Microwave Linear Analog Computers (MiLACs) for Communications: Opportunities and Challenges

Future wireless systems will require ever larger antenna arrays and heavier signal processing, making conventional digital multiple-input multiple-output (MIMO) architectures difficult to scale. In this paper, we show that a possible solution is to offload part of the processing from the digital to the analog domain. This can be done through linear microwave networks designed to compute directly using the communication signals at radio frequency (RF). These networks, denoted as microwave linear analog computers (MiLACs), can perform useful matrix operations instantly through wave propagation. Remarkably, although MiLACs are linear, the output signals can depend nonlinearly on the tunable parameters of the network, enabling the computation of operations beyond simple linear transforms. In particular, MiLACs can realize matrix inversion and pseudo-inversion with complexity scaling quadratically with matrix size, rather than cubically, which is essential in zero-forcing beamforming. We then review how MiLAC-aided MIMO architectures can reduce the number of RF chains, relax the resolution requirements on digital-to-analog converters (DACs) and analog-to-digital converters (ADCs), and decrease the beamforming complexity. We finally discuss the main challenges related to MiLAC and promising directions for future research.

Channel Estimation and Beamforming for Microwave Linear Analog Computers (MiLACs)-Aided Multiuser MISO Systems

Microwave linear analog computers (MiLACs) have recently gained attention for future gigantic multiple-input multiple-output (MIMO) systems by enabling beamforming with greatly reduced hardware and computational cost. However, channel estimation for MiLAC-aided multiuser systems remains an open problem. Conventional channel estimation requires many radio-frequency (RF) chains to access full-dimensional received signals, followed by massive digital processing, which undermines the advantages of MiLAC-aided systems in reducing the number of RF chains and computational complexity. In this paper, we propose computationally efficient channel estimation and beamforming schemes for MiLAC-aided multiuser multiple-input single-output (MU-MISO) systems with a limited number of RF chains. We consider the general case where different user groups experience different channel correlation matrices. By exploiting the rank deficiency of these matrices, the proposed schemes use MiLAC to compress the full-dimensional received signals in the analog domain, making them compatible with the available RF chains while preserving the essential channel information. Then, in the digital domain, only low-dimensional channel estimation is performed based on these compressed observations, substantially reducing computational cost. We further show how regularized zero-forcing beamforming (R-ZFBF) can be efficiently realized from the low-dimensional channel estimates through a cascade of two MiLACs, which offers greater computational flexibility than a single MiLAC. Numerical results show that the proposed schemes reduce computational complexity up to $1540\times$ and $16108\times$, for channel estimation and beamforming, respectively, while achieving performance comparable to digital baselines.

Microwave Linear Analog Computer (MiLAC) for Simultaneous Active and Passive Beamforming

Microwave linear analog computers (MiLACs) have recently emerged to enable high-performance and efficient beamforming in the analog domain. In this paper, we introduce a dual-functionality framework for MiLAC-aided transceivers. Beyond analog-domain precoding/combining (active beamforming), a MiLAC and its antenna array can simultaneously act as a reconfigurable intelligent surface (RIS) (passive beamforming). This allows the MiLAC to execute beamforming for transmission/reception while reflecting external incident signals. We provide an optimal reconfiguration strategy for this dual-functional MiLAC, and characterize the fundamental limits on the trade-off between active and passive rate, namely the capacity region bounds and the sum-rate capacity.

Active Beyond-Diagonal Reconfigurable Intelligent Surfaces: Modeling, Architecture Design, and Optimization

Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) are an emerging RIS 2.0 technology for future wireless communication. However, BD-RISs are primarily passive without active amplification, suffering from severe multiplicative path loss. To address the concern of multiplicative path loss, in this work we investigate the active BD-RIS including the modeling, architecture design, and optimization. We first analyze the active BD-RIS using multiport network theory with scattering parameters and derive a physical and electromagnetic compliant active BD-RIS aided communication model. We also design two new active BD-RIS architectures, namely fully- and group-connected active BD-RISs. Based on the proposed model and architecture, we investigate the active BD-RIS aided single-input single-output system and derive the closed-form optimal solution and scaling law of the signal-to-noise ratio. We further investigate the active BD-RIS aided multiple-input multiple-output system and propose an iterative algorithm based on quadratically constrained quadratic programming to maximize the spectral efficiency. Numerical results are provided and show that the active BD-RIS can achieve higher spectral efficiency than the active/passive diagonal RIS and passive BD-RIS. For example, to achieve the same spectral efficiency, the number of elements required by active BD-RIS is less than half of that required by active diagonal RIS, showing the advantages of active BD-RIS.

Physics-Compliant Modeling and Optimization of MIMO Systems Aided by Microwave Linear Analog Computers

Microwave linear analog computer (MiLAC) has emerged as a promising architecture for implementing linear multiple-input multiple-output (MIMO) processing in the analog domain, with radio frequency (RF) signals. Existing studies on MiLAC-aided communications rely on idealized channel models and neglect antenna mutual coupling. However, since MiLAC performs processing at RF, mutual coupling becomes critical and alters the implemented operation, not only the channel characteristics. In this paper, we develop a physics-compliant model for MiLAC-aided MIMO systems accounting for mutual coupling with multiport network theory. We derive end-to-end system models for scenarios with MiLACs at the transmitter, the receiver, or both, showing how mutual coupling impacts the linear transformation implemented by the MiLACs. Furthermore, we formulate and solve a mutual coupling aware MiLAC optimization problem, deriving a closed-form globally optimal solution that maximizes the received signal power. We establish the fundamental performance limits of MiLAC with mutual coupling, and derive three analytical results. First, mutual coupling is beneficial in MiLAC-aided systems, on average. Second, with mutual coupling, MiLAC performs as digital architectures equipped with a matching network, while having fewer RF chains. Third, with mutual coupling, MiLAC always outperforms digital architectures with no matching network. Numerical simulations confirm our theoretical findings.

Capacity of Two-User Wireless Systems Aided by Movable Signals

Movable signals have emerged as a third approach to enable smart radio environments (SREs), complementing reconfigurable intelligent surfaces (RISs) and flexible antennas. This paper investigates their potential to enhance multi-user wireless systems. Focusing on two-user systems, we characterize the capacity regions of the multiple access channel (MAC) and broadcast channel (BC). Interestingly, movable signals can dynamically adjust the operating frequency to orthogonalize the user channels, thereby significantly expanding the capacity regions. We also study frequency optimization, constraining it in a limited frequency range, and show that movable signals provide up to 45% sum rate gain over fixed signals.

Channel Estimation in MIMO Systems Aided by Microwave Linear Analog Computers (MiLACs)

Microwave linear analog computers (MiLACs) have recently emerged as a promising solution for future gigantic multiple-input multiple-output (MIMO) systems, enabling beamforming with greatly reduced hardware and computational cost. However, channel estimation for MiLAC-aided systems remains an open problem. Conventional least squares (LS) and minimum mean square error (MMSE) estimation rely on intensive digital computation, which undermines the benefits offered by MiLACs. In this letter, we propose efficient LS and MMSE channel estimation schemes for MiLAC-aided MIMO systems. By designing training precoders and combiners implemented by MiLACs, both LS and MMSE estimation are performed fully in the analog domain, achieving identical performance to their digital counterparts while significantly reducing computational complexity, transmit RF chains, analog-to-digital/digital-to-analog converters (ADCs/DACs) resolution requirements, and peak-to-average power ratio (PAPR). Numerical results verify the effectiveness and advantages of the proposed schemes.

Microwave Linear Analog Computer (MiLAC)-aided Multiuser MISO: Fundamental Limits and Beamforming Design

As wireless communication systems evolve toward the 6G era, ultra-massive/gigantic MIMO is envisioned as a key enabling technology. Recently, microwave linear analog computer (MiLAC) has emerged as a promising approach to realize beamforming entirely in the analog domain, thereby alleviating the scalability challenges associated with gigantic MIMO. In this paper, we investigate the fundamental beamforming flexibility and design of lossless and reciprocal MiLAC-aided beamforming for MU-MISO systems. We first provide a rigorous characterization of the set of beamforming matrices achievable by MiLAC. Based on this characterization, we prove that MiLAC-aided beamforming does not generally achieve the full flexibility of digital beamforming, while offering greater flexibility than conventional phase-shifter-based analog beamforming. Furthermore, we propose a hybrid digital-MiLAC architecture and show that it achieves digital beamforming flexibility when the number of radio frequency (RF) chains equals the number of data streams, halving that required by conventional hybrid beamforming. We then formulate the MiLAC-aided sum-rate maximization problem for MU-MISO systems. To solve the problem efficiently, we reformulate the MiLAC-related constraints as a convex linear matrix inequality and establish a low-dimensional subspace property that significantly reduces the problem dimension. Leveraging these results, we propose WMMSE-based algorithms for solving the resulting problem. Simulation results demonstrate that MiLAC-aided beamforming achieves performance close to that of digital beamforming in gigantic MIMO systems. Compared with hybrid beamforming, it achieves comparable or superior performance with lower hardware and computational complexity by avoiding symbol-level digital processing and enabling low-resolution digital-to-analog converters (DACs).

Movable Beyond-Diagonal Reconfigurable Intelligent Surfaces: Moving, Interconnecting, or Both?

This letter proposes a movable beyond-diagonal reconfigurable intelligent surfaces (MA-BD-RIS) design, combining inter-element connectivity and movability for channel enhancement. We study a MA-BD-RIS assisted multi-user multiple input single output system where beamforming, BD-RIS configuration, and elements positions are jointly optimized to maximize the sum-rate. An efficient algorithm is developed, incorporating closed-form beamforming, a low-complexity partially proximal alternating direction method of multipliers for BD-RIS design, and successive convex approximation for element placement. Simulations show that the high-movability structure yields superior performance in small-scale RIS and rich scattering scenarios, while the high-connectivity structure dominates in large-scale RIS and massive transmit array configurations.

Low-Complexity Planar Beyond-Diagonal RIS Architecture Design Using Graph Theory

Reconfigurable intelligent surfaces (RISs) enable programmable control of the wireless propagation environment and are key enablers for future networks. Beyond-diagonal RIS (BD-RIS) architectures enhance conventional RIS by interconnecting elements through tunable impedance components, offering greater flexibility with higher circuit complexity. However, excessive interconnections between BD-RIS elements require multi-layer printed circuit board (PCB) designs, increasing fabrication difficulty. In this letter, we use graph theory to characterize the BD-RIS architectures that can be realized on double-layer PCBs, denoted as planar-connected RISs. Among the possible planar-connected RISs, we identify the ones with the most degrees of freedom, expected to achieve the best performance under practical constraints.