Passive six-dimensional movable antennas (6DMAs) can be realized by mounting an intelligent reflecting surface (IRS) on a unmanned aerial vehicle (UAV) and tuning its three-dimensional (3D) deployment and 3D orientation. However, the performance of UAV-enabled passive 6DMAs is highly sensitive to mechanical jitters caused by wind and platform vibration, which can severely limit the communication performance. To resolve this issue, this letter investigates the robust deployment and orientation optimization for UAV-enabled passive 6DMAs, aiming to maximize the worst-case received signal-to-noise ratio (SNR) at a receiver in the presence of bounded jitters. However, this problem is extremely difficult to solve due to its high dimension and worst-case formulation. To tackle this challenge, a particle swarm optimization (PSO) algorithm is first developed, where the sequential quadratic programming (SQP) algorithm is employed to derive the worst-case SNR among all possible jitters for any given 6DMA deployment and orientation. To gain more insights, we further consider a simplified case with pitch jitters only and develop a set of first-order surrogate functions to approximate the received SNR. By this means, closed-form optimal orientation solutions are obtained under mild conditions, which explicitly characterize the impacts of jitters on the communication performance. Numerical results show that the proposed method consistently outperforms the non-robust design that ignores the jitters.

Intelligent reflecting surface (IRS) is composed of numerous passive reflecting elements and can be mounted on unmanned aerial vehicles (UAVs) to achieve six-dimensional (6D) movement by adjusting the UAV's three-dimensional (3D) location and 3D orientation simultaneously. Hence, in this paper, we investigate a new UAV-enabled passive 6D movable antenna (6DMA) architecture by mounting an IRS on a UAV and address the associated joint deployment and beamforming optimization problem. In particular, we consider a passive 6DMA-aided multicast system with a multi-antenna base station (BS) and multiple remote users, aiming to jointly optimize the IRS's location and 3D orientation, as well as its passive beamforming to maximize the minimum received signal-to-noise ratio (SNR) among all users under the practical angle-dependent signal reflection model. However, this optimization problem is challenging to be optimally solved due to the intricate relationship between the users' SNRs and the IRS's location and orientation. To tackle this challenge, we first focus on a simplified case with a single user, showing that one-dimensional (1D) orientation suffices to achieve the optimal performance. Next, we show that for any given IRS's location, the optimal 1D orientation can be derived in closed form, based on which several useful insights are drawn. To solve the max-min SNR problem in the general multi-user case, we propose an alternating optimization (AO) algorithm by alternately optimizing the IRS's beamforming and location/orientation via successive convex approximation (SCA) and hybrid coarse- and fine-grained search, respectively. To avoid undesirable local sub-optimal solutions, a Gibbs sampling (GS) method is proposed to generate new IRS locations and orientations for exploration in each AO iteration. Numerical results validate our theoretical analyses.

In this paper, we study measurement-driven signal-to-interference-plus-noise ratio (SINR) maximization for a multi-reconfigurable intelligent surface (RIS)-aided single-input single-output (SISO) system with unknown strong interference sources. Specifically, the objective is to optimize the reflection coefficients such that the SINR is maximized at the receiver. As the interference channels are unknown, such an optimization problem is a black-box optimization problem with an objective function whose closed-form analytical expression is unknown. To address the high-dimensional black-box optimization problem with discrete variable constraints, we introduce a group-based phase parameterization that significantly reduces the search dimension. Building on this model, we develop a group-based zeroth-order adaptive moment (ZO-AdaMM) algorithm. Simulation results show that the proposed grouping strategy markedly accelerates the convergence speed and achieves a superior interference suppression performance under limited measurement budgets, especially in the small-budget regime.

This paper investigates the potential of movable antennas (MAs) to enhance physical layer security within a multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) system. We consider a practical scenario where the transmitter operates with imperfect eavesdropper channel state information (ECSI), knowing only the instantaneous line-of-sight (LoS) component and the statistical properties of non-line-of-sight (NLoS) component. To rigorously quantify secrecy performance under the ECSI uncertainty, we adopt the ergodic secrecy rate (ESR) as the metric. Since deriving an exact analytical expression for the ESR is intractable, we leverage random matrix theory to derive a deterministic equivalent. This avoids heavy Monte Carlo simulations and also provides explicit insights into the effects of channel spatial statistics on secrecy performance. Building upon the deterministic equivalent, we formulate a joint maximization problem for the transmit precoding matrix and the antenna positions at the legitimate transmitter. To tackle the non-convexity of this optimization problem, we develop a comprehensive alternating optimization framework. Specifically, the precoding matrix is optimized via a majorization-minimization (MM) algorithm, where the gradient is computed by solving an implicit fixed-point equation. For the antenna position optimization, the complexity of the objective function prevents the construction of standard MM surrogate. To this end, we further propose a novel AMSGrad-based surrogate function that relies solely on gradient information. We provide a rigorous theoretical proof that guarantees the convergence of this proposed algorithm despite relaxing the strict majorization conditions.

Intelligent reflecting surface (IRS) is emerging as a transformative technology for next-generation wireless communication and sensing systems. In this letter, we consider the problem of adaptive beamforming (ABF) for a single-antenna receiver aided by a nearby IRS, where the receiver aims to extract signals from a desired direction in the presence of $K$ strong, unknown interferences. Specifically, we propose to maximize the signal-to-interference-plus-noise ratio (SINR) by optimizing the reflection coefficients of the IRS. Unlike conventional ABF methods, we do not have direct access to the signal-plus-interference covariance matrix. Instead, only a limited number of quadratic compressive measurements can be obtained. To close this gap, we present a sample-efficient analytical solution via implicit inference of the interference covariance matrix. Simulation results demonstrate that our method significantly improves the SINR over state-of-the-art approaches.

Reconfigurable antennas, including reconfigurable intelligent surface (RIS), movable antenna (MA), fluid antenna (FA), and other advanced antenna techniques, have been studied extensively in the context of reshaping wireless propagation environments for 6G and beyond wireless communications. Nevertheless, how to reconfigure/optimize the real-time controllable coefficients to achieve a favorable end-to-end wireless channel remains a substantial challenge, as it usually requires accurate modeling of the complex interaction between the reconfigurable devices and the electromagnetic waves, as well as knowledge of implicit channel propagation parameters. In this paper, we introduce a derivative-free optimization (a.k.a., zeroth-order (ZO) optimization) technique to directly optimize reconfigurable coefficients to shape the wireless end-to-end channel, without the need of channel modeling and estimation of the environmental propagation parameters. We present the fundamental principles of ZO optimization and discuss its potential advantages in wireless channel reconfiguration. Two case studies for RIS and movable antenna enabled systems are provided to show the superiority of ZO-based methods as compared to state-of-the-art techniques. Finally, we outline promising future research directions and offer concluding insights on derivative-free optimization for reconfigurable antenna technologies.

We study the problem of interference cancelation with the aid of an intelligent reflecting surface (IRS), where the objective is to determine the reflection coefficients at the IRS such that the interference signals are canceled at the receiver. Specifically, we are interested in a “blind” scenario where the channel state information (CSI) between the interference sources and the receiver is unknown. To tackle this challenging problem, we propose a sample-efficient blind approach which utilizes a small number of average received signal power measurements to automatically identify a reflection coefficient vector that is orthogonal to the cascaded interference channels and thus nullifies the interference signals at the receiver. Simulation results show that the proposed method can effectively cancel the interference signals and enhance the signal-to-interference-plus-noise ratio (SINR).

Movable antennas (MAs), traditionally explored in antenna design, have recently garnered significant attention in wireless communications due to their ability to dynamically adjust the antenna positions to changes in the propagation environment. However, previous research has primarily focused on characterizing the performance limits of various MA-assisted wireless communication systems, with less emphasis on their practical implementation. To address this gap, in this article, we propose several general MA architectures that extend existing designs by varying several key aspects to cater to different application scenarios and tradeoffs between cost and performance. Additionally, we draw from fields such as antenna design and mechanical control to provide an overview of candidate implementation methods for the proposed MA architectures, utilizing either direct mechanical or equivalent electronic control. Simulation results are finally presented to support our discussion.

In this article, we consider the problem of joint transceiver design for millimeter-wave (mmWave)/terahertz (THz) multiuser MIMO integrated sensing and communication (ISAC) systems. Such a problem is formulated into a nonconvex optimization problem, with the objective of maximizing a weighted sum of communication users' rates and the passive radar's signal-to-clutter-and-noise ratio (SCNR). By exploring a low-dimensional subspace property of the optimal precoder, a low-dimensional subspace property-inspired block-coordinate-descent (LS-BCD)-based algorithm is proposed with remarkably reduced computational complexity. Our analysis reveals that the hybrid analog/digital beamforming structure can attain the same performance as that of a fully digital precoder, provided that the number of radio frequency (RF) chains is no less than the number of resolvable signal paths. Also, through expressing the precoder as a sum of a communication-precoder and a sensing-precoder, we develop an analytical solution to the joint transceiver design problem by generalizing the idea of block diagonalization (BD) to the ISAC system. Simulation results show that with a proper tradeoff parameter, the proposed methods can achieve a decent compromise between communication and sensing, where the performance of each communication/sensing task experiences only a mild performance loss as compared with the performance attained by optimizing exclusively for a single task.

Intelligent reflecting surface (IRS) can be mounted on an unmanned aerial vehicle (UAV) to enhance terrestrial communication performance by leveraging its passive beamforming and the UAV’s six-dimensional (6D) movement, i.e., three-dimensional (3D) rotation and 3D positioning, known as passive 6D movable antennas (6DMAs). In this paper, we investigate the use of UAV-mounted passive 6DMAs for secure communications. In particular, beyond conventional signal nulling, we propose a new space nulling scheme by leveraging the 6D movement and 180° half-space reflection of the IRS, such that eavesdroppers are excluded from the reflection space. Our goal is to maximize the achievable rate at the legitimate user subject to the space-nulling constraint at an eavesdropper by jointly optimizing the IRS’s position and 3D rotation. As this problem is difficult to be optimally solved, we first derive the IRS’s optimal 3D rotation in closed-form for any given UAV/IRS position by recasting it as an equivalent lower-dimensional problem. Then, we proceed to optimize the IRS’s position via an exhaustive search. Both analytical and numerical results demonstrate that the proposed space-nulling scheme can achieve near-optimal performance in terms of secrecy rate maximization under certain conditions.

Terahertz (THz) communication systems suffer severe blockage issues, which may significantly degrade the communica tion coverage and quality. Bending beams, capable of adjusting their propagation direction to bypass obstacles, have recently emerged as a promising solution to resolve this issue by engineer ing the propagation trajectory of the beam. However, traditional bending beam generation methods rely heavily on the specific geometric properties of the propagation trajectory and can only achieve sub-optimal performance. In this paper, we propose a new and general bending beamforming method by adopting the convex optimization techniques. In particular, we formulate the bending beamforming design as a max-min optimization problem, aiming to optimize the analog or digital transmit beamforming vector to maximize the minimum received signal power among all positions along the bending beam trajectory. However, the resulting problem is non-convex and difficult to be solved optimally. To tackle this difficulty, we apply the successive convex approximation (SCA) technique to obtain a high-quality suboptimal solution. Numerical results show that our proposed bending beamforming method outperforms the traditional method and shows robustness to the obstacle in the environment.

Intelligent reflecting surface (IRS) is deemed as a promising technology to improve the spectral and energy efficiency of wireless communications. Unlike conventional single-and double-IRS reflections, this paper investigates the channel estimation problem in a triple-IRS-reflection aided wireless communication system, which offers greater flexibility to bypass dense obstacles in the environment. However, due to the complex cascaded channel formed by the three IRSs, conventional IRS channel estimation techniques cannot be directly applied. To tackle this difficulty, we propose a new channel estimation method for triple-IRS-reflection channels. Specifically, we first recast the triple-IRS-reflection channel into a more tractable form, which is the inner product of the composite reflection pattern of the three IRSs and their cascaded channel. Based on this form, the cascaded channel can be efficiently estimated by varying the composite reflection patterns and applying the least-square method. To minimize the mean squared error (MSE), we optimize the reflection patterns of the three IRSs and show that their optimal patterns can be independently determined based on three arbitrary unitary matrices. Numerical results show that our proposed channel estimation algorithm can achieve significantly lower MSE than other baseline schemes.

In this paper, we consider the problem of adaptive beamforming (ABF) for intelligent reflecting surface (IRS)- assisted systems, where a single antenna receiver, aided by a close-by IRS, tries to decode signals from a legitimate transmitter in the presence of multiple unknown interference signals. Such a problem is formulated as an ABF problem with the objective of minimizing the average received signal power subject to certain constraints. Unlike canonical ABF in array signal processing, we do not have direct access to the covariance matrix that is needed for solving the ABF problem. Instead, for our problem, we only have some quadratic compressive measurements of the covariance matrix. To address this challenge, we propose a sample-efficient method that directly solves the ABF problem without explicitly inferring the covariance matrix. Compared with the methods which explicitly recover the covariance matrix from its quadratic compressive measurements, our proposed method achieves a substantial improvement in terms of sample efficiency. Simulation results show that our method, using a small number of measurements, can effectively nullify the interference signals and enhance the signal-to-interference-plus-noise ratio (SINR).

Target-mounted intelligent reflecting surfaces (IRS) introduce a novel degree of freedom (DoF) in controlling the target’s radar cross section (RCS), thereby enabling numerous advanced applications in wireless sensing and integrated sensing and communication (ISAC) systems. Nevertheless, a comprehensive analytical framework characterizing the impact of IRS reflection coefficients on wireless sensing performance remains largely unexplored in existing literature. To address this gap, this paper investigates sensing mutual information (SMI) in a general scenario where a sensing transmitter (TX) sends random signals to multiple targets each equipped with an IRS, and multiple sensing receivers (RXs) process the received echoes. We derive a closed-form tight upper bound on SMI and propose an efficient manifold optimization-based method to maximize it by jointly optimizing the transmit precoder and IRS reflection coefficients. Simulation results validate our analysis and demonstrate substantial enhancements in SMI achieved by the proposed method.

Improving the fundamental performance trade-off in integrated sensing and communication (ISAC) systems has been deemed as one of the most significant challenges. To address it, we propose in this letter a novel ISAC system that leverages an unmanned aerial vehicle (UAV)-mounted intelligent reflecting surface (IRS) and the UAV's maneuverability in six-dimensional (6D) space, i.e., three-dimensional (3D) location and 3D rotation, thus referred to as passive 6D movable antenna (6DMA). We aim to maximize the signal-to-noise ratio (SNR) for sensing a single target while ensuring a minimum SNR at a communication user equipment (UE), by jointly optimizing the transmit beamforming at the ISAC base station (BS), the 3D location and orientation as well as the reflection coefficients of the IRS. To solve this challenging non-convex optimization problem, we propose a two-stage approach. In the first stage, we aim to optimize the IRS's 3D location, 3D orientation, and reflection coefficients to enhance both the channel correlations and power gains for sensing and communication. Given their optimized parameters, the optimal transmit beamforming at the ISAC BS is derived in closed form. Simulation results demonstrate that the proposed passive 6DMA-enabled ISAC system significantly improves the sensing and communication trade-off by simultaneously enhancing channel correlations and power gains, and outperforms other baseline schemes.

In this letter, we propose an analytical solution for recovering a low-rank positive semi-definite (PSD) matrix from its rank-one measurements. We show that by utilizing a set of structured measurement vectors, we can analytically determine the null space of this low-rank PSD matrix. Based on the result, the PSD matrix can be efficiently recovered. Our analysis shows that the proposed method only requires(N-K)(2K+1)+K2 measurements to guarantee exact recovery of the PSD matrix, where N$\ and K respectively denote the dimension and the rank of the PSD matrix. Numerical results show that the proposed method achieves a considerable improvement over existing state-of-the-art methods in terms of both sample complexity and computational efficiency. Specifically, the proposed method helps improve the computational efficiency by an order of magnitude as compared with existing methods.

Movable antennas (MAs) have emerged as a disruptive technology in wireless communications for enhancing spatial degrees of freedom through continuous antenna repositioning within predefined regions, thereby creating favorable channel propagation conditions. In this paper, we study the problem of position optimization for MA-enabled multi-user MISO systems, where a base station (BS), equipped with multiple MAs, communicates with multiple users each equipped with a single fixed-position antenna (FPA). To circumvent the difficulty of acquiring the channel state information (CSI) from the transmitter to the receiver over the entire movable region, we propose a derivative-free approach for MA position optimization. The basic idea is to treat position optimization as a closed-box optimization problem and calculate the gradient of the unknown objective function using zeroth-order (ZO) gradient approximation techniques. Specifically, the proposed method does not need to explicitly estimate the global CSI. Instead, it adaptively refines its next movement based on previous measurements such that it eventually converges to an optimum or stationary solution. Simulation results show that the proposed derivative-free approach is able to achieve higher sample and computational efficiencies than the CSI estimation-based position optimization approach, particularly for challenging scenarios where the number of multi-path components (MPCs) is large or the number of pilot signals is limited.

In this paper, we consider the problem of joint transceiver design for millimeter wave (mmWave)/Terahertz (THz) multi-user MIMO integrated sensing and communication (ISAC) systems. Such a problem is formulated into a nonconvex optimization problem, with the objective of maximizing a weighted sum of communication users' rates and the passive radar's signal-to-clutter-and-noise-ratio (SCNR). By exploring a low-dimensional subspace property of the optimal precoder, a low-complexity block-coordinate-descent (BCD)-based algorithm is proposed. Our analysis reveals that the hybrid analog/digital beamforming structure can attain the same performance as that of a fully digital precoder, provided that the number of radio frequency (RF) chains is no less than the number of resolvable signal paths. Also, through expressing the precoder as a sum of a communication-precoder and a sensing-precoder, we develop an analytical solution to the joint transceiver design problem by generalizing the idea of block-diagonalization (BD) to the ISAC system. Simulation results show that with a proper tradeoff parameter, the proposed methods can achieve a decent compromise between communication and sensing, where the performance of each communication/sensing task experiences only a mild performance loss as compared with the performance attained by optimizing exclusively for a single task.

Integration sensing and communication (ISAC) has been envisaged as a promising candidate for 6G wireless communications. In this paper, we address a user-centric environment sensing and mapping on millimeter-Wave (mmWave) orthogonal frequency division multiplexing (OFDM) systems. By leveraging the inherent sparse characteristics of mmWave channels, the received signal in terms of the single-bounce reflected paths is formulated by a low-rank third-order tensor that admits a tensor rank decomposition. A structured CANDECOMP/PARAFAC (CP) decomposition based method is then developed to extract the sensing channel parameters for environment mapping. Simulation results show that the proposed method can achieve a centi-meter accuracy of localization and mapping.

We consider the problem of channel estimation and joint active and passive beamforming for reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We show that, with a well-designed frame-based training protocol, the received pilot signal can be organized into a low-rank third-order tensor that admits a canonical polyadic decomposition (CPD). Based on this observation, we propose two CPD-based methods for estimating the cascade channels associated with different subcarriers. The proposed methods exploit the intrinsic low-rankness of the CPD formulation, which is a result of the sparse scattering characteristics of mmWave channels, and thus have the potential to achieve a significant training overhead reduction. Specifically, our analysis shows that the proposed methods have a sample complexity that scales quadratically with the sparsity of the cascade channel. Also, by utilizing the singular value decomposition-like structure of the effective channel, this paper develops a joint active and passive beamforming method based on the estimated cascade channels. Simulation results show that the proposed CPD-based channel estimation methods attain mean square errors that are close to the Cramer-Rao bound (CRB) and present a clear advantage over the compressed sensing-based method. In addition, the proposed joint beamforming method can effectively utilize the estimated channel parameters to achieve superior beamforming performance.