Movable Antennas for Robust Wireless Sensing via Joint Cramér-Rao Bound and Sidelobe Minimization

This paper presents a novel design approach for movable antenna (MA)-enabled wireless sensing systems by jointly minimizing the Cramér-Rao bound (CRB) and the maximum sidelobe level (MSL) of the ambiguity function via antenna position optimization. In particular, the mean squared error (MSE) of angle-of-arrival (AoA) estimation is decomposed into a local estimation error within the mainlobe of the ambiguity function (i.e., CRB) and an additional ambiguity error caused by its sidelobes. Since the MSE is dominated by the CRB in the high-signal-to-noise ratio (SNR) regime but by the sidelobes of the ambiguity function in the low-SNR regime, our analysis reveals a fundamental trade-off between CRB minimization and MSL minimization in the moderate-SNR regime. Specifically, minimizing the CRB prefers a narrower mainlobe, where antennas are concentrated near the two edges of the one-dimensional (1-D) movement region; whereas minimizing the MSL favors a wider mainlobe, where antennas are distributed more densely near the center of the movement region. Inspired by this and to ensure robust sensing performance across different SNR regimes, we formulate an optimization problem to minimize the CRB subject to a prescribed MSL constraint via antenna position optimization. An efficient successive convex approximation (SCA) algorithm is developed to optimize the antenna position vector (APV), and a 1-D linear search method is proposed to determine the optimal MSL threshold that minimizes the actual MSE for any given SNR. Numerical results demonstrate that the proposed scheme effectively balances the trade-off between MSL and CRB minimization, thus achieving a significantly lower AoA estimation MSE across the entire SNR range compared to conventional uniform and non-uniform fixed-position antenna (FPA) arrays.

Rotatable Antenna-Enhanced Wireless Sensing with Uniform Sparse Array via Tensor Decomposition

In this letter, we propose a new wireless sensing system equipped with a rotatable antenna (RA) array to enhance the sensing performance of a uniform sparse array (USA). To tackle the severe spatial undersampling issues, we propose a novel tensor decomposition-based direction-of-arrival (DOA) estimation algorithm. Specifically, we introduce a synchronous multiple rotation pattern for active target probing such that the received signals across multiple rotations to capture the diverse spatial degree of freedoms. Subsequently, we mathematically formulate the received signals across successive rotations as a third-order tensor, and leverage the canonical polyadic decomposition to obtain the factor matrices incorporating the DOA of targets. By analyzing the extrema distribution laws of array steering vector correlation (SVC) and gain SVC of RAs, we propose to combine the array and gain factor matrices via the Kronecker product, which theoretically guarantees the unambiguous DOA estimation. Simulation results demonstrate that the proposed RA-enhanced tensor decomposition-based algorithm achieves high-precision and unambiguous sensing performance compared to conventional uniform dense arrays and omnidirectional antenna systems.

Slow Movable Antenna System Design Based on Cell-Specific Long-Term Angular Power Spectrum

Movable antenna (MA) has recently emerged as a promising paradigm for enhancing wireless communication performance by exploiting spatial degrees of freedom through flexible antenna repositioning. However, most existing designs rely on short-term user-specific instantaneous/statistical channel state information (CSI), which incurs excessive channel estimation overhead and complexity due to frequent antenna movement. To address this issue, this paper proposes a new design framework for antenna position optimization over a much longer timescale based on the cell-level statistical channel information acquired at the base station (BS). To this end, a cell-specific statistical channel model is developed for MA-aided multiuser communication systems, based on which the antenna position optimization framework for maximizing the ergodic system utility is formulated. Then, the covariance-eigenvalues-balancing antenna positions (CEBAP) design is derived to asymptotically approximate optimal solutions by statistically reducing users' channel correlation. Notably, the CEBAP solution solely depends on the BS-side angular power spectrum (APS) of wireless channels for mobile users across the cell, which significantly alleviates the overhead of channel acquisition and antenna movement, and yet remains effective for improving various system utilities over long timescales, such as weighted sum rate and minimum signal-to-interference-plus-noise ratio. Moreover, a low-complexity log-barrier penalized optimization (LOBPO) method is proposed to numerically solve the CEBAP. Simulation results based on realistic urban layouts and ray-tracing channels demonstrate consistent performance gains of the proposed CEBAP over fixed-position antenna systems across different utility functions, which closely approaches the upper bound achieved by instantaneous CSI-based MA optimization for moderately large antenna regions.

3-D Trajectory Optimization for Robust Direction Sensing in Movable Antenna Systems

This paper presents a novel wireless sensing system where a movable antenna (MA) continuously moves and receives sensing signals within a three-dimensional (3-D) region to enhance sensing performance compared with conventional fixed-position antenna (FPA)-based sensing. We show that the performance of direction vector estimation for a target is fundamentally related to the 3-D MA trajectory in terms of the mean square angular error lower-bound (MSAEB), which is adopted as a coordinate-invariant performance metric. In particular, the closed-form expression of the MSAEB is derived as a function of the trajectory covariance matrix. Theoretical analysis shows that two-dimensional (2-D) antenna movement suffers from performance divergence for target direction close to the endfire direction of the 2-D MA plane, whereas 3-D movement can achieve isotropic sensing performance over the entire angular region. To achieve robust sensing performance, we formulate a min-max optimization problem to minimize the maximum (worst-case) MSAEB over a given continuous angular region wherein the target is located. An efficient successive convex approximation (SCA) algorithm is developed to optimize the 3-D MA trajectory and obtain a locally optimal solution. Numerical results demonstrate that the proposed 3-D MA sensing scheme is able to significantly reduce the worst-case mean square angular error (MSAE) compared with conventional arrays with FPAs and MA systems with 2-D movement only, thus achieving more accurate and robust direction estimation over the entire angular region.

6D Movable Antenna Enhanced Cell-free MIMO: Two-timescale Decentralized Beamforming and Antenna Movement Optimization

This paper investigates a six-dimensional movable antenna (6DMA)-aided cell-free multi-user multiple-input multiple-output (MIMO) communication system. In this system, each distributed access point (AP) can flexibly adjust its array orientation and antenna positions to adapt to spatial channel variations and enhance communication performance. However, frequent antenna movements and centralized beamforming based on global instantaneous channel state information (CSI) sharing among APs entail extremely high signal processing delay and system overhead, which is difficult to be practically implemented in high-mobility scenarios with short channel coherence time. To address these practical implementation challenges and improve scalability, a two-timescale decentralized optimization framework is proposed in this paper to jointly design the beamformer, antenna positions, and array orientations. In the short timescale, each AP updates its receive beamformer based on local instantaneous CSI and global statistical CSI. In the long timescale, the central processing unit optimizes the antenna positions and array orientations at all APs based on global statistical CSI to maximize the ergodic sum rate of all users. The resulting optimization problem is non-convex and involves highly coupled variables, thus posing significant challenges for obtaining efficient solutions. To address this problem, a constrained stochastic successive convex approximation algorithm is developed. Numerical results demonstrate that the proposed 6DMA-aided cell-free system with decentralized beamforming significantly outperforms other antenna movement schemes with less flexibility and even achieves a performance comparable to that of the centralized beamforming benchmark.

AI Signal Processing Paradigm for Movable Antenna: From Geometric Optimization to Electromagnetic Reconfigurability

As 6G wireless communication systems evolve toward intelligence and high reconfigurability, the limitations of traditional fixed antenna (TFA) has become increasingly prominent, with geometrically movable antenna (GMA) and electromagnetically reconfigurable antenna (ERA) emerging as key technologies to break through this bottleneck. GMA activates spatial degrees of freedom (DoF) by dynamically adjusting antenna positions, ERA regulates radiation characteristics using tunable metamaterials, thereby introducing DoF in the electromagnetic domain. However, the ``geometric-electromagnetic dual reconfiguration" paradigm formed by their integration poses severe challenges of high-dimensional hybrid optimization to signal processing. To address this issue, we integrate the geometric optimization of GMA and the electromagnetic reconfiguration of ERA for the first time, propose a unified modeling framework for movable and reconfigurable antenna (MARA), investigate the channel modeling and spectral efficiency (SE) optimization for GMA, ERA, and MARA. Besides, we systematically review artificial intelligence (AI)-based solutions, focusing on analyzing the advantages of AI over traditional algorithms in high-dimensional non-convex optimization computations. This paper fills the gap in existing literature regarding the lack of a comprehensive review on the AI-driven signal processing paradigm under geometric-electromagnetic dual reconfiguration and provides theoretical support for the design and optimization of 6G wireless systems with high SE and flexibility.

Movable-Antenna Trajectory Optimization for Wireless Sensing: CRB Scaling Laws over Time and Space

In this paper, we present a new wireless sensing system utilizing a movable antenna (MA) that continuously moves and receives sensing signals to enhance sensing performance over the conventional fixed-position antenna (FPA) sensing. We show that the angle estimation performance is fundamentally determined by the MA trajectory, and derive the Cramer-Rao bound (CRB) of the mean square error (MSE) for angle-of-arrival (AoA) estimation as a function of the trajectory for both one-dimensional (1D) and two-dimensional (2D) antenna movement. For the 1D case, a globally optimal trajectory that minimizes the CRB is derived in closed form. Notably, the resulting CRB decreases cubically with sensing time in the time-constrained regime, whereas it decreases linearly with sensing time and quadratically with the movement line segment's length in the space-constrained regime. For the 2D case, we aim to achieve the minimum of maximum (min-max) CRBs of estimation MSE for the two AoAs with respect to the horizontal and vertical axes. To this end, we design an efficient alternating optimization algorithm that iteratively updates the MA's horizontal or vertical coordinates with the other being fixed, yielding a locally optimal trajectory. Numerical results show that the proposed 1D/2D MA-based sensing schemes significantly reduce both the CRB and actual AoA estimation MSE compared to conventional FPA-based sensing with uniform linear/planar arrays (ULAs/UPAs) as well as various benchmark MA trajectories. Moreover, it is revealed that the steering vectors of our designed 1D/2D MA trajectories have low correlation in the angular domain, thereby effectively increasing the angular resolution for achieving higher AoA estimation accuracy.

A Tutorial on Movable Antennas for Wireless Networks

Movable antenna (MA) has been recognized as a promising technology to enhance the performance of wireless communication and sensing by enabling antenna movement. Such a significant paradigm shift from conventional fixed antennas (FAs) to MAs offers tremendous new opportunities towards realizing more versatile, adaptive and efficient next-generation wireless networks such as 6G. In this paper, we provide a comprehensive tutorial on the fundamentals and advancements in the area of MA-empowered wireless networks. First, we overview the historical development and contemporary applications of MA technologies. Next, to characterize the continuous variation in wireless channels with respect to antenna position and/or orientation, we present new field-response channel models tailored for MAs, which are applicable to narrowband and wideband systems as well as far-field and near-field propagation conditions. Subsequently, we review the state-of-the-art architectures for implementing MAs and discuss their practical constraints. A general optimization framework is then formulated to fully exploit the spatial degrees of freedom (DoFs) in antenna movement for performance enhancement in wireless systems. In particular, we delve into two major design issues for MA systems. First, we address the intricate antenna movement optimization problem for various communication and/or sensing systems to maximize the performance gains achievable by MAs. Second, we deal with the challenging channel acquisition issue in MA systems for reconstructing the channel mapping between arbitrary antenna positions inside the transmitter and receiver regions. Moreover, we show existing prototypes developed for MA-aided communication/sensing and the experimental results based on them. Finally, the extension of MA design to other wireless systems and its synergy with other emerging wireless technologies are discussed.

Movable Antenna Enhanced Integrated Sensing and Communication Via Antenna Position Optimization

In this paper, we propose an integrated sensing and communication (ISAC) system aided by the movable-antenna (MA) array, which can improve the communication and sensing performance via flexible antenna movement over conventional fixed-position antenna (FPA) array. First, we consider the downlink multiuser communication, where each user is randomly distributed within a given three-dimensional zone with local movement. To reduce the overhead of frequent antenna movement, the antenna position vector (APV) is designed based on users' statistical channel state information (CSI), so that the antennas only need to be moved in a large timescale. Then, for target sensing, the Cramer-Rao bounds (CRBs) of the estimation mean square error for different spatial angles of arrival (AoAs) are derived as functions of MAs' positions. Based on the above, we formulate an optimization problem to maximize the expected minimum achievable rate among all communication users, with given constraints on the maximum acceptable CRB thresholds for target sensing. An alternating optimization algorithm is proposed to iteratively optimize one of the horizontal and vertical APVs of the MA array with the other being fixed. Numerical results demonstrate that our proposed MA arrays can significantly enlarge the trade-off region between communication and sensing performance compared to conventional FPA arrays with different inter-antenna spacing. It is also revealed that the steering vectors of the designed MA arrays exhibit low correlation in the angular domain, thus effectively reducing channel correlation among communication users to enhance their achievable rates, while alleviating ambiguity in target angle estimation to achieve improved sensing accuracy.

Movable Antenna Enabled Near-Field Communications: Channel Modeling and Performance Optimization

Movable antenna (MA) technology offers promising potential to enhance wireless communication by allowing flexible antenna movement. To maximize spatial degrees of freedom (DoFs), larger movable regions are required, which may render the conventional far-field assumption for channels between transceivers invalid. In light of it, we investigate in this paper MA-enabled near-field communications, where a base station (BS) with multiple movable subarrays serves multiple users, each equipped with a fixed-position antenna (FPA). First, we extend the field response channel model for MA systems to the near-field propagation scenario. Next, we examine MA-aided multiuser communication systems under both digital and analog beamforming architectures. For digital beamforming, spatial division multiple access (SDMA) is utilized, where an upper bound on the minimum signal-to-interference-plus-noise ratio (SINR) across users is derived in closed form. A low-complexity algorithm based on zero-forcing (ZF) is then proposed to jointly optimize the antenna position vector (APV) and digital beamforming matrix (DBFM) to approach this bound. For analog beamforming, orthogonal frequency division multiple access (OFDMA) is employed, and an upper bound on the minimum signal-to-noise ratio (SNR) among users is derived. An alternating optimization (AO) algorithm is proposed to iteratively optimize the APV, analog beamforming vector (ABFV), and power allocation until convergence. For both architectures, we further explore MA design strategies based on statistical channel state information (CSI), with the APV updated less frequently to reduce the antenna movement overhead. Simulation results demonstrate that our proposed algorithms achieve performance close to the derived bounds and also outperform the benchmark schemes using dense or sparse arrays with FPAs.