Karhunen-Loève Expansion for Fluid Antenna Systems: Information-Theoretic Optimal Channel Compression and Outage Analysis

Fluid antenna systems (FAS) achieve spatial diversity by dynamically switching among $N$ densely packed ports, but the resulting spatially correlated Rayleigh channels render exact outage analysis intractable. Existing block-correlation models (BCM) impose structural approximations on the channel covariance matrix that can introduce optimistic performance bias. This paper proposes a principled Karhunen-Loève (KL) expansion framework that decomposes the $N$-dimensional correlated FAS channel into independent eigenmodes and performs a controlled rank-$K$ truncation, reducing the outage analysis to a $K$-dimensional integration with $K \ll N$. Closed-form outage expressions are derived for the rank-1 and rank-2 cases, and a general Gauss-Hermite quadrature formula is provided for arbitrary $K$. On the theoretical front, it is proved via Anderson's inequality that the KL approximation \emph{always} overestimates the outage probability, providing a conservative guarantee essential for secure system design. Leveraging the Slepian--Landau--Pollak concentration theorem, it is established that only $K^* = 2\lceil W \rceil + 1$ eigenmodes are needed regardless of $N$, where $W$ is the normalized aperture. It is further shown that the KL truncation achieves the Gaussian rate-distortion bound, certifying it as the information-theoretically optimal channel compression. Extensive numerical results confirm that (i) theoretical predictions match Monte Carlo simulations, (ii) the entropy fraction converges faster than the power fraction, (iii) the KL framework uniformly outperforms BCM in approximation accuracy while avoiding the optimistic bias inherent in block-diagonal models, and (iv) the effective degrees of freedom scale with the aperture rather than the number of ports.

A Gaussian Process Framework for Outage Analysis in Continuous-Aperture Fluid Antenna Systems

This paper develops a comprehensive analytical framework for the outage probability of fluid antenna system (FAS)-aided communications by modeling the antenna as a continuous aperture and approximating the Jakes (Bessel) spatial correlation with a Gaussian kernel $ρ_G(δ) = e^{-π^2δ^2}$. Three complementary analytical strategies are pursued. First, the Karhunen--Loève (KL) expansion under the Gaussian kernel is derived, yielding closed-form outage expressions for the rank-1 and rank-2 truncations and a Gauss--Hermite formula for arbitrary rank~$K$, with effective degrees of freedom $K_{\mathrm{eff}}^G \approx π\sqrt{2}\, W$. Second, rigorous two-sided outage bounds are established via Slepian's inequality and the Gaussian comparison theorem: by sandwiching the true correlation between equi-correlated models with $ρ_{\min}$ and $ρ_{\max}$, closed-form upper and lower bounds that avoid the optimistic bias of block-correlation models are obtained. Third, a continuous-aperture extreme value theory is developed using the Adler--Taylor expected Euler characteristic method and Piterbarg's theorem. The resulting outage expression $P_{\mathrm{out}} \approx 1 - e^{-x}(1 + π\sqrt{2}\, W\, x)$ depends only on the aperture~$W$ and threshold~$x$, is independent of the port count~$N$, and is identical for the Jakes and Gaussian models since both share the second spectral moment $λ_2 = 2π^2$. A Pickands-constant refinement for the deep-outage regime and a threshold-dependent effective diversity $N_{\mathrm{eff}} \approx 1 + π\sqrt{2}\, W\, x$ are further derived. Numerical results confirm that the Gaussian approximation incurs less than 10\% relative outage error for $W \leq 2$ and that the continuous-aperture formula converges with as few as $N \approx 10W$ ports.

Physical Layer Security for FAS-Aided Short-Packet Systems: A Variable Block-Correlation Approach

This paper presents a comprehensive physical layer security (PLS) framework for fluid antenna system (FAS)-aided short-packet communications under the variable block-correlation model (VBCM). We consider a downlink wiretap scenario in which a base station transmits confidential short packets to a legitimate receiver user (RU) in the presence of an eavesdropper user (EU), where both the RU and EU are equipped with fluid antennas. Unlike existing FAS security analyses that rely on constant block-correlation models or infinite-blocklength assumptions, we incorporate the VBCM to accurately capture the non-uniform spatial correlation structure inherent in practical FAS deployments. By employing a piecewise linear approximation of the decoding error probability and Gauss-Chebyshev quadrature, we derive closed-form and asymptotic expressions for the average achievable secrecy throughput (AAST). We further prove that the AAST is monotonically non-decreasing in the number of RU ports, which reduces the three-dimensional joint optimization of transmit power, blocklength, and port number to a two-dimensional grid search (GS). Numerical results demonstrate that the FAS-aided system achieves up to an order-of-magnitude secrecy throughput improvement over conventional fixed-position antenna systems, and reveal that blocklength selection is the most critical design parameter in the joint optimization.

Near-Field NLOS Localization via Position-Unknown HRIS:From Self-Localization to Target Positioning

Current reconfigurable intelligent surface (RIS)-aided near-field (NF) localization methods assume the RIS position is known a priori, and it has limited their practical applicability. This paper applies a hybrid RIS (HRIS) at an unknown position to locate non-line-of-sight (NLOS) NF targets. To this end, we first propose a two-stage gridless localization framework for achieving HRIS self-localization, and then determine the positions of the NF targets. In the first stage, we use the NF Fresnel approximation to convert the signal model into a virtual far-field model through delay-based cross-correlation of centrally symmetric HRIS elements. Such a conversion will naturally extend the aperture of the virtual array. A single-snapshot decoupled atomic norm minimization (DANM) algorithm is then proposed to locate an NF target relative to the HRIS, which includes a two-dimensional (2-D) direction of arrival (DOA) estimation with automatic pairing, the multiple signal classification (MUSIC) method for range estimation, and a total least squares (TLS) method to eliminate the Fresnel approximation error. In the second stage, we leverage the unique capability of HRIS in simultaneous sensing and reflection to estimate the HRIS-to-base station (BS) direction vectors using atomic norm minimization (ANM), and derive the three-dimensional (3-D) HRIS position with two BSs via the least squares (LS)-based geometric triangulation. Furthermore, we propose a semidefinite relaxation (SDR)-based HRIS phase optimization method to enhance the received signal power at the BSs, thereby improving the HRIS localization accuracy, which, in turn, enhances NF target positionings. The Cramer-Rao bound (CRB) for the NF target parameters and the position error bound (PEB) for the HRIS coordinates are derived as performance benchmarks.

Fluid Antennas Meet Intelligent Surfaces: Security Analysis of NOMA Systems Under Hardware Impairments

The revolutionary convergence of fluid antenna systems (FAS) and reconfigurable intelligent surfaces (RIS) creates unprecedented opportunities for secure wireless communications, yet the practical implications of hardware impairments on this promising combination remain largely unexplored. This paper investigates the security performance of non-orthogonal multiple access (NOMA) systems when fluid antennas (FAs) meet intelligent surfaces under realistic hardware constraints. We develop a comprehensive analytical framework that captures the complex interplay between adaptive spatial diversity, intelligent signal reflection, and hardware-induced distortions in short-packet communications. Through novel piecewise linear approximations and block-correlation models, we derive tractable expressions for average secure block error rate (BLER) that reveal fundamental performance limits imposed by hardware impairments. Our analysis demonstrates that while the synergy between FAs and intelligent surfaces offers remarkable degrees of freedom for security enhancement, practical hardware imperfections create performance ceilings that persist regardless of spatial diversity gains. The theoretical framework exposes critical design trade-offs between system complexity and achievable security performance, showing that hardware quality becomes a decisive factor in realizing the full potential of FAS-RIS architectures. Extensive simulations validate our analytical insights and provide practical design guidelines for implementing secure NOMA systems that effectively balance the benefits of fluid-intelligent cooperation against the constraints of realistic hardware limitations.

Beyond $λ/2$: Can Arbitrary EMVS Arrays Achieve Unambiguous NLOS Localization?

Conventional radar array design mandates interelement spacing not exceeding half a wavelength ($λ/2$) to avoid spatial ambiguity, fundamentally limiting array aperture and angular resolution. This paper addresses the fundamental question: Can arbitrary electromagnetic vector sensor (EMVS) arrays achieve unambiguous reconfigurable intelligent surface (RIS)-aided localization when element spacing exceeds $λ/2$? We provide an affirmative answer by exploiting the multi-component structure of EMVS measurements and developing a synergistic estimation and optimization framework for non-line-of-sight (NLOS) bistatic multiple input multiple output (MIMO) radar. A third-order parallel factor (PARAFAC) model is constructed from EMVS observations, enabling natural separation of spatial, polarimetric, and propagation effects via the trilinear alternating least squares (TALS) algorithm. A novel phase-disambiguation procedure leverages rotational invariance across the six electromagnetic components of EMVSs to resolve $2π$ phase wrapping in arbitrary array geometries, allowing unambiguous joint estimation of two-dimensional (2-D) direction of departure (DOD), two-dimensional direction of arrival (DOA), and polarization parameters with automatic pairing. To support localization in NLOS environments and enhance estimation robustness, a reconfigurable intelligent surface (RIS) is incorporated and its phase shifts are optimized via semidefinite programming (SDP) relaxation to maximize received signal power, improving signal-to-noise ratio (SNR) and further suppressing spatial ambiguities through iterative refinement.

From Optimization to Learning: Dual-Approach Resource Allocation for Over-the-Air Edge Computing Under Execution Uncertainty

The exponential proliferation of mobile devices and data-intensive applications in future wireless networks imposes substantial computational burdens on resource-constrained devices, thereby fostering the emergence of over-the-air computation (AirComp) as a transformative paradigm for edge intelligence.} To enhance the efficiency and scalability of AirComp systems, this paper proposes a comprehensive dual-approach framework that systematically transitions from traditional mathematical optimization to deep reinforcement learning (DRL) for resource allocation under execution uncertainty. Specifically, we establish a rigorous system model capturing execution uncertainty via Gamma-distributed computational workloads, resulting in challenging nonlinear optimization problems involving complex Gamma functions. For single-user scenarios, we design advanced block coordinate descent (BCD) and majorization-maximization (MM) algorithms, which yield semi-closed-form solutions with provable performance guarantees. However, conventional optimization approaches become computationally intractable in dynamic multi-user environments due to inter-user interference and resource contention. To this end, we introduce a Deep Q-Network (DQN)-based DRL framework capable of adaptively learning optimal policies through environment interaction. Our dual methodology effectively bridges analytical tractability with adaptive intelligence, leveraging optimization for foundational insight and learning for real-time adaptability. Extensive numerical results corroborate the performance gains achieved via increased edge server density and validate the superiority of our optimization-to-learning paradigm in next-generation AirComp systems.

An Fluid Antenna Array-Enabled DOA Estimation Method: End-Fire Effect Suppression

Direction of Arrival (DOA) estimation serves as a critical sensing technology poised to play a vital role in future intelligent and ubiquitous communication systems. Despite the development of numerous mature super-resolution algorithms, the inherent end-fire effect problem in fixed antenna arrays remains inadequately addressed. This work proposed a novel array architecture composed of fluid antennas. By exploiting the spatial reconfigurability of their positions to equivalently modulate the array steering vector and integrating it with the classical MUSIC algorithm, this approach achieved high-precision DOA estimation. Simulation results demonstrated that the proposed method delivers outstanding estimation performance even in highly challenging end-fire regions.

Reimagining Wireless Connectivity: The FAS-RIS Synergy for 6G Smart Cities

Fluid antenna system (FAS) represents the concept of treating antenna as a reconfigurable physical-layer resource to broaden system design and network optimization and inspire next-generation reconfigurable antennas. FAS can unleash new degree of freedom (DoF) via antenna reconfigurations for novel spatial diversity. Reconfigurable intelligent surfaces (RISs) on the other hand can reshape wireless propagation environments but often face limitations from double path-loss and minimal signal processing capability when operating independently. This article envisions a transformative FAS-RIS integrated architecture for future smart city networks, uniting the adaptability of FAS with the environmental control of RIS. The proposed framework has five key applications: FAS-enabled base stations (BSs) for large-scale beamforming, FAS-equipped user devices with finest spatial diversity, and three novel RIS paradigms -- fluid RIS (FRIS) with reconfigurable elements, FAS-embedded RIS as active relays, and enormous FAS (E-FAS) exploiting surface waves on facades to re-establish line-of-sight (LoS) communication. A two-timescale control mechanism coordinates network-level beamforming with rapid, device-level adaptation. Applications spanning from simultaneous wireless information and power transfer (SWIPT) to integrated sensing and communications (ISAC), with challenges in co-design, channel modeling, and optimization, are discussed. This article concludes with simulation results demonstrating the robustness and effectiveness of the FAS-RIS system.

FAS-RIS for V2X: Unlocking Realistic Performance Analysis with Finite Elements

The synergy of fluid antenna systems (FAS) and reconfigurable intelligent surfaces (RIS) is poised to unlock robust Vehicle-to-Everything (V2X) communications. However, a critical gap persists between theoretical predictions and real-world performance. Existing analyses predominantly rely on the Central Limit Theorem (CLT), an assumption valid only for a large number of RIS elements, which fails to represent practical, finite-sized deployments constrained by cost and urban infrastructure. This paper bridges this gap by presenting a novel framework that unlocks a realistic performance analysis for FAS-RIS systems with finite elements. Leveraging a Gamma distribution approximation, we derive a new, tractable closed-form expression for the outage probability. Numerical results validate our approach, demonstrating that it offers a significantly more accurate performance characterization than conventional CLT-based methods, particularly in the practical regime of small-scale RIS. This work provides a crucial foundation for the design and deployment of reliable FAS-RIS-aided vehicular networks.