As the sixth-generation (6G) networks evolve towards a deep integration of communication and computation (ICC), they face challenges of inherent interference and resource competition between heterogeneous services. To address this issue, this paper investigates an uplink ICC system enhanced by a stacked intelligent metasurface (SIM), where SIM’s unique multi-layer structure transforms the wireless channel into a controllable, task-oriented medium. The system is designed to support the coexistence of over-the-air computation (AirComp) tasks, which require high-precision results, and traditional tasks that demand high-quality communication. To this end, we formulate a joint optimization framework aiming to minimize the total mean squared error (MSE) of all computation tasks while strictly guaranteeing the communication quality of service (QoS). To solve the highly non-convex problem of synergistically designing the system resources, we propose an efficient alternating optimization (AO) algorithm. Simulation results demonstrate that the proposed algorithm not only converges rapidly but also achieves up to a 95.2% reduction in total computation MSE compared to an ICC system without SIM, while also significantly outperforming other benchmark schemes, validating the great potential of SIM in proactively managing multi-service conflicts and enabling efficient ICC.

This paper proposes a novel method for estimating the direction of arrival (DOA) in a time-modulated linear array (TMLA) based on the Golay-paired Hadamard (GPH) matrix. The objective is to address challenges presented by conventional TMLAs of limitations in the directional range due to the energy dispersion of radiation. To tackle this challenge, we construct a complete complementary set through the recursive derivation of the GPH matrix. From this set, we select mutually paired sequences that maintain an equal number of activated radio frequency switches, thereby designing an optimized time-modulated sequence. Theoretical analysis demonstrates that the proposed method can form an approximately flat sum beam across the entire spatial domain, thus facilitating an expansion of the directional measurement range. Furthermore, the DOA estimation is utilized by the multiple signal classification (MUSIC) algorithm. Simulation results validate the effectiveness of the proposed method. Specifically, the root mean square error is reduced by about$2.5^{\circ }$in the case of$\rm{SNR}$of$-10 \rm{ dB}$.

While stacked intelligent metasurfaces (SIMs) have demonstrated significant technical and cost advantages in multiuser scenarios, existing literature universally assumes ideal transceiver hardware. Addressing this gap, this paper investigates the design and optimization of a SIM-assisted multiuser downlink multiple-input single-output (MISO) system under practical transceiver hardware impairments (HWIs). To accurately capture distortion effects at both the base station (BS) and user equipment, we adopt an aggregate HWI model based on improper Gaussian statistics. The considered impairments include finite-resolution digital-to-analog converters (DACs), power amplifier (PA) nonlinearities, in-phase/quadrature (I/Q) imbalance, and other radio-frequency (RF) front-end non-idealities. We formulate a sum-rate (SR) maximization problem that jointly optimizes digital beamforming at the BS and multi-layer analog beamforming at the SIM. To tackle this highly non-convex optimization challenge, we propose a closed-form-based iterative algorithm that alternately updates BS and SIM beamforming with guaranteed convergence. Extensive simulations validate the effectiveness of the proposed algorithm, quantify the impact of different HWI sources, and demonstrate that SIM deployment significantly improves system robustness, mitigates HWI-induced performance degradation, and reduces DAC resolution requirements without substantial performance loss.

Stacked intelligent metasurface (SIM) extends the concept of single-layer reconfigurable holographic surfaces (RHS) by incorporating a multi-layered structure, thereby providing enhanced control over electromagnetic wave propagation and improved signal processing capabilities. This study investigates the potential of SIM in enhancing the rate fairness in multiuser downlink systems by addressing two key optimization problems: maximizing the minimum rate (MR) and maximizing the geometric mean of rates (GMR). The former strives to enhance the minimum user rate, thereby ensuring fairness among users, while the latter relaxes fairness requirements to strike a better trade-off between user fairness and system sum-rate (SR). For the MR maximization, we adopt a consensus alternating direction method of multipliers (ADMM)-based approach, which decomposes the approximated problem into sub-problems with closed-form solutions. For GMR maximization, we develop an alternating optimization (AO)-based algorithm that also yields closed-form solutions and can be seamlessly adapted for SR maximization. Numerical results validate the effectiveness and convergence of the proposed algorithms. Comparative evaluations show that MR maximization ensures near-perfect fairness, while GMR maximization balances fairness and system SR. Furthermore, the two proposed algorithms respectively outperform existing related works in terms of MR and SR performance. Lastly, SIM with lower power consumption achieves performance comparable to that of multi-antenna digital beamforming.

Recent studies have shown that the stacked intelligent metasurfaces (SIM) can exploit inter-layer electromagnetic (EM) wave transmission for wave-domain signal processing. This enables over-the-air computing with characteristics such as high-speed operation, low energy consumption, and support for multitasking parallel processing. By leveraging these advantages, SIM show great potential in substituting or augmenting customized communication functions in conventional wireless systems. To support various transmitter-customized communication functions, we design a novel multiple-input multiple-output (MIMO) transmitter architecture based on SIM and develop corresponding detection algorithms. Initially, we present a SIM-enabled MIMO transceiver model. Unlike conventional wireless communication, the SIM-enabled transmitter automatically performs customized functions, such as precoding and channel encoding, as the EM waves propagate within the layers. At the receiver side, minimum mean square error (MMSE) and maximum likelihood (ML) detectors are adopted as benchmarks, and their theoretical performance bounds are derived accordingly. Furthermore, we propose a data-enhanced deep unfolding algorithm, namely orthogonal approximate message passing causal dilated convolutional transformer (OAMP-CDT), to demonstrate the performance of customized functions based on SIM. Simulation results verify that the proposed SIM-enabled MIMO transmitter supports customized functions via over-the-air signal processing, and the proposed OAMP-CDT algorithm outperforms the same series of algorithms, such as orthogonal approximate message passing (OAMP) and OAMP-Net2.

Multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems rely on digital or hybrid digital and analog designs for beamforming against frequency-selective fading, which suffer from high hardware complexity and energy consumption. To address this, this work introduces a fully-analog stacked intelligent metasurfaces (SIM) architecture that directly performs wave-domain beamforming, enabling diagonalization of the end-to-end channel matrix and inherently eliminating inter-antenna interference (IAI) for MIMO OFDM transmission. By leveraging cascaded programmable metasurface layers, the proposed system establishes multiple parallel subchannels, significantly improving multi-carrier transmission efficiency while reducing hardware complexity. To optimize the SIM phase shift matrices, a block coordinate descent and penalty convex-concave procedure (BCD-PCCP) algorithm is developed to iteratively minimize the channel fitting error across subcarriers. Simulation results validate the proposed approach, determining the maximum effective bandwidth and demonstrating substantial performance improvements. Moreover, for a MIMO OFDM system operating at 28 GHz with 16 subcarriers, the proposed SIM configuration method achieves over 300% enhancement in channel capacity compared to conventional SIM configuration that only accounts for the center frequency.

Stacked intelligent metasurfaces (SIM) enable fine-grained wave-domain signal processing, but their wideband deployment is impeded by two structural factors: (i) a single, quasi-static SIM phase tensor must adapt to all subcarriers, and (ii) multiuser scheduling changes the subcarrier activation pattern frame by frame, requiring rapid reconfiguration. To address these, we propose a SIM-enhanced wideband multiuser transceiver built on orthogonal frequency-division multiplexing with index modulation (OFDM-IM). The sparse activation of OFDM-IM confines high-fidelity equalization to the active tones, effectively widening the usable bandwidth. To make the design reliability-aware, we directly target the worst-link bit-error rate (BER) and adopt a max-min per-tone signal-to-interference-plus-noise ratio (SINR) as a principled surrogate, turning the reliability optimization tractable. For frame-rate inference and interpretability, we propose an unfolding projected-gradient-descent network (UPGD-Net) that unrolls across the SIM's layers and algorithmic iterations with a learnable per-iteration step size. Simulations demonstrate that the proposed framework achieves fast convergence and significant BER gains over fully-digital baselines. Notably, the design exhibits superior robustness against errors and outperforms large-aperture hybrid precoding benchmarks in both sum rate and energy efficiency. By combining structural sparsity with a BER-driven, deep-unfolded optimization backbone, the proposed framework effectively resolves the key wideband deficiencies of SIM.

With the development of sixth-generation (6G) wire-less communication networks, the security challenges are becoming increasingly prominent, especially for mobile users (MUs). As a promising solution, physical layer security (PLS) technology leverages the inherent characteristics of wireless channels to provide security assurance. Particularly, stacked intelligent metasurface (SIM) directly manipulates electromagnetic waves through their multilayer structures, offering significant potential for enhancing PLS performance in an energy efficient manner. Thus, in this work, we investigate an SIM-assisted secure communication system for MUs under the threat of an eavesdropper, addressing practical challenges such as channel uncertainty in mobile environments, multiple MU interference, and residual hardware impairments. Consequently, we formulate a joint power and phase shift optimization problem (JPPSOP), aiming at maximizing the achievable secrecy rate (ASR) of all MUs. Given the non-convexity and dynamic nature of this optimization problem, we propose an enhanced proximal policy optimization algorithm with a bidirectional long short-term memory mechanism, an offpolicy data utilization mechanism, and a policy feedback mechanism (PPO-BOP). Through these mechanisms, the proposed algorithm can effectively capture short-term channel fading and long-term MU mobility, improve sample utilization efficiency, and enhance exploration capabilities. Extensive simulation results demonstrate that PPO-BOP significantly outperforms benchmark strategies and other deep reinforcement learning algorithms in terms of ASR.

Stacked intelligent metasurfaces (SIMs), which integrate multiple programmable metasurface layers, have recently emerged as a promising technology for advanced wave-domain signal processing. SIMs benefit from flexible spatial degree-of-freedom (DoF) while reducing the requirement for costly radio-frequency (RF) chains. However, current state-of-the-art SIM designs face challenges such as complex phase shift optimization and energy attenuation from multiple layers. To address these aspects, we propose incorporating meta-fibers into SIMs, with the aim of reducing the number of layers and enhancing the energy efficiency. First, we introduce a meta-fiber-connected 2-layer SIM that exhibits the same flexible signal processing capabilities as conventional multi-layer structures, and explains the operating principle. Subsequently, we formulate and solve the optimization problem of minimizing the mean square error (MSE) between the SIM channel and the desired channel matrices. Specifically, by designing the phase shifts of the meta-atoms associated with the transmitting-SIM and receiving-SIM, a non-interference system with parallel subchannels is established. In order to reduce the computational complexity, a closed-form expression for each phase shift at each iteration of an alternating optimization (AO) algorithm is proposed. We show that the proposed algorithm is applicable to conventional multi-layer SIMs. The channel capacity bound and computational complexity are analyzed to provide design insights. Finally, numerical results are illustrated, demonstrating that the proposed two-layer SIM with meta-fiber achieves over a 25% improvement in channel capacity while reducing the total number of meta-atoms by 59% as compared with a conventional seven-layer SIM.

We propose a novel doubly-dispersive (DD) multiple-input multiple-output (MIMO) channel model incorporating flexible intelligent metasurfaces (FIMs), which is suitable for integrated sensing and communications (ISAC) in high-mobility scenarios. We then discuss how the proposed FIM-parameterized DD (FPDD) channel model can be applied in a logical manner to multicarrier waveforms that are known to perform well in DD environments, namely, orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), and affine frequency division multiplexing (AFDM). Leveraging the proposed model, we formulate an achievable rate maximization problem with a strong sensing constraint for all the aforementioned waveforms, which we then solve via a gradient ascent algorithm with closed-form gradients presented as a bonus. Our numerical results indicate that the achievable rate is significantly impacted by the emerging FIM technology with careful parametrization essential in obtaining strong ISAC performance across all waveforms suitable to mitigating the effects of DD channels.

This paper introduces an interference-free multi-stream transmission architecture leveraging stacked intelligent metasurfaces (SIMs), from a new perspective of interference exploitation. Unlike traditional interference exploitation precoding (IEP) which relies on computational hardware circuitry, we perform the precoding operations within the analog wave domain provided by SIMs. However, the benefits of SIM-enabled IEP are limited by the nonlinear distortion (NLD) caused by power amplifiers. A hardware-efficient interference-free transmitter architecture is developed to exploit SIM’s high and flexible degree of freedom (DoF), where the NLD on modulated symbols can be directly compensated in the wave domain. Moreover, we design a frame-level SIM configuration scheme and formulate a max-min problem on the safety margin function. With respect to the optimization of SIM phase shifts, we propose a recursive oblique manifold (ROM) algorithm to tackle the complex coupling among phase shifts across multiple layers. A flexible DoF-driven antenna selection (AS) scheme is explored in the SIM-enabled IEP system. Using an ROM-based alternating optimization (ROM-AO) framework, our approach jointly optimizes transmit AS, SIM phase shift design, and power allocation (PA), and develops a greedy safety margin-based AS algorithm. Simulations show that the proposed SIM-enabled frame-level IEP scheme significantly outperforms benchmarks. Specifically, the strategy with AS and PA can achieve a 20 dB performance gain compared to the case without any strategy under the 12 dB signal-to-noise ratio, which confirms the superiority of the NLD-aware IEP scheme and the effectiveness of the proposed algorithm.

Typical reconfigurable intelligent surface (RIS) implementations include metasurfaces with almost passive unit elements capable of reflecting their incident waves in controllable ways, enhancing wireless communications in a cost-effective manner. In this paper, we advance the concept of intelligent metasurfaces by introducing a flexible array geometry, termed flexible intelligent metasurface (FIM), which supports both element movement (EM) and passive beamforming (PBF). In particular, based on the single-input single-output (SISO) system setup, we first compare three modes of FIM, namely, EM-only, PBF-only, and EM-PBF, in terms of received signal power under different FIM and channel setups. The PBF-only mode, which only adjusts the reflecting phase, shows less effective than the EM-only mode in enhancing received signal strength. The EM-PBF mode, which optimizes both element positions and phases, further enhances performance. Additionally, we investigate the channel estimation problem for FIM systems by designing a protocol that gathers EM and PBF measurements, enabling the formulation of a compressive sensing problem for joint cascaded and direct channel estimation. We then propose a sparse recovery algorithm called clustering mean-field variational sparse Bayesian learning, which enhances estimation performance while maintaining low complexity.

Accurate acquisition of channel state information (CSI) is essential for fully harnessing the potential of stacked intelligent metasurfaces (SIMs) in communication systems. In this paper, we address the channel estimation (CE) problem in SIM-based multi-user (MU) millimeter-wave (mmWave) near-field communication systems. To address the severe path loss and blockage in mmWave communication systems, many meta-atoms are typically integrated into each layer of the SIM. Then, the number of radio frequency (RF) chains at the base station (BS) is fewer than that of meta-atoms per layer, resulting in an underdetermined problem. Additionally, the increase in the number of meta-atoms in each layer expands the SIM’s near-field region, leading to the user equipment (UEs) being mostly situated in this region, necessitating precise modeling of the channel under the spherical wavefront assumption. To address these issues, we introduce a compressed sensing (CS)-based CE protocol to tackle the underdetermined problem. In contrast to the traditional CS-based estimation framework, we investigate a polar-domain channel representation to tackle the severe energy spread effect of the classical angular-domain channel representation in near-field communication systems. Specifically, we design a novel polar-domain transform matrix for uniform planar arrays (UPAs), thereby transforming the CE problem into a sparse recovery task of the paths’ support set and complex gains. To overcome the limitations of the sparse Bayesian learning (SBL) framework in tackling high-dimensional dictionaries, we propose a low-complexity polar-domain SBL (LCPD-SBL) algorithm, which significantly reduces computational complexity without compromising estimation accuracy. Numerical simulation results demonstrate that the proposed polar-domain transform matrix yields a better estimation accuracy than traditional angular-domain approaches. Additionally, the proposed LCPD-SBL algorithm can be faster than existing SBL methods by up to 4× while sustaining the same estimation performance.

Stacked intelligent metasurfaces (SIMs) have emerged as a promising technology for realizing wave-domain signal processing, while the fixed SIMs will limit the communication performance of the system compared to the mobile SIMs. In this work, we consider a UAV-mounted SIMs (UAV-SIMs) assisted communication system, where UAVs as base stations (BSs) can cache the data processed by SIMs, and also as mobile vehicles flexibly deploy SIMs to enhance the communication performance. To this end, we formulate a UAV-SIM-based joint optimization problem (USBJOP) to comprehensively consider the association between UAV-SIMs and users, the locations of UAV-SIMs, and the phase shifts of UAV-SIMs, aiming to maximize the network capacity. Due to the non-convexity and NP-hardness of USBJOP, we decompose it into three sub-optimization problems, which are the association between UAV-SIMs and users optimization problem (AUUOP), the UAV location optimization problem (ULOP), and the UAV-SIM phase shifts optimization problem (USPSOP). Then, these three sub-optimization problems are solved by an alternating optimization (AO) strategy. Specifically, AUUOP and ULOP are transformed to a convex form and then solved by the CVX tool, while we employ a layer-by-layer iterative optimization method for USPSOP. Simulation results verify the effectiveness of the proposed strategy under different simulation setups.

Flexible intelligent metasurface (FIM) technology has emerged as a promising solution for enhancing wireless communication performance. In contrast to traditional rigid reconfigurable intelligent surfaces (RIS), an FIM consists of an array of electromagnetic (EM) elements, each capable of flexibly adjusting its position along the direction perpendicular to the surface to collaboratively morph the surface shape. In this paper, an optimization problem for maximizing the weighted sum-rate (WSR) in an FIM-aided multicell multi-user multiple-input single-output (MU-MISO) system is investigated. We jointly optimize the beamforming at the base station (BS), the phase shift matrix, and the FIM surface shape. To address this problem, we propose an efficient alternating optimization framework, where we employ the weighted minimum mean square error (WMMSE) method to reformulate the problem and the block coordinate descent (BCD) algorithm to iteratively update the variables. Specifically, we utilize the Riemannian Conjugate Gradient (RCG) algorithm to optimize the phase shift matrix, and the projected gradient descent (PGD) method to optimize the FIM surface shape. Additionally, the optimal beamforming vectors are obtained in closed form. Finally, simulation results demonstrate the superiority of FIM over conventional RIS in various scenarios.

This study investigates the application of non-orthogonal multiple access (NOMA) to enable massive connectivity for a stacked intelligent metasurface (SIM) system that performs signal processing in the electromagnetic wave domain. To realize the full potential of NOMA assisted SIM systems, a radio resource allocation problem is accordingly formulated to jointly optimize the key decision variables, including the decoding order of users, the transmit power at the base station, as well as the phase shift at the SIM. By adhereing to the users’ quality-of-service (QoS) requirements, as well as the power budget of the base station, the problem is aimed at maximizing the admission rate of the system. Due to the problem’s inherent non-convexity and complexity, we recast it as a Markov decision process and employ a quantile regression deep Q-network (QRDQN) agent to optimize the decision variables. Recognizing the mobility of users and the dynamic reconfiguration of the system, we further enhance the QR-DQN model’s adaptability and generalization capabilities by incorporating a meta-learning strategy. Simulation results demonstrate that integrating NOMA with SIM systems yields a significant increase of 39% in the average number of served users compared to the conventional orthogonal multiple access based approach. The proposed resource allocation mechanism additionally improves deep deterministic policy gradient (DDPG) in literature by 27% in the number of served users.

Conventional digital beamforming for wideband multiuser orthogonal frequency-division multiplexing (OFDM) demands numerous power-hungry components, increasing hardware costs and complexity. By contrast, the stacked intelligent metasurfaces (SIM) can perform wave-based precoding at near-light speed, drastically reducing baseband overhead. However, realizing SIM-enhanced fully-analog beamforming for wideband multiuser transmissions remains challenging, as the SIM configuration has to handle interference across all subcarriers. To address this, this paper proposes a flexible subcarrier allocation strategy to fully reap the SIM-assisted fully-analog beamforming capability in an orthogonal frequency-division multiple access (OFDMA) system, where each subcarrier selectively serves one or more users to balance interference mitigation and resource utilization of SIM. We propose an iterative algorithm to jointly optimize the subcarrier assignment matrix and SIM transmission coefficients, approximating an interference-free channel for those selected subcarriers. Results show that the proposed system has low fitting errors yet allows each user to exploit more subcarriers. Further comparisons highlight a fundamental trade-off: our system achieves near-zero interference and robust data reliability without incurring the hardware burdens of digital precoding.

Stacked intelligent metasurfaces (SIMs), emerging as a revolutionary programmable electromagnetic architecture, have demonstrated unprecedented capabilities in manipulating wireless propagation environments. However, the existing research on SIM-aided downlink communication does not consider the fairness among users. Therefore, this paper studies a SIM-aided hybrid analog-digital system, which aims to fairly guarantee the communication quality of each user while minimizing the transmission power. The hybrid system avails of a SIM for enhancing the communication channel with digital precoding to effectively suppress the interference between users. To this end, we formulate a transmit power minimization problem under quality-of-service constraints, solved by an efficient alternating optimization (AO) algorithm. Simulation results demonstrate that compared to conventional fully digital multiuser multiple-input single-output (MISO) systems, the proposed SIM-aided hybrid system requires 6.93 dBm less transmit power under the same signal-to-interference-plus-noise ratio (SINR) constraints for users. This work reveals the SIM’s powerful wave-based beamforming capabilities, providing effective solutions for energy-efficient networks with low hardware cost.

As spectrum congestion intensifies in wireless communication, efficient spectrum utilization through advanced sensing techniques has become increasingly important. This paper proposes a joint carrier frequency and two-dimensional (2-D) Direction of Arrival (DOA) estimation algorithm with signal recovery, utilizing identical-delay channels and sub-Nyquist sampling rates with a Uniform Rectangular Array (URA). Compared to multi-coset structures, the proposed method places identical-delay channels only along the edges of the URA, eliminating the need for additional ADCs and reducing hardware cost. Moreover, by leveraging tensor techniques, the spatial structure of the array is preserved, and the parameter pairing problem is avoided, leading to higher precision in estimation. Simulation results demonstrate the superior performance of the proposed method.

Unmanned aerial vehicle (UAV) communication plays a pivotal role in achieving ubiquitous connectivity for the sixth-generation (6G) networks. Accurate and real-time direction of arrival (DOA) estimation is crucial for beamforming in UAV communication systems. However, the existing high-precision DOA estimation algorithms encounter high computational complexity when being implemented on a UAV with the on-board signal processing constraints. To tackle this issue, a hybrid optical-electric neural network (HOENN) is utilized for DOA estimation, which is capable of generating angular spectrum based solely on amplitude observation. The proposed HOENN consists of two components: a stacked intelligent metasurfaces (SIM)-enabled diffractive neural network, which is mounted on UAV and can process signals in the wave domain at the speed of light with low energy consumption, and a fully connected layer for processing the received amplitude signal. Finally, the simulation results validate that the HOENN achieves significant performance gain compared to the conventional beamforming (CBF) method, albeit with its lower cost and RF-related power consumption.

Stacked intelligent metasurface (SIM) as an advanced signal processing paradigm enables real-time processing of electromagnetic waves at the speed of light. Benefiting from this technology, the current paper studies the downlink transmission of a wireless network, where a SIM-deployed base station (BS) serves two disjoint sets of energy- and information-oriented terminals via simultaneous wireless information and power transfer (SWIPT). Toward optimizing the performance of this system, a resource allocation problem is formulated for characterizing the fundamental trade-off between the aggregate information rate and the overall harvested energy. By virtue of its tightly-coupled and non-convex nature, we equivalently transform this problem to a Markov decision process (MDP) form. Next, we train an asynchronous advantage actor critic (A3C) agent on the MDP-reformulated problem for optimizing the transmit power of the BS and the electromagnetic response of the SIM, in a joint fashion. Subsequently, by taking into account the mobility of terminals, we further enrich the adaptability of the trained A 3 C agent via meta-learning. It is numerically revealed that incorporating SIM leads to an approximate 30 % enhancement in the energy efficiency of existing SWIPT systems.

Flexible intelligent metasurfaces (FIMs) constitute a promising technology that could significantly boost the wireless network capacity. An FIM is essentially a soft array made up of many low-cost radiating elements that can independently emit electromagnetic signals. What's more, each element can flexibly adjust its position, even perpendicularly to the surface, to morph the overall 3D shape. In this paper, we study the potential of FIMs in point-to-point multiple-input multiple-output (MIMO) communications, where two FIMs are used as transceivers. In order to characterize the capacity limits of FIM-aided narrowband MIMO transmissions, we formulate an optimization problem for maximizing the MIMO channel capacity by jointly optimizing the 3D surface shapes of the transmitting and receiving FIMs, as well as the transmit covariance matrix, subject to a specific total transmit power constraint and to the maximum morphing range of the FIM. To solve this problem, we develop an efficient block coordinate descent (BCD) algorithm. The BCD algorithm iteratively updates the 3D surface shapes of the FIMs and the transmit covariance matrix, while keeping the other fixed. Numerical results verify that FIMs can achieve higher MIMO capacity than traditional rigid arrays. In some cases, the MIMO channel capacity can be doubled by employing FIMs.

Stacked intelligent metasurfaces (SIMs), composed of a multi-layered structure, have emerged as a powerful computing tool and analog signal processing platform for enabling task-oriented semantic communications (SemCom). However, SIMs lack nonlinear inference capabilities, thus motivating the emergence of the hybrid optical-electronic neural network (HOENN) that cascades a SIM and an electronic neural network (ENN). In this work, we investigate a disaster recognition taskoriented SemCom setting by leveraging the HOENN technology. Specifically, the HOENN is made of an optical neural network (ONN) using SIM mounted on an unmanned aerial vehicle (UAV) and a shallow ENN at the ground receiving station (GRS). The SIM automatically processes semantic information modulated on electromagnetic waves, with reduced energy consumption and ultrafast processing speed. At the GRS, the energy signals are processed by the shallow ENN to enhance the system's inference capability. The aim is to recognize the disaster according to the captured geomorphic images. To this end, we utilize a stochastic gradient descent algorithm to train the HOENN efficiently to minimize the cross-entropy between the recognized and actual semantics. Numerical results show that the HOENN surpasses the performance of using either ONN or ENN alone, achieving$\mathbf{9 7 \%}$recognition accuracy.

Accurate acquisition of channel state information is crucial for unlocking the potential of stacked intelligent metasurface (SIM)-assisted communication systems. This paper investigates the channel estimation (CE) problem in SIM-assisted multi-user (MU) millimeter-wave (mmWave) near-field communication systems. We aim to solve the underdetermined problem caused by the large-scale deployment of nearly-passive meta-atoms, where the number of antennas at the base station (BS) is smaller than the number of meta-atoms on the last layer of the SIM. Specifically, we first design a polar-domain transform matrix for uniform planar arrays (UPA) to convert the near-field channel into a polar-domain representation. Moreover, we leverage the channel sparsity in the polar domain and the sparse Bayesian learning (SBL) technique to recover the channel parameters. Additionally, a covariance-free expectation maximization (CoFEM) algorithm is introduced to reduce the computational complexity of the SBL. Numerical simulation results indicate that in SIM-assisted near-field mmWave communications, the algorithms based on the proposed polar-domain transform matrix outperform existing angular-domain approaches. Moreover, the CoFEM algorithm significantly reduces the computational complexity compared to SBL methods.

This paper centers around a multi-antenna unmanned aerial vehicle (UAV) which leverages stacked intelligent metasurface (SIM) as a green technology for signal processing at the electromagnetic wave domain. To assess the performance of this system, a radio resource allocation problem is accordingly formulated for jointly optimizing the motion trajectory and transmit power at the UAV, as well as the electromagnetic response at the SIM as decision variables. Since the problem is non-convex and challenging to solve, we reformulate it in Markov decision process form and train a distributed distributional deep deterministic policy gradient (D4PG) agent to optimize its decision variables. Concerning the significant mobility of the UAV and thus remarkable rearrangement of the system, we enhance the adaptability and generalization of the trained D4PG model by integrating meta-learning strategy. According to simulations, wave-domain beamforming via SIM at UAV leads to 40% and 22% reduction in average energy consumption, compared fullydigital and beamspace beamforming, respectively.

This endeavor centers around downlink transmission of a base station (BS), outfitted with a stacked intelligent metasurface (SIM) that realizes an energy-efficient wave-domain multi-user beamforming. The underlying network includes mobile devices with multimedia service requirements, including web surfing, HTTP live video streaming and voice-over-LTE (VoLTE). Rather than conventional quality-of-service (QoS) metrics, we assess the satisfaction level of users relying on quality-of-experience (QoE) criteria. Invoking mean opinion score (MOS) as the subjective measurement of QoE, we also evaluate the overall efficacy of this system by posing a resource allocation optimization problem aimed at maximizing the achievable MOS of all users, while adhering to their minimum MOS requirements and the maximum transmit power budget of the BS. Due to the interdependency of optimization variables and non-convex nature of the problem, we first reformulate it in Markov decision process, which captures its dynamic traits. Relying on the MDP model, a conservative Q-learning (CQL) agent is trained for jointly designing the optimization variables, including the BS downlink transmit power, as well as the electromagnetic response of the SIM. In light of real-time mobility of users and the resulting non-trivial network dynamism, we further utilize meta-learning technique to enhance the adaptability and generalization of the CQL agent. Numerically, it is demonstrated that, respectively, 31%, 44% and 26% superior average MOS is achieved, for web, video and audio services, compared to traditional QoS-driven resource allocation.

This research investigates a wireless system in which a base station (BS), outfitted with a stacked intelligent meta-surface (SIM), performs wave-domain multi-user beamforming in downlink transmission. The communication benefits from the assistance of an active reconfigurable intelligent surface (RIS) that amplifies incoming signal strength to extend the network coverage. System performance is evaluated through the formulation of a resource allocation optimization problem aimed at maximizing the number of served users while adhering to their quality-of-service demands and the maximum transmit power budget of the BS. Due to the complex interdependencies among optimization variables and the non-convex nature of the problem, we first reformulate it in Markov decision process, which captures its dynamic traits. Subsequently, a maximum a posteriori policy optimization (MPO) agent is trained for jointly designing the optimization variables, including the BS transmit power, the electromagnetic response of the SIM, as well as the amplitude/phase of the active RIS. In light of real-time mobility of users and non-trivial network dynamism, we invoke the integration of meta-learning technique to enhance the adaptability and generalization of the MPO model. Numerically, it is demonstrated that incorporating an active RIS upscales the number of served users by 57% and 113%, on average, in comparison with existing passive RIS-assisted and conventional SIM-enabled systems, respectively.

Reconfigurable intelligent surface (RIS) has emerged as a groundbreaking paradigm in shaping the future of wireless systems in late years. Derived from RISs, stacked intelligent metasurface (SIM), by enabling the real-time modulation of electromagnetic waves at the speed of light, and simultaneous transmitting and reflecting RIS (STAR-RIS), by drastically enhancing the coverage extension of cellular networks, appear to revolutionize the future of wireless communication. This letter delves into the synergization of SIM and STAR-RIS in a wireless system, where a base station (BS), outfitted with a SIM, benefits from a STAR-RIS to serve downlink receivers. The performance of the system is examined through the formulation of a resource allocation optimization problem, which seeks to maximize the system’s data rate, subject to constraints on receivers’ quality-of-service and the BS’s transmit power budget. Given the interdependency of variables and its inherently non-convex nature, the problem is firstly transformed into a Markov decision process form, which encapsulates its dynamic characteristics. Thereafter, a natural actor critic (NAC) agent is employed to holistically optimize the problem variables, including the transmit power at the BS, the electromagnetic response at the SIM and the reflection coefficients at the STAR-RIS. Furthermore, to account for the real-time mobility of receivers and thus the dynamism of the network, we enhance the adaptability of the trained NAC model via meta-learning technique. Simulation results reveal that the introduction of a STAR-RIS improves the system data rate, by 21% and 38% on average, compared to existing RIS-enabled and conventional SIM-based systems, respectively.

Reconfigurable intelligent surface (RIS) technology holds immense potential for increasing the performance of wireless networks. Therefore, RIS is also regarded as one of the solutions to address communication challenges in high-mobility scenarios, such as Doppler shift and fast fading. This paper investigates a high-speed train (HST) multiple-input single-output (MISO) communication system aided by a RIS. We propose a block coordinate descent (BCD) algorithm to jointly optimize the RIS phase shifts and the transmit beamforming vectors to maximize the channel gain. Numerical results are provided to demonstrate that the proposed algorithm significantly enhances the system performance, achieving an average channel gain improvement of 15 dB compared to traditional schemes. Additionally, the introduction of RIS eliminates outage probability and improves key performance metrics such as achievable rate, channel capacity, and bit error rate (BER). These findings highlight the critical role of RIS in enhancing HST communication systems.

The increase in antenna apertures and transmission frequencies in next-generation wireless networks is catalyzing advancements in near-field communications (NFC). In this paper, we investigate secure transmission in near-field multi-user multiple-input single-output (MU-MISO) scenarios. Specifically, with the advent of extremely large-scale antenna arrays (ELAA) applied in the NFC regime, the spatial degrees of freedom in the channel matrix are significantly enhanced. This creates an expanded null space that can be exploited for designing secure communication schemes. Motivated by this observation, we propose a near-field dynamic hybrid beamforming architecture incorporating artificial noise, which effectively disrupts eavesdroppers at any undesired positions, even in the absence of their channel state information (CSI). Furthermore, we comprehensively analyze the dynamic precoder’s performance in terms of the average signal-to-interference-plus-noise ratio, achievable rate, secrecy capacity, secrecy outage probability, and the size of the secrecy zone. In contrast to far-field secure transmission techniques that only enhance security in the angular dimension, the proposed algorithm exploits the unique properties of spherical wave characteristics in NFC to achieve secure transmission in both the angular and distance dimensions. Remarkably, the proposed algorithm is applicable to arbitrary modulation types and array configurations. Numerical results demonstrate that the proposed method achieves approximately 20% higher rate capacity compared to zero-forcing and the weighted minimum mean squared error precoders.

Flexible intelligent metasurfaces (FIMs) show great potential for improving the wireless network capacity in an energy-efficient manner. An FIM is a soft array consisting of several low-cost radiating elements. Each element can independently emit electromagnetic signals, while flexibly adjusting its position even perpendicularly to the overall surface to ‘morph’ its 3D shape. More explicitly, compared to a conventional rigid antenna array, an FIM is capable of finding an optimal 3D surface shape that provides improved signal quality. In this paper, we study point-to-point multiple-input multiple-output (MIMO) communications between a pair of FIMs. In order to characterize the capacity limits of FIM-aided MIMO transmissions over frequency-flat fading channels, we formulate a transmit optimization problem for maximizing the MIMO channel capacity by jointly optimizing the 3D surface shapes of the transmitting and receiving FIMs as well as the MIMO transmit covariance matrix, subject to the total transmit power constraint and to the maximum perpendicular morphing range of the FIM. To solve this problem, we develop an efficient block coordinate descent (BCD) algorithm. The BCD algorithm iteratively updates the 3D surface shapes of the FIMs and the transmit covariance matrix, while keeping the other fixed, to find a locally optimal solution. Numerical results verify that FIMs can achieve higher MIMO capacity than that of the conventional rigid arrays. In particular, the MIMO channel capacity can be doubled by the proposed BCD algorithm under some setups.

Intelligent metasurfaces may be harnessed for realizing efficient holographic multiple-input and multiple-output (MIMO) systems, at a low hardware-cost and high energy-efficiency. As part of this family, we propose a hybrid beamforming design for stacked intelligent metasurfaces (SIM) aided wideband wireless systems relying on the near-field channel model. Specifically, the holographic beamformer is designed based on configuring the phase shifts in each layer of the SIM for maximizing the sum of the baseband eigen-channel gains of all users. To optimize the SIM phase shifts, we propose a layer-by-layer iterative algorithm for optimizing the phase shifts in each layer alternately. Then, the minimum mean square error (MMSE) transmit precoding method is employed for the digital beamformer to support multi-user access. Furthermore, the mitigation of the SIM phase tuning error is also taken into account in the digital beamformer by exploiting its statistics. The power sharing ratio of each user is designed based on the iterative waterfilling power allocation algorithm. Additionally, our analytical results indicate that the spectral efficiency attained saturates in the high signal-to-noise ratio (SNR) region due to the phase tuning error resulting from the imperfect SIM hardware quality. The simulation results show that the SIM-aided holographic MIMO outperforms the state-of-the-art (SoA) single-layer holographic MIMO in terms of its achievable rate. We further demonstrate that the near-field channel model allows the SIM-based transceiver design to support multiple users, since the spatial resources represented both by the angle domain and the distance domain can be exploited.

Recently, stacked intelligent metasurfaces (SIMs) have aroused widespread discussions as an innovative technology for directly processing electromagnetic (EM) wave signals. By stacking multiple programmable metasurface layers, an SIM has the ability to provide additional spatial degrees of freedom without the introduction of expensive radio-frequency chains, which may outperform reconfigurable intelligent surfaces (RISs) with single-layer structures. For the sake of alleviating information leakage risks in wireless communications, artificial noise (AN) has arisen as a physical-layer security technology with severe hardware constraints, which is impracticable in single-input single-output (SISO) systems. Therefore, we deploy an SIM at the transmitter (Alice) to accomplish joint modulation, beamforming, and AN in SISO systems. As such, an artificial neural network structured SIM aims to convert an input carrier signal into a desired output signal. Subsequently, we formulate the fitting problem between the actual output signal and the desired signal. Moreover, we introduce a regularization parameter to improve the energy efficiency. In order to tackle this resultant non-convex problem, we provide an alternating optimization algorithm to iteratively determine each variable. For the sake of reducing the computational complexity, we derive closed-form expressions for each phase shift and transmit power. Furthermore, we theoretically analyze the secrecy rate and computational complexity. By considering the signal deviation introduced by SIM, we derive upper and lower bounds of the secrecy rate to provide fundamental insights. Finally, simulation results demonstrate that the SIM-aided SISO system is capable of realizing secure communications efficiently, while the introduced power regularization parameter saved over 2 dB transmit power for a 5-layer SIM without amplifying the fitting error.

Intelligent metasurfaces have recently emerged as a promising technology that enables the customization of wireless environments by harnessing large numbers of low-cost reconfigurable scattering elements. However, prior studies have predominantly focused on single-layer metasurfaces, which have limitations in terms of wave-domain processing capabilities due to practical hardware limitations. In contrast, this paper introduces a novel stacked intelligent metasurface (SIM) design. Specifically, we investigate the integration of SIM into the downlink of a multiuser multiple-input single-output (MISO) communication system, where an SIM, consisting of a multilayer metasurface structure, is deployed at the base station (BS) to facilitate transmit beamforming in the electromagnetic wave domain. This eliminates the need for conventional digital beamforming and high-resolution digital-to-analog converters at the BS. To this end, an optimization problem is formulated to maximize the sum rate of all user equipments by jointly optimizing the transmit power allocation at the BS and the wave-based beamforming at the SIM, subject to constraints on the transmit power budget and discrete phase shifts. Furthermore, we propose a computationally efficient algorithm for solving the formulated joint optimization problem and elaborate on the potential benefits of employing SIM in wireless networks. Numerical results are illustrated to corroborate the effectiveness of the proposed SIM-enabled wave-based beamforming design and to evaluate the performance improvement achieved by the proposed algorithm compared to various benchmark schemes. It is demonstrated that considering the same number of transmit antennas, the proposed SIM-based system achieves about 200% improvement in terms of sum rate compared to conventional MISO systems. The code for this paper is available athttps://github.com/JianchengAn.

Flexible intelligent metasurface (FIM) technology shows promise in terms of enhancing both the spectral and energy efficiency of wireless networks. An FIM is composed of an array of low-cost radiating elements, each of which can independently radiate electromagnetic signals, while flexibly adjusting its position along the direction perpendicular to the surface by a process termed as “morphing”. This is of particular interest for wireless communication systems operating at millimeter-wave and terahertz frequencies, where deep fading generally occurs within a few millimeters. Hence, in contrast to conventional rigid 2D antenna arrays, the FIM surface shape may be reconfigured to improve the channel quality by beneficial 3D morphing. In this paper, we investigate the multiuser downlink, where an FIM deployed at a base station (BS) communicates with multiple single-antenna users. We formulate an optimization problem for minimizing the total downlink transmit power at the BS, by jointly optimizing the transmit beamforming and FIM surface shape, subject to an individual signal-to-interference-plus-noise ratio (SINR) constraint of each user as well as a constraint on the maximum FIM morphing range. To solve this problem, we first consider a simple single-user scenario and show that the optimal 3D surface shape is achieved by independently adjusting each FIM element to the position having the strongest channel gain. However, in realistic multiuser scenarios, FIM surface-shape morphing involves complex tradeoffs. To address this issue, an efficient alternating optimization method is proposed to iteratively update the FIM surface shape and the transmit beamformer to gradually reduce the transmit power. Additionally, we analyze the performance gain of the FIM, showcasing a logarithmic received power scaling law versus its maximum morphing range. Finally, simulation results show that the FIM reduces the transmit power by about 3 dB compared to conventional rigid 2D arrays at a given data rate. The code for this paper is available athttps://github.com/JianchengAn.

Cell-free (CF) massive multiple-input multiple-output (mMIMO) systems are emerging as promising alternatives to cellular networks, especially in ultra-dense environments. However, further capacity enhancement requires the deployment of more access points (APs), which will lead to high costs and high energy consumption. To address this issue, in this paper, we explore the integration of low-power, low-cost stacked intelligent metasurfaces (SIM) into CF mMIMO systems to enhance AP capabilities. The key point is that SIM performs precoding-related matrix operations in the wave domain. As a consequence, each AP antenna only needs to transmit data streams for a single user equipment (UE), eliminating the need for complex baseband digital precoding. Then, we formulate the problem of joint AP-UE association and precoding at APs and SIMs to maximize the system sum rate. Due to the non-convexity and high complexity of the formulated problem, we propose a two-stage signal processing framework to solve it. In particular, in the first stage, we propose an AP antenna greedy association (AGA) algorithm to minimize UE interference. In the second stage, we introduce an alternating optimization (AO)-based algorithm that separates the joint power and wave-based precoding optimization problem into two distinct sub-problems: the complex quadratic transform method is used for AP antenna power control, and the projection gradient ascent (PGA) algorithm is employed to find suboptimal solutions for the SIM wave-based precoding. Finally, the numerical results validate the effectiveness of the proposed framework and assess the performance enhancement achieved by the algorithm in comparison to various benchmark schemes. The results show that, with the same number of SIM meta-atoms, the proposed algorithm improves the sum rate by approximately 275% compared to the benchmark scheme.

In this paper, we explore the integration of low-power, low-cost stacked intelligent metasurfaces (SIM) into cell-free (CF) massive multiple-input multiple-output (mMIMO) systems to enhance access point (AP) capabilities and address high power consumption and cost challenges. Specifically, we investigate the uplink performance of a SIM-enhanced CF mMIMO system and propose a novel system framework. First, the closed-form expressions of the spectral efficiency (SE) are obtained using the unique two-layer signal processing framework of CF mMIMO systems. Second, to mitigate inter-user interference, an interference-based greedy algorithm for pilot allocation is introduced. Third, a wave-based beamforming algorithm for SIM is proposed, based only on statistical channel state information, which effectively reduces the fronthaul costs. Finally, two different power control algorithms are proposed to improve the performance of UE with inferior channel conditions. The results indicate that increasing the number of SIM layers and meta-atoms leads to significant performance improvements and allows for a reduction in the number of APs and AP antennas, thus lowering the costs. In particular, the best SE performance is achieved with the deployment of 20 APs plus 1200 SIM meta-atoms. Finally, the proposed wave-based beamforming algorithm can enhance the SE performance of SIM-enhanced CF-mMIMO systems by 57%, significantly outperforming traditional CF mMIMO systems.

Flexible antenna arrays (FAAs), distinguished by their rotatable, bendable, and foldable properties, are extensively employed in flexible radio systems to achieve customized radiation patterns. This paper aims to illustrate that FAAs, capable of dynamically adjusting surface shapes, can enhance communication performances with both omni-directional and directional antenna patterns, in terms of multi-path channel power and channel angle Cramér-Rao bounds. To this end, we develop a mathematical model that elucidates the impacts of the variations in antenna positions and orientations as the array transitions from a flat to a rotated, bent, and folded state, all contingent on the flexible degree-of-freedom. Moreover, since the array shape adjustment operates across the entire beamspace, especially with directional patterns, we discuss the sum-rate in the multi-sector base station that covers the 360° communication area. Particularly, to thoroughly explore the multi-sector sum-rate, we propose separate flexible precoding (SFP), joint flexible precoding (JFP), and semi-joint flexible precoding (SJFP), respectively. In our numerical analysis comparing the optimized FAA to the fixed uniform planar array, we find that the bendable FAA achieves a remarkable 156% sum-rate improvement compared to the fixed planar array in the case of JFP with the directional pattern. Furthermore, the rotatable FAA exhibits notably superior performance in SFP and SJFP cases with omni-directional patterns, with respective 35% and 281%.

A flexible intelligent metasurface (FIM) is composed of an array of low-cost radiating elements, each of which can independently radiate electromagnetic signals and flexibly adjust its position through a 3D surface-morphing process. In our system, an FIM is deployed at a base station (BS) that transmits to multiple single-antenna users. We formulate an optimization problem for minimizing the total downlink transmit power at the BS by jointly optimizing the transmit beamforming and the FIM’s surface shape, subject to an individual signal-to-interference-plus-noise ratio (SINR) constraint for each user as well as to a constraint on the maximum morphing range of the FIM. To address this problem, an efficient alternating optimization method is proposed to iteratively update the FIM’s surface shape and the transmit beamformer to gradually reduce the transmit power. Finally, our simulation results show that at a given data rate the FIM reduces the transmit power by about 3 dB compared to conventional rigid 2D arrays.

Reconfigurable intelligent surface (RIS) have emerged as a transformative technology capable of reshaping wireless channels to significantly enhance the efficiency of wireless communication networks in a cost-effective manner. However, the prevailing RIS reflection coefficient optimization scheme presents a significant challenge due to its dependence on channel state information (CSI), which results in excessive pilot overhead and error propagation. To address this issue, this paper proposes a probability update (PU) based dynamic codebook for RIS-aided multiuser multiple-input single-output (MU-MISO) communication systems. Specifically, we implement a learning-from-training strategy that dynamically updates the codebook independently of CSI. This process involves assigning a probability vector to the RIS reflecting elements to generate the codebook, with subsequent iterative updates to the probability vector based on codebook training outcomes. Moreover, numerical results illustrate that the proposed scheme can effectively cater to diverse system by flexibly balancing the training overhead and system performance. Finally, despite channel estimation errors, the proposed scheme outperforms passive beamforming and the existing codebook schemes, while significantly reducing training overhead and implementation complexity.

With the increase of antenna aperture and the utilization of high frequencies, near-field communications (NFC) have emerged as a critical trend in next-generation wireless networks. This paper examines the security of NFC by designing a dynamic precoder for secure multi-user multiple-input single-output (MU-MISO) transmission, which boosts signal quality of legitimate users, while mitigating inter-user interference and distorting the signals for eavesdroppers at any undesired position. Utilizing the array response control (ARC) framework, we derive a closed-form expression of the dynamic precoder while satisfying power constraints. Furthermore, we analyze the key performance metrics of the closed-form dynamic precoder such as average signal-to-interference-plus-noise ratio (SINR), achievable rate, and secrecy capacity. The numerical results demonstrate that the proposed precoder leveraging the inherent spherical wavefront features in NFC significantly enhances the secure transmission performance across both angular and radial dimensions. Additionally, the proposed dynamic precoder can be readily applied to diverse modulation schemes and array configurations while maintaining low computational complexity.

This paper addresses key challenges caused by high sampling rates in wideband joint spectrum sensing applications. A joint Direction of Arrival (DOA) and frequency estimation algorithm is proposed by utilizing the Cross-Covariance Matrix (CCM) constructed from the outputs of an efficient undersampling array receiver with multiple elements, only one of which is connected with multiple time-delay branches. In contrast to previous autocorrelation-based methods, the proposed method reduces the impact of noise and doubles the maximum unit time-delay, resulting in improved estimation performance. Additionally, it does not impose restrictions on the number of array sensors and time-delay channels, which allows for more flexibility in the allocation of resources for the receiver. In the simulation, the proposed algorithm demonstrates outstanding performance.

In the context of perceiving spatial information, researchers extensively investigate the use of large-scale arrays due to their numerous advantages such as high precision and resolution, as well as increased degrees of freedom. However, large-scale arrays may be impractical in certain applications due to the prohibitive hardware cost. To address this bottleneck, a switch-element array structure composed of a switch network offers an appealing low-cost alternative by multiplexing the Radio Frequency (RF) chains. With this novel array architecture, we explore the direction-of-arrival (DOA) estimation problem and examine the inherent signal structures. Subsequently, two DOA estimation algorithms based on a dynamic-dictionary sparse representation are developed, namely the Jointly-Selected Orthogonal Matching Pursuit (JSOMP) algorithm and the Auxiliary Variable Joint Alternating Optimization (AVJAO) algorithm. The performance of the proposed algorithms is demonstrated through simulation results.

Staked intelligent metasurface (SIM) based techniques are developed to perform two-dimensional (2D) direction-of-arrival (DOA) estimation. In contrast to conventional designs, an advanced SIM in front of a receiver array automatically performs the 2D discrete Fourier transform (DFT) as the incident waves propagate through it. To arrange for the SIM to carry out this task, we design a gradient descent algorithm for iteratively updating the phase shift of each meta-atom in the SIM to minimize the fitting error between the SIM's response and the 2D DFT matrix. To further improve the DOA estimation accuracy, we configure the phase shifts in the input layer of the SIM to generate a set of 2D DFT matrices having orthogonal spatial frequency bins. Extensive numerical simulations verify the capability of a well-trained SIM to perform the 2D DFT. Specifically, it is demonstrated that a SIM having an optical computational speed achieves an MSE of 10–4in 2D DOA estimation.

Stacked intelligent metasurfaces (SIM) represents an advanced signal processing paradigm that enables over-the-air processing of electromagnetic waves at the speed of light. Its multi-layer structure exhibits customizable increased computational capability compared to conventional single-layer reconfigurable intelligent surfaces and metasurface lenses. In this paper, we deploy SIM to improve the performance of multi-user multiple-input single-output (MISO) wireless systems with low complexity transmit radio frequency (RF) chains. In particular, an optimization formulation for the joint design of the SIM phase shifts and the transmit power allocation is presented, which is efficiently solved via a customized deep reinforcement learning (DRL) approach that continuously observes pre-designed states of the SIM-parametrized smart wireless environment. The presented performance evaluation results showcase the proposed method's capability to effectively learn from the wireless environment while outperforming conventional precoding schemes under low transmit power conditions. Finally, a whitening process is presented to further augment the robustness of the proposed scheme.

Intelligent surfaces represent a breakthrough technology capable of customizing the wireless channel cost-effectively. However, the existing works generally focus on planar wavefront, neglecting near-field spherical wavefront characteristics caused by large array aperture and high operation frequencies in the terahertz (THz). Additionally, the single-layer reconfigurable intelligent surface (RIS) lacks the signal processing ability to mitigate the computational complexity at the base station (BS). To address this issue, we introduce a novel stacked intelligent metasurfaces (SIM) comprised of an array of programmable metasurface layers. The SIM aims to substitute conventional digital baseband architecture to execute computing tasks with ultra-low processing delay, albeit with a reduced number of radio-frequency (RF) chains and low-resolution digital-to-analog converters. In this paper, we present a SIM-aided multiuser multiple-input single-output (MU-MISO) near-field system, where the SIM is integrated into the BS to perform beamfocusing in the wave domain and customize an end-to-end channel with minimized inter-user interference. Finally, the numerical results demonstrate that near-field communication achieves superior spatial gain over the far-field, and the SIM effectively suppresses inter-user interference as the wireless signals propagate through it.

This paper focuses on the wideband frequency invariant (FI) deterministic beamformer design problem for mitigating beam squint and presents a spatial response variation (SRV)-constrained array response control (ARC) synthesis approach. By regarding the SRV matrix as the covariance matrix of an extra virtual colored noise, we extend the ARC-based narrowband beampattern synthesis techniques to wide band FI scenarios. Furthermore, we introduce the FI maximum magnitude response (FI-MMR) based design principle, which maximizes the array magnitude response at the main-beam direction on the reference frequency. Based on this principle, we present an iterative FI beampattern synthesis algorithm under arbitrary array configurations. Simulation results show the effectiveness of the proposed algorithm in comparison with several popular FI beampattern synthesis techniques.

Reconfigurable intelligent surface (RIS) provides a new electromagnetic response control solution, which can reshape the characteristics of wireless channels. In this paper, we propose a novel environment-aware codebook protocol for RIS-assisted multi-user multiple-input single-output (MU-MISO) systems. Specifically, we first introduce a channel training protocol which consists of off-line and on-line stages. Secondly, we propose an environment-aware codebook generation scheme, which utilizes the statistical channel state information and alternating optimization method to generate codewords offline. Then, in the on-line stage, we use these pre-designed codewords to configure the RIS, and the optimal codeword resulting in the highest sum rate is adopted for assisting in the downlink data transmission. Thirdly, we analyze the theoretical performance of the proposed protocol considering the channel estimation errors. Finally, numerical simulations are provided to verify our theoretical analysis and the performance of the proposed scheme.

Stacked intelligent metasurface (SIM) is an emerging programmable metasurface architecture that can imple-ment signal processing directly in the electromagnetic wave domain, thereby enabling efficient implementation of ultra-massive multiple-input multiple-output (MIMO) transceivers with a limited number of radio frequency (RF) chains. Channel estimation (CE) is challenging for SIM-enabled communication systems due to the multilayer architecture of SIM, and because we need to estimate large dimensional channels between the SIM and users with a limited number of RF chains. To efficiently solve this problem, we develop a novel hybrid digital-wave domain channel estimator, in which the received training symbols are first processed in the wave domain within the SIM layers, and then processed in the digital domain. The wave domain channel estimator, parametrized by the phase shifts applied by the meta-atoms in all layers, is optimized to minimize the mean squared error (MSE) using a gradient descent algorithm, within which the digital part is optimally updated. For an SIM-enabled multi-user system equipped with 4 RF chains and a 6-layer SIM with 64 meta-atoms each, the proposed estimator yields an MSE that becomes close to that achieved by fully digital CE in a massive MIMO system employing 64 RF chains. This high CE accuracy is achieved at the cost of a training overhead that can be reduced by exploiting the potential low rank of channel correlation matrices.

Deploying reconfigurable intelligent surfaces (RIS) near source and destination is of practical interest for improving the link quality of vehicle-to-vehicle (V2V) wireless systems. However, the accurate channel modeling and RIS tile deployment constitute a pair of challenges to evaluate the system performance such as error performance, capacity, etc. In this paper, we investigate the double-RIS channel characteristics and propose a geometry-based triple-cylinder model, where the RIS sub-surface/tile is enabled to assist V2V systems and other elements are turned off. To determine tile locations on RIS surface, we formulate an optimization problem by maximizing the end-to-end channel gain and solve it using gradient ascent (GA) method. Following this, channel correlation function, channel capacity, and outage probability are derived according to the proposed model. Five typical mobile scenarios are discussed to validate the convergence of proposed GA algorithm, where the results show that channel gain can converge to its maximum with optimized tile locations. In addition, channel correlation under different parameters and conditions are explored. Simulation results validate the enhanced channel capacity and outage probability obtained by optimizing the tile locations.

As a promising non-password authentication technology, radio frequency (RF) fingerprinting can greatly improve wireless security. Recent work has shown that RF fingerprinting based on deep learning significantly outperforms conventional approaches. However, this superiority relies largely on using plenty of labeled data for supervised learning, whereas training deep neural networks on a small dataset generally falls into overfitting, resulting in performance degradation. Considering that it is often easier to obtain enough unlabeled data in practice, we leverage deep semisupervised learning for RF fingerprinting, which largely relies on a composite data augmentation scheme specifically designed for wireless communication signals, combined with two popular techniques: 1) consistency-based regularization and 2) pseudo-labeling. Experimental results on both simulated and real-world datasets demonstrate that our proposed method for semisupervised RF fingerprinting is far superior to other competing ones, and it achieves remarkable performance almost close to that of fully supervised learning, with a very limited number of examples available.

The user-centric cell-free network has emerged as an appealing technology to improve the wireless communication’s capacity of the Internet of Things (IoT) networks thanks to its ability to eliminate intercell interference effectively. However, the cell-free network inevitably brings in higher hardware cost and backhaul overhead as a larger number of base stations (BSs) are deployed. Additionally, severe channel fading in high-frequency bands constitutes another crucial issue that limits the practical application of the cell-free network. In order to address the above challenges, we amalgamate the cell-free system with another emerging technology, namely reconfigurable intelligent surface (RIS), which can provide high spectrum and energy efficiency with low hardware cost by reshaping the wireless propagation environment intelligently. To this end, we formulate a weighted sum-rate (WSR) maximization problem for RIS-assisted cell-free systems by jointly optimizing the BS precoding matrix and the RIS reflection coefficient vector. Subsequently, we transform the complicated WSR problem to a tractable optimization problem and propose a distributed cooperative alternating direction method of multipliers (ADMMs) to fully utilize parallel computing resources. Inspired by the model-based algorithm unrolling concept, we unroll our solver to a learning-based deep distributed ADMM (D2-ADMM) network framework. To improve the efficiency of the D2-ADMM in distributed BSs, we develop a monodirectional information exchange strategy with a small signaling overhead. In addition to benefiting from domain knowledge, D2-ADMM adaptively learns hyperparameters and nonconvex solvers of the intractable RIS design problem through data-driven end-to-end training. Finally, numerical results demonstrate that the proposed D2-ADMM achieves around 210% improvement in capacity compared with the distributed noncooperative algorithm and almost 96% compared with the centralized algorithm.

Stacked intelligent metasurfaces (SIMs) are capable of emulating reconfigurable physical neural networks by utilizing electromagnetic (EM) waves as carriers. They can also perform various complex computational and signal processing tasks. An SIM is constructed by densely integrating multiple metasurface layers, each consisting of a large number of small meta-atoms that can control the EM waves passing through it. In this paper, we harness an SIM for two-dimensional (2D) direction-of-arrival (DOA) estimation. In contrast to conventional designs, an advanced SIM in front of a receiver array can be designed to automatically compute the 2D discrete Fourier transform (DFT) as the incident waves propagate through it. As a result, a receiver array can directly observe the angular spectrum of the incoming signal, and it can estimate the DOA by simply using probes to detect the energy distribution on the receiver array. This avoids the need for power inefficient radio frequency chains. To enable an SIM to perform the 2D DFT in the wave domain, we formulate an optimization problem that minimizes the mean square error (MSE) between the SIM’s EM response and the 2D DFT matrix. Then, a gradient descent algorithm is customized for iteratively updating the phase shift applied by each meta-atom of the SIM. To further improve the DOA estimation accuracy, we configure the phase shifts of the input layer of the SIM to generate a set of 2D DFT matrices associated with orthogonal spatial frequency bins. Additionally, we analytically evaluate the performance of the proposed SIM-based DOA estimator by deriving a tight upper bound for the MSE. Extensive numerical simulations verify the capability of an optimized SIM to perform DOA estimation and corroborate the theoretical analysis. Specifically, we show that an SIM is capable of performing DOA estimation with an MSE of the order of$10^{-4}$.

Large-scale multiple-input and multiple-output (MIMO) systems are capable of achieving high date rate. However, given the high hardware cost and excessive power consumption of massive MIMO systems, as a remedy, intelligent metasurfaces have been designed for efficient holographic MIMO (HMIMO) systems. In this paper, we propose a HMIMO architecture based on stacked intelligent metasurfaces (SIM) for the uplink of cell-free systems, where the SIM is employed at the access points (APs) for improving the spectral- and energy-efficiency. Specifically, we conceive distributed beamforming for SIM-assisted cell-free networks, where both the SIM coefficients and the local receiver combiner vectors of each AP are optimized based on the local channel state information (CSI) for the local detection of each user equipment (UE) information. Afterward, the central processing unit (CPU) fuses the local detections gleaned from all APs to detect the aggregate multi-user signal. Specifically, to design the SIM coefficients and the combining vectors of the APs, a low-complexity layer-by-layer iterative optimization algorithm is proposed for maximizing the equivalent gain of the channel spanning from the UEs to the APs. At the CPU, the weight vector used for combining the local detections from all APs is designed based on the minimum mean square error (MMSE) criterion, where the hardware impairments (HWIs) are also taken into consideration based on their statistics. The simulation results show that the SIM-based HMIMO outperforms the conventional single-layer HMIMO in terms of the achievable rate. We demonstrate that both the HWI of the radio frequency (RF) chains at the APs and the UEs limit the achievable rate in the high signal-to-noise-ratio (SNR) region.

Reconfigurable intelligent surface (RIS) provides a new electromagnetic response control solution, which can proactively reshape the characteristics of wireless channel environments. In RIS-assisted communication systems, the acquisition of channel state information (CSI) and the optimization of reflecting coefficients constitute major design challenges. To address these issues, codebook-based solutions have been developed recently, which, however, are mostly environment-agnostic. In this paper, a novel environment-aware codebook protocol is proposed, which can significantly reduce both pilot overhead and computational complexity, while maintaining expected communication performance. Specifically, first of all, a channel training framework is introduced to divide the training phase into several blocks. In each block, we directly estimate the composite end-to-end channel and focus only on the transmit beamforming. Second, we propose an environment-aware codebook generation scheme, which first generates a group of channels based on statistical CSI, and then obtains their corresponding RIS configuration by utilizing the alternating optimization (AO) method offline. In each online training block, the RIS is configured based on the corresponding codeword in the environment-aware codebook, and the optimal codeword resulting in the highest sum rate is adopted for assisting in the downlink data transmission. Third, we analyze the theoretical performance of the environment-aware codebook-based protocol taking into account the channel estimation errors. Finally, numerical simulations are provided to verify our theoretical analysis and the performance of the proposed scheme. In particular, the simulation results demonstrate that our protocol is more competitive than conventional environment-agnostic codebooks.

Stacked intelligent metasurfaces (SIM) is a revolutionary technology, which can outperform its single-layer counterparts by performing advanced signal processing relying on wave propagation. In this work, we exploit SIM to enable transmit precoding and receiver combining in holographic multiple-input multiple-output (HMIMO) communications, and we study the achievable rate by formulating a joint optimization problem of the SIM phase shifts at both sides of the transceiver and the covariance matrix of the transmitted signal. Notably, we propose its solution by means of an iterative optimization algorithm that relies on the projected gradient method, and accounts for all optimization parameters simultaneously. We also obtain the step size guaranteeing the convergence of the proposed algorithm. Simulation results provide fundamental insights such the performance improvements compared to the single-RIS counterpart and conventional MIMO system. Remarkably, the proposed algorithm results in the same achievable rate as the alternating optimization (AO) benchmark but with a less number of iterations.

Reconfigurable intelligent surface (RIS) is a promising technology that enables the customization of electromagnetic propagation environments in next-generation wireless networks. In this paper, we investigate the optimal pilot power allocation during the channel estimation stage to improve the ergodic channel gain of RIS-assisted systems under practical imperfect channel state information (CSI). Specifically, we commence by deriving an explicit closed-form expression of the ergodic channel gain of a multi-RIS-aided communication system that takes into account channel estimation errors. Then, we formulate the pilot power allocation problem to maximize the ergodic channel gain under imperfect CSI, subject to the average pilot power constraint. Then, the method of Lagrange multipliers is invoked to obtain the optimal pilot power allocation solution, which indicates that allocating more power to the pilots for estimating the weak reflection channels is capable of effectively improving the ergodic channel gain under imperfect CSI. Finally, extensive simulation results corroborate our theoretical analysis.

Reconfigurable intelligent surface has recently emerged as a promising technology for shaping the wireless environment by leveraging massive low-cost reconfigurable elements. Prior works mainly focus on a single-layer metasurface that lacks the capability of suppressing multiuser interference. By contrast, we propose a stacked intelligent metasurface (SIM)-enabled transceiver design for multiuser multiple-input single-output downlink communications. Specifically, the SIM is endowed with a multilayer structure and is deployed at the base station to perform transmit beamforming directly in the electromagnetic wave domain. As a result, an SIM-enabled transceiver overcomes the need for digital beamforming and operates with low-resolution digital-to-analog converters and a moderate number of radio-frequency chains, which significantly reduces the hardware cost and energy consumption, while substantially decreasing the pre-coding delay benefiting from the processing performed in the wave domain. To leverage the benefits of SIM-enabled transceivers, we formulate an optimization problem for maximizing the sum rate of all the users by jointly designing the transmit power allocated to them and the analog beamforming in the wave domain. Numerical results based on a customized alternating optimization algorithm corroborate the effectiveness of the proposed SIM-enabled analog beamforming design as compared with various benchmark schemes. Most notably, the proposed analog beamforming scheme is capable of substantially decreasing the precoding delay compared to its digital counterpart.

The recently developed reconfigurable intelligent surfaces (RISs) are capable of improving the coverage of space–air–ground integrated networks (SAGINs), where the signals can be reflected in the desired direction without relying on power-thirsty radio-frequency (RF) chains. However, in the face of the substantially increased Doppler frequency, the classic orthogonal frequency-division multiplexing (OFDM) becomes inadequate in supporting RIS for the following reasons. First, the detrimental doubly selective fading leads to intersymbol interference (ISI) and intercarrier interference (ICI), which result in error floors for OFDM operating in the time–frequency (TF) domain. Second, it is far from trivial to configure RIS based on the time-varying fading channels. Third, the interpolation-based TF-domain channel estimation methods become impractical for the high-Doppler and high-dimensional RIS systems. Against this background, in this article, we propose the powerful 2-D orthogonal time–frequency space (OTFS) modulation for RIS-aided SAGINs, which transforms the time-varying fading encountered in the TF-domain to the time-invariant fading in the delay-Doppler (DD) domain. More explicitly, first, for the first time in the literature, we devise the DD-domain channel model of RIS-assisted SAGINs in the face of doubly selective fading. Second, in order to facilitate the RIS configuration in the DD-domain, we propose to create “virtual” Doppler frequencies that guide the phase changes at the RIS, even though the RIS phase rotations do not suffer from Doppler effects. Third, we conceive an attractive DD-domain RIS channel estimation method that can support both OFDM and OTFS, where the TF-domain interpolation is eliminated. Our simulation results demonstrate that the proposed DD-domain RIS configuration and channel estimation methods for both OFDM and OTFS are capable of mitigating the error floors encountered in the TF-domain. Furthermore, our simulation results confirm that OTFS-based RIS-assisted SAGIN systems are capable of outperforming their OFDM counterparts and exhibit excellent performance across a wide range of SAGIN channel parameters including the Ricean K factor, Doppler frequency, delay spread, coverage distance, and carrier frequency.

A revolutionary technology relying on Stacked Intelligent Metasurfaces (SIM) is capable of carrying out advanced signal processing directly in the native electromagnetic (EM) wave regime. An SIM is fabricated by a sophisticated amalgam of multiple stacked metasurface layers, which may outperform its single-layer metasurface counterparts, such as reconfigurable intelligent surfaces (RIS) and metasurface lenses. We harness this new SIM for implementing holographic multiple-input multiple-output (HMIMO) communications without requiring excessive radio-frequency (RF) chains, which is a substantial benefit compared to existing implementations. First of all, we propose an HMIMO communication system based on a pair of SIM at the transmitter (TX) and receiver (RX), respectively. In sharp contrast to the conventional MIMO designs, SIM is capable of automatically accomplishing transmit precoding and receiver combining, as the EM waves propagate through them. As such, each spatial stream can be directly radiated and recovered from the corresponding transmit and receive port. Secondly, we formulate the problem of minimizing the error between the actual end-to-end channel matrix and the target diagonal one, representing a flawless interference-free system of parallel subchannels. This is achieved by jointly optimizing the phase shifts associated with all the metasurface layers of both the TX-SIM and RX-SIM. We then design a gradient descent algorithm to solve the resultant non-convex problem. Furthermore, we theoretically analyze the HMIMO channel capacity bound and provide some fundamental insights. Finally, extensive simulation results are provided for characterizing our SIM-aided HMIMO system, which quantifies its substantial performance benefits, e.g., 150% capacity improvement over both conventional MIMO and its RIS-aided counterparts.

Integrating sensing functionalities is envisioned as a distinguishing feature of next-generation mobile networks, which has given rise to the development of a novel enabling technology– Integrated Sensing and Communication (ISAC). Portraying the theoretical performance bounds of ISAC systems is fundamentally important to understand how sensing and communication functionalities interact (e.g., competitively or cooperatively) in terms of resource utilization, while revealing insights and guidelines for the development of effective physical-layer techniques. In this paper, we characterize the fundamental performance tradeoff between the detection probability for target monitoring and the user’s achievable rate in ISAC systems. To this end, we first discuss the achievable rate of the user under sensing-free and sensing-interfered communication scenarios. Furthermore, we derive closed-form expressions for the probability of false alarm (PFA) and the successful probability of detection (PD) for monitoring the target of interest, where we consider both communication-assisted and communication-interfered sensing scenarios. In addition, the effects of the unknown channel coefficient are also taken into account in our theoretical analysis. Based on our analytical results, we then carry out a comprehensive assessment of the performance tradeoff between sensing and communication functionalities. Specifically, we formulate a power allocation problem to minimize the transmit power at the base station (BS) under the constraints of ensuring a required PD for perception as well as the communication user’s quality of service requirement in terms of achievable rate. It indicates that, on the one hand, there exists an intrinsic tradeoff between sensing and communication performance under the mutual-interfered scenarios; On the other hand, with prior knowledge of the baseband waveform, these two functionalities might mutually assist each other to enhance the performance. Finally, simulation results corroborate the accuracy of our theoretical analysis and the effectiveness of the proposed power allocation solutions showing the advantages of the ISAC system over the conventional radar and communication coexistence counterpart.

Reconfigurable intelligent surface (RIS) is capable of improving the wireless system performance by steering the reflected signal in the desired direction. One of the major challenges is that both the transceiver and RIS have to be jointly optimized, where the optimization problems have to be reformulated for different system models and scenarios. To circumvent this challenge, new low-complexity antenna selection (AS) algorithms for transceiver-agnostic RIS configuration are proposed. Given a multiple-input multiple-output (MIMO) channel, the proposed RIS-AS opts for accurately aligning the RIS both with the transmit antenna (TA) and receive antenna (RA) for the sake of maximizing the MIMO channel’s overall output power. The proposed RIS-AS only has to configure the RIS alone, i.e. without iterations with the transceiver optimization. As a result, the proposed RIS-AS has the compelling benefit that they are generically applicable, regardless of the specific transceiver architecture. Our simulation results confirm that the proposed RIS-AS is capable of supporting any MIMO configuration, regardless of their closed/open-loop, single-/ full-RF and multiplexing-/diversity-oriented setups.

Reconfigurable intelligent surfaces (RISs) are capable of enhancing the capacity of wireless networks at a low cost. In practical RIS-assisted communication systems, the acquisition of channel state information (CSI) and RIS reflection optimization constitute a pair of challenges. In this paper, a low-complexity channel estimation and passive beamforming design is proposed.First of all, we conceive a low-complexity framework for maximizing the achievable rate of RIS-assisted multiple-input multiple-output (MIMO) systems having discrete phase shifts at each RIS element. In contrast to existing solutions, the proposed arrangement partitions the channel training stage into several phases, where the RIS reflection coefficients are pre-designed and the effective superposed channel is estimated instead of separately training the source-destination and source-RIS-destination links. Based on this, the active beamformer can be designed at low complexity and the RIS reflection optimization is performed by selecting that one from the pre-designed training set which maximizes the achievable rate.Secondly, we propose novel techniques for generating the training set of RIS reflection coefficients. The theoretical performance of the proposed scheme is analyzed and compared to the optimal RIS configuration.Finally, our simulation results demonstrate that the proposed framework is more competitive than its existing counterparts when relying on imperfect CSI, especially for rapidly time-varying channels having short channel coherence time.