Pilot Allocation for Multi-Hop Over-the-Air Neural Inference under Imperfect CSI

A multi-hop amplify-and-forward (AF) relay network can emulate a fully connected (FC) neural network layer via over-the-air (OTA) computation. However, achieving high emulation accuracy requires accurate channel state information (CSI) across all links in the multi-hop network. In this work, we investigate the impact of CSI errors on classification performance. We propose five heuristic schemes for allocating the total channel training time (pilots) across hops and compare their effectiveness. Numerical results reveal a clear trade-off between channel training overhead and classification accuracy. In particular, with sufficient pilot power and balanced allocation of channel training resources, the system can achieve classification accuracy close to that of the digital baseline.

Relay-Assisted Activation-Integrated SIM for Wireless Physical Neural Networks

Wireless physical neural networks (WPNNs) have emerged as a promising paradigm for performing neural computation directly in the physical layer of wireless systems, offering low latency and high energy efficiency. However, most existing WPNN implementations primarily rely on linear physical transformations, which fundamentally limits their expressiveness. In this work, we propose a relay-assisted WPNN architecture based on activation-integrated stacked intelligent metasurfaces (AI-SIMs), where each passive metasurface layer enabling linear wave manipulation is cascaded with an activation metasurface layer that realizes nonlinear processing in the analog domain. By deliberately structuring multi-hop wireless propagation, the relay amplification matrix and the metasurface phase-shift matrices jointly act as trainable network weights, while hardware-implemented activation functions provide essential nonlinearity. Simulation results demonstrate that the proposed architecture achieves high classification accuracy, and that incorporating hardware-based activation functions significantly improves representational capability and performance compared with purely linear physical implementations.

Realization of a Fully Connected Neural Layer Over-the-Air through Multi-hop Amplify-and-Forward Relays

We study the problem of implementing a fully-connected layer of a neural network using wireless over-the-air computing. We assume a multi hop system with a multi-antenna transmitter and receiver, along with a number of multi-hop amplify-and-forward relay devices in between. We formulate an optimization problem that optimizes the transmitter precoder, receiver combiner and amplify-and-forward gains, subject to relay device power constraint and transmitter power constraint. We propose an alternating optimization framework that optimizes the imitation accuracy. Simulation study results reveal that multi-hop relaying achieves an almost perfect classification accuracy when used in a neural network.

Wireless Physical Neural Networks (WPNNs): Opportunities and Challenges

Wireless communication systems exhibit structural and functional similarities to neural networks: signals propagate through cascaded elements, interact with the environment, and undergo transformations. Building upon this perspective, we introduce a unified paradigm, termed \textit{wireless physical neural networks (WPNNs)}, in which components of a wireless network, such as transceivers, relays, backscatter, and intelligent surfaces, are interpreted as computational layers within a learning architecture. By treating the wireless propagation environment and network elements as differentiable operators, new opportunities arise for joint communication-computation designs, where system optimization can be achieved through learning-based methods applied directly to the physical network. This approach may operate independently of, or in conjunction with, conventional digital neural layers, enabling hybrid communication learning pipelines. In the article, we outline representative architectures that embody this viewpoint and discuss the algorithmic and training considerations required to leverage the wireless medium as a computational resource. Through numerical examples, we highlight the potential performance gains in processing, adaptability, efficiency, and end-to-end optimization, demonstrating the promise of reconfiguring wireless systems as learning networks in next-generation communication frameworks.

Secure Transmission for Cell-Free Symbiotic Radio Communications with Movable Antenna: Continuous and Discrete Positioning Designs

In this paper, we study a movable antenna (MA) empowered secure transmission scheme for reconfigurable intelligent surface (RIS) aided cell-free symbiotic radio (SR) system. Specifically, the MAs deployed at distributed access points (APs) work collaboratively with the RIS to establish high-quality propagation links for both primary and secondary transmissions, as well as suppressing the risk of eavesdropping on confidential primary information. We consider both continuous and discrete MA position cases and maximize the secrecy rate of primary transmission under the secondary transmission constraints, respectively. For the continuous position case, we propose a two-layer iterative optimization method based on differential evolution with one-in-one representation (DEO), to find a high-quality solution with relatively moderate computational complexity. For the discrete position case, we first extend the DEO based iterative framework by introducing the mapping and determination operations to handle the characteristic of discrete MA positions. To further reduce the computational complexity, we then design an alternating optimization (AO) iterative framework to solve all variables within a single layer. In particular, we develop an efficient strategy to derive the sub-optimal solution for the discrete MA positions, superseding the DEO-based method. Numerical results validate the effectiveness of the proposed MA empowered secure transmission scheme along with its optimization algorithms.

Intelligent Metasurface-Enabled Integrated Sensing and Communication: Unified Framework and Key Technologies

As the demand for ubiquitous connectivity and high-precision environmental awareness grows, integrated sensing and communication (ISAC) has emerged as a key technology for sixth-generation (6G) wireless networks. Intelligent metasurfaces (IMs) have also been widely adopted in ISAC scenarios due to their efficient, programmable control over electromagnetic waves. This provides a versatile solution that meets the dual-function requirements of next-generation networks. Although reconfigurable intelligent surfaces (RISs) have been extensively studied for manipulating the propagation channel between base and mobile stations, the full potential of IMs in ISAC transceiver design remains under-explored. Against this backdrop, this article explores emerging IM-enabled transceiver designs for ISAC systems. It begins with an overview of representative IM architectures, their unique principles, and their inherent advantages in EM wave manipulation. Next, a unified ISAC framework is established to systematically model the design and derivation of diverse IM-enabled transceiver structures. This lays the foundation for performance optimization, trade-offs, and analysis. The paper then discusses several critical technologies for IM-enabled ISAC transceivers, including dedicated channel modeling, effective channel estimation, tailored beamforming strategies, and dual-functional waveform design.

Realizing Fully-Connected Layers Over the Air via Reconfigurable Intelligent Surfaces

By leveraging the waveform superposition property of the multiple access channel, over-the-air computation (AirComp) enables the execution of digital computations through analog means in the wireless domain, leading to faster processing and reduced latency. In this paper, we propose a novel approach to implement a neural network (NN) consisting of digital fully connected (FC) layers using physically reconfigurable hardware. Specifically, we investigate reconfigurable intelligent surfaces (RISs)-assisted multiple-input multiple-output (MIMO) systems to emulate the functionality of a NN for over-the-air inference. In this setup, both the RIS and the transceiver are jointly configured to manipulate the ambient wireless propagation environment, effectively reproducing the adjustable weights of a digital FC layer. We refer to this new computational paradigm as \textit{AirFC}. We formulate an imitation error minimization problem between the effective channel created by RIS and a target FC layer by jointly optimizing over-the-air parameters. To solve this non-convex optimization problem, an extremely low-complexity alternating optimization algorithm is proposed, where semi-closed-form/closed-form solutions for all optimization variables are derived. Simulation results show that the RIS-assisted MIMO-based AirFC can achieve competitive classification accuracy. Furthermore, it is also shown that a multi-RIS configuration significantly outperforms a single-RIS setup, particularly in line-of-sight (LoS)-dominated channels.

Over-the-Air Inference over Multi-hop MIMO Networks

A novel over-the-air machine learning framework over multi-hop multiple-input and multiple-output (MIMO) networks is proposed. The core idea is to imitate fully connected (FC) neural network layers using multiple MIMO channels by carefully designing the precoding matrices at the transmitting nodes. A neural network dubbed PrototypeNet is employed consisting of multiple FC layers, with the number of neurons of each layer equal to the number of antennas of the corresponding terminal. To achieve satisfactory performance, we train PrototypeNet based on a customized loss function consisting of classification error and the power of latent vectors to satisfy transmit power constraints, with noise injection during training. Precoding matrices for each hop are then obtained by solving an optimization problem. We also propose a multiple-block extension when the number of antennas is limited. Numerical results verify that the proposed over-the-air transmission scheme can achieve satisfactory classification accuracy under a power constraint. The results also show that higher classification accuracy can be achieved with an increasing number of hops at a modest signal-to-noise ratio (SNR).

Robust Transmission Design for Reconfigurable Intelligent Surface and Movable Antenna Enabled Symbiotic Radio Communications

This paper explores the application of movable antenna (MA), a cutting-edge technology with the capability of altering antenna positions, in a symbiotic radio (SR) system enabled by reconfigurable intelligent surface (RIS). The goal is to fully exploit the capabilities of both MA and RIS, constructing a better transmission environment for the co-existing primary and secondary transmission systems. For both parasitic SR (PSR) and commensal SR (CSR) scenarios with the channel uncertainties experienced by all transmission links, we design a robust transmission scheme with the goal of maximizing the primary rate while ensuring the secondary transmission quality. To address the maximization problem with thorny non-convex characteristics, we propose an alternating optimization framework that utilizes the General S-Procedure, General Sign-Definiteness Principle, successive convex approximation (SCA), and simulated annealing (SA) improved particle swarm optimization (SA-PSO) algorithms. Numerical results validate that the CSR scenario significantly outperforms the PSR scenario in terms of primary rate, and also show that compared to the fixed-position antenna scheme, the proposed MA scheme can increase the primary rate by 1.62 bps/Hz and 2.37 bps/Hz for the PSR and CSR scenarios, respectively.

Element-Grouping Strategy for Intelligent Reflecting Surface: Performance Analysis and Algorithm Optimization

As a revolutionary paradigm for intelligently controlling wireless channels, intelligent reflecting surface (IRS) has emerged as a promising technology for future sixth-generation (6G) wireless communications. While IRS-aided communication systems can achieve attractive high channel gains, existing schemes require plenty of IRS elements to mitigate the ``multiplicative fading'' effect in cascaded channels, leading to high complexity for real-time beamforming and high signaling overhead for channel estimation. In this paper, the concept of sustainable intelligent element-grouping IRS (IEG-IRS) is proposed to overcome those fundamental bottlenecks. Specifically, based on the statistical channel state information (S-CSI), the proposed grouping strategy intelligently pre-divide the IEG-IRS elements into multiple groups based on the beam-domain grouping method, with each group sharing the common reflection coefficient and being optimized in real time using the instantaneous channel state information (I-CSI). Then, we further analyze the asymptotic performance of the IEG-IRS to reveal the substantial capacity gain in an extremely large-scale IRS (XL-IRS) aided single-user single-input single-output (SU-SISO) system. In particular, when a line-of-sight (LoS) component exists, it demonstrates that the combined cascaded link can be considered as a ``deterministic virtual LoS'' channel, resulting in a sustainable squared array gain achieved by the IEG-IRS. Finally, we formulate a weighted-sum-rate (WSR) maximization problem for an IEG-IRS-aided multiuser multiple-input single-output (MU-MISO) system and a two-stage algorithm for optimizing the beam-domain grouping strategy and the multi-user active-passive beamforming is proposed.