Joint Communication and Trajectory Design for Movable Antenna Systems

Movable antennas (MAs) have attracted significant attention in wireless communications due to their ability to reconfigure channel conditions by flexibly adjusting the antenna positions within a confined region. However, MA movement generally incurs a non-negligible delay, which may significantly limit the data transmission time at optimized positions. To tackle this challenge, this paper investigates a new joint communication and trajectory optimization problem, where each MA transmits while moving along an optimized trajectory to prolong the effective data transmission time. Focusing on a single-MA system, our goal is to maximize the average data rate by optimizing the MA's positions over time, subject to its maximum velocity constraints. However, this continuous-time antenna position optimization problem is highly non-convex and challenging to solve. To tackle this challenge, we first consider a special case with two channel paths and derive the optimal MA trajectory in closed form. For other general cases, we ingeniously reformulate the average rate maximization problem into a fixed-hop shortest path problem in graph theory by sampling the antenna movement region into a multitude of discrete points, and solve it optimally. Simulation results demonstrate that our proposed algorithm can significantly improve the data rate compared to other baseline schemes.

Bistatic Integrated Sensing and Communication in the Presence of a Disco Reconfigurable Intelligent Surface: Disruption, Enhancement, or Both?

Integrated sensing and communication (ISAC) is widely regarded as one of the key enabling technologies for future sixth-generation (6G) wireless communication systems. In this work, we investigate a bistatic ISAC system in the presence of a disco reconfigurable intelligent surface (DRIS), whose random and time-varying reflection coefficients emulate a "disco ball." The introduction of the DRIS breaks the underlying assumption in existing ISAC systems that the sensing and communication channels remain static or quasi-static within the channel coherence time. We first develop a bistatic system model incorporating the DRIS and characterize all involved wireless channels. Then, an ISAC waveform design that balances sensing and communication performance is proposed by formulating a Pareto optimization problem, where the trade-off is controlled through a tunable factor. Communication and sensing performance in the bistatic ISAC system are quantified by the signal-to-interference-plus-noise ratio (SINR) and the Cramer-Rao lower bound (CRLB), respectively. To quantify the impact of the DRIS on the bistatic ISAC system, we derive the statistical characteristics of DRIS-induced active channel aging (ACA) channels for communications and the cascaded DRIS-based sensing channel. Then, we establish a theoretical lower bound on the SINR and closed-form CRLB expressions in the presence of a DRIS. The analysis reveals several distinctive properties of the DRIS in bistatic ISAC systems. In particular, the DRIS degrades communication performance significantly due to the introduction of ACA interference. In contrast, with respect to sensing performance, the DRIS decreases the estimation accuracy of the angle of departure (AoD) while concurrently enhancing that of the angle of arrival (AoA). Numerical results validate the derived theoretical analysis and confirm these DRIS-induced behaviors.

Flexible Cylindrical Array-Aided Secure Wireless Communications

Flexible-geometry arrays based on movable antennas have shown considerable potential for improving wireless communication performance. In this letter, we investigate a multiuser multiple-input single-output (MU-MISO) downlink secure communication system aided by a flexible cylindrical array (FCLA) and artificial noise (AN), where each antenna element rotates along circular tracks while the circular slices move along a vertical axis. To guarantee transmission security, we aim to maximize the achievable sum rate at multiple legitimate information receivers by jointly optimizing transmit beamforming, AN covariance matrix, and antenna placement under secrecy constraints for an eavesdropper. While the resulting problem is intractable to solve, we develop a block coordinate descent (BCD)-based framework that combines the Lagrangian dual transform, tight semidefinite relaxation (SDR), and Nesterov-accelerated projected gradient descent (PGD). Numerical results show that the proposed algorithm converges rapidly and achieves significant sum-rate gains over benchmark schemes by exploiting the geometry flexibility of the array.

Terahertz Beam Squint Mitigation via Six-Dimensional Movable Antennas

Analog beamforming holds great potential for future terahertz (THz) communications due to its ability to generate high-gain directional beams with low-cost phase shifters. However, conventional analog beamforming may suffer substantial performance degradation in wideband systems due to the beam squint effect. Instead of relying on high-cost true-time delayers, we propose an efficient six-dimensional movable antenna (6DMA) architecture to mitigate the beam-squint effect. In particular, we study a wideband wide-beam coverage problem in this paper, aiming to maximize the minimum beamforming gain over a given range of azimuth/elevation angles and frequencies by jointly optimizing the analog beamforming vector, the MA positions within a two-dimensional (2D) region, and the three-dimensional (3D) rotation angles of the antenna array. However, this problem is non-convex and intractable to solve optimally due to the coupling of the spatial and frequency domains and that of the antenna weights, positions and rotation. To tackle this problem, we first derive an optimal solution to it in a special case with azimuth or elevation angle coverage only. It is shown that rotating a uniform linear array (ULA) is sufficient to achieve global optimality and eliminate beam-squint effects. While for other general cases, an alternating optimization (AO) algorithm is proposed to obtain a high-quality suboptimal solution, where the antennas' beamforming weights, positions, and rotation angles are alternately optimized by combining successive convex approximation (SCA), sequential update with Gibbs sampling (GS), and hybrid coarse- and fine-grained search. Simulation results demonstrate that our proposed scheme can significantly outperform conventional antenna arrays without antenna movement or rotation, thus offering a cost-effective solution for wideband transmission over THz bands.

An Unsupervised Normalizing Flow-Based Neyman-Pearson Detector for Covert Communications in the Presence of Disco Reconfigurable Intelligent Surfaces

Covert communications, also known as low probability of detection (LPD) communications, offer a higher level of privacy protection compared to cryptography and physical-layer security (PLS) by hiding the transmission within ambient environments. Here, we investigate covert communications in the presence of a disco reconfigurable intelligent surface (DRIS) deployed by the warden Willie, which simultaneously reduces his detection error probabilities and degrades the communication performance between Alice and Bob, without relying on either channel state information (CSI) or additional jamming power. However, the introduction of the DRIS renders it intractable for Willie to construct a Neyman-Pearson (NP) detector, since the probability density function (PDF) of the test statistic is analytically intractable under the Alice-Bob transmission hypothesis. Moreover, given the adversarial relationship between Willie and Alice/Bob, it is unrealistic to assume that Willie has access to a labeled training dataset. To address these challenges, we propose an unsupervised masked autoregressive flow (MAF)-based NP detection framework that exploits prior knowledge inherent in covert communications. We further define the false alarm rate (FAR) and the missed detection rate (MDR) as monitoring performance metrics for Willie, and the signal-to-jamming-plus-noise ratio (SJNR) as a communication performance metric for Alice-Bob transmissions. Furthermore, we derive theoretical expressions for SJNR and uncover unique properties of covert communications in the presence of a DRIS. Simulations validate the theory and show that the proposed unsupervised MAF-based NP detector achieves performance comparable to its supervised counterpart.

Movable Antenna-Enhanced Near-Field Flexible Beamforming: Performance Analysis and Optimization

As an emerging wireless communication technology, movable antennas (MAs) offer the ability to adjust the spatial correlation of steering vectors, enabling more flexible beamforming compared to fixed-position antennas (FPAs). In this paper, we investigate the use of MAs for two typical near-field beamforming scenarios: beam nulling and multi-beam forming. In the first scenario, we aim to jointly optimize the positions of multiple MAs and the beamforming vector to maximize the beam gain toward a desired direction while nulling interference toward multiple undesired directions. In the second scenario, the objective is to maximize the minimum beam gain among all the above directions. However, both problems are non-convex and challenging to solve optimally. To gain insights, we first analyze several special cases and show that, with proper positioning of the MAs, directing the beam toward a specific direction can lead to nulls or full gains in other directions in the two scenarios, respectively. For the general cases, we propose a discrete sampling method and an alternating optimization algorithm to obtain high-quality suboptimal solutions to the two formulated problems. Furthermore, considering the practical limitations in antenna positioning accuracy, we analyze the impact of position errors on the performance of the optimized beamforming and MA positions, by introducing a Taylor series approximation for the near-field beam gain at each target. Numerical results validate our theoretical findings and demonstrate the effectiveness of our proposed algorithms.

Movable Antenna Enhanced Multi-Region Beam Coverage: A Multi-Notch-Filter-Inspired Design

Movable antenna (MA) has emerged as a promising technology to enhance wireless communication performance by exploiting the new degree of freedom (DoF) via antenna position optimization. In this letter, we investigate the MA-enhanced wide beam coverage over multiple subregions in the spatial domain. Specifically, we aim to maximize the minimum beam gain over the desired subregions by jointly optimizing the transmit beamforming and antenna position vector (APV). Although this problem is non-convex, we propose an efficient algorithm to solve it by leveraging the similarity between the considered multi-region coverage and classical multi-notch filter (MNF) design. In particular, we construct a spatial MNF-based transmit beamforming vector by assuming a continuous amplitude and phase-shift profile within the antenna movement region. Based on this continuous profile, we propose a sequential update algorithm to select an optimal subset of MA positions for multi-region coverage, jointly with a Gibbs sampling (GS) procedure to avoid undesired local optimum. Numerical results show that our proposed algorithm can significantly outperform conventional fixed position antennas (FPAs) and achieve a comparable performance to the alternating optimization (AO) algorithm with dramatically lower complexity.

Rotatable Antenna Array-Enhanced Null Steering: Performance Analysis and Optimization

Conventional fixed-orientation antenna (FOA) arrays offer limited degrees of freedom (DoF) for flexible beamforming such as null steering. To address this limitation, we propose a new rotatable antenna array (RAA) architecture in this paper, which enables three-dimensional (3D) rotational control of an antenna array to provide enhanced spatial flexibility for null steering. To characterize its performance, we aim to jointly optimize the 3D rotational angles of the RAA, to maximize the beam gain over a given desired direction, while nulling those over multiple interference directions under zero-forcing (ZF) beamforming. However, this problem is non-convex and challenging to tackle due to the highly nonlinear expression of the beam gain in terms of the rotational angles. To gain insights, we first examine several special cases including both isotropic and directional antenna radiation patterns, deriving the conditions under which full beam gain can be achieved over the desired direction while meeting the nulling constraints for interference directions. These conditions clearly indicate that compared with FOA arrays, RAAs can significantly relax the angular separation requirement for achieving effective null steering. For other general cases, we propose a sequential update algorithm, that iteratively refines the 3D rotational angles by discretizing the 3D angular search space. To avoid undesired local optimum, a Gibbs sampling (GS) procedure is also employed between two consecutive rounds of sequential update for solution exploration. Simulation results verify our analytical results and show superior null-steering performance of RAAs to FOA arrays.

Position Optimization for Two-layer Movable Antenna Systems

Movable antenna (MA) is a promising technology for improving the performance of wireless communication systems by providing new degrees-of-freedom (DoFs) in antenna position optimization. However, existing works on MA systems have mostly considered element-wise single-layer MA (SL-MA) arrays, where all the MAs move within the given movable region, hence inevitably incurring high control complexity and hardware cost in practice. To address this issue, we propose in this letter a new two-layer MA array (TL-MA), where the positions of MAs are jointly determined by the large-scale movement of multiple subarrays and the small-scale fine-tuning of per-subarray MAs. In particular, an optimization problem is formulated to maximize the sum-rate of the TL-MA-aided communication system by jointly optimizing the subarray-positions, per-subarray (relative) MA positions, and receive beamforming. To solve this non-convex problem, we propose an alternating optimization (AO)-based particle swarm optimization (PSO) algorithm, which alternately optimizes the positions of subarrays and per-subarray MAs, given the optimal receive beamforming. Numerical results verify that the proposed TL-MA significantly reduces the sum-displacement of MA motors (i.e., the total moving distances of all motors) of element-wise SL-MA, while achieving comparable rate performance.

Performance Optimization for Movable Antenna Enhanced MISO-OFDM Systems

Movable antenna (MA) technology offers a flexible approach to enhancing wireless channel conditions by adjusting antenna positions within a designated region. While most existing works focus on narrowband MA systems, this paper investigates MA position optimization for an MA-enhanced multiple-input single-output (MISO) orthogonal frequency-division multiplexing (OFDM) system. This problem appears to be particularly challenging due to the frequency-flat nature of MA positioning, which should accommodate the channel conditions across different subcarriers. To overcome this challenge, we discretize the movement region into a multitude of sampling points, thereby converting the continuous position optimization problem into a discrete point selection problem. Although this problem is combinatorial, we develop an efficient partial enumeration algorithm to find the optimal solution using a branch-and-bound framework, where a graph-theoretic method is incorporated to effectively prune suboptimal solutions. In the low signal-to-noise ratio (SNR) regime, a simplified graph-based algorithm is also proposed to obtain the optimal MA positions without the need for enumeration. Simulation results reveal that the proposed algorithm outperforms conventional fixed-position antennas (FPAs), while narrowband-based antenna position optimization can achieve near-optimal performance.