS. Numerical results demonstrate outstanding channel estimation overhead reduction over existing schemes in BD-RIS assisted systems.

Enabling Gigantic MIMO Beamforming with Analog Computing

In our previous work, we have introduced a microwave linear analog computer (MiLAC) as an analog computer that processes microwave signals linearly, demonstrating its potential to reduce the computational complexity of specific signal processing tasks. In this paper, we extend these benefits to wireless communications, showcasing how MiLAC enables gigantic multiple-input multiple-output (MIMO) beamforming entirely in the analog domain. MiLAC-aided beamforming can implement regularized zero-forcing beamforming (R-ZFBF) at the transmitter and minimum mean square error (MMSE) detection at the receiver, while significantly reducing hardware costs by minimizing the number of radio-frequency (RF) chains and only relying on low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In addition, it eliminates per-symbol operations by completely avoiding digital-domain processing and remarkably reduces the computational complexity of R-ZFBF, which scales quadratically with the number of antennas instead of cubically. Numerical results show that it can perform R-ZFBF with a computational complexity reduction of up to 7400 times compared to digital beamforming.

Analog Computing with Microwave Networks

Analog computing has been recently revived due to its potential for energy-efficient and highly parallel computations. In this paper, we investigate analog computers that linearly process microwave signals, named microwave linear analog computers (MiLACs), and their applications in signal processing for communications. We model a MiLAC as a multiport microwave network with tunable impedance components, which enables the execution of mathematical operations by reconfiguring the microwave network and applying input signals at its ports. We demonstrate that a MiLAC can efficiently compute the linear minimum mean square error (LMMSE) estimator, widely used in multiple-input multiple-output (MIMO) communications beamforming and detection, with remarkably low computational complexity, unachievable through digital computing. Specifically, the LMMSE estimator can be computed with complexity growing with the square of its input size, rather than the cube, with revolutionary applications to gigantic MIMO beamforming and detection.

Channel Coding meets Sequence Design via Machine Learning for Integrated Sensing and Communications

For integrated sensing and communications, an intriguing question is whether information-bearing channel-coded signals can be reused for sensing - specifically ranging. This question forces the hitherto non-overlapping fields of channel coding (communications) and sequence design (sensing) to intersect by motivating the design of error-correcting codes that have good autocorrelation properties. In this letter, we demonstrate how machine learning (ML) is well-suited for designing such codes, especially for short block lengths. As an example, for rate 1/2 and block length 32, we show that even an unsophisticated ML code has a bit-error rate performance similar to a Polar code with the same parameters, but with autocorrelation sidelobes 24dB lower. While a length-32 Zadoff-Chu (ZC) sequence has zero autocorrelation sidelobes, there are only 16 such sequences and hence, a 1/2 code rate cannot be realized by using ZC sequences as codewords. Hence, ML bridges channel coding and sequence design by trading off an ideal autocorrelation function for a large (i.e., rate-dependent) codebook size.

T-Parameters Based Modeling for Stacked Intelligent Metasurfaces: Tractable and Physically Consistent Model

This work develops a physically consistent model for stacked intelligent metasurfaces (SIM) using multiport network theory and transfer scattering parameters (T-parameters). Unlike the scattering parameters (S-parameters) model, which is highly complex and non-tractable due to its nested nature and excessive number of matrix inversions, the developed T-parameters model is less complex and more tractable due to its explicit and compact nature. This work further derives the constraints of T-parameters for a lossless reciprocal reconfigurable intelligent surfaces (RISs). A gradient descent algorithm (GDA) is proposed to maximize the sum rate in SIM-aided multiuser scenarios, and the results show that accounting for mutual coupling and feedback between consecutive layers can improve the sum rate. In addition, increasing the number of SIM layers with a fixed total number of elements degrades the sum rate when our exact and simplified channel models are used, unlike the simplified channel model with the Rayleigh-Sommerfeld diffraction coefficients which improves the sum rate.

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.