Movable Antenna Systems

• Movable Antenna Systems are wireless architectures with repositionable elements that transform static array geometry into a dynamic spatial resource.
• They leverage spatial channel variations and constructive/destructive interference to optimize signal gain, beamforming, and MIMO capacity.
• MA frameworks integrate movement-aware optimization with physical-layer design, enhancing applications in communications, sensing, and physical-layer security.

Movable antenna (MA) systems are wireless transceiver architectures in which antenna elements are not fixed at predetermined coordinates but can be physically repositioned within bounded regions, and in more general settings can also be rotated, so that antenna geometry itself becomes an optimization variable alongside beamforming, power allocation, and waveform design. Across the recent literature, the defining premise is that wireless channels vary continuously over space even within compact wavelength-scale regions; by moving the antenna to more favorable positions, an MA system can improve desired-signal gain, suppress interference, reshape MIMO eigenstructure, or alter sensing beampatterns in ways unavailable to fixed-position antennas (FPAs) (Zhu et al., 2022, Zhu et al., 2023, Zhu et al., 25 Feb 2025).

1. Conceptual basis and channel representation

The central modeling shift introduced by MA research is from fixed geometry to reconfigurable geometry. In conventional FPA systems, array responses are determined entirely by static element placement. In MA systems, antenna positions at the transmitter, the receiver, or both are variable within prescribed regions, so the effective channel becomes a function of antenna coordinates. This is why the literature repeatedly treats MA as a new spatial degree of freedom rather than merely a different beamforming parameterization (Zhu et al., 2023, Zhu et al., 25 Feb 2025).

A standard far-field field-response model writes the channel between a transmit position $\mathbf{t}$ and a receive position $\mathbf{r}$ as

$$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$

where $\mathbf{g}(\mathbf{t})$ and $\mathbf{f}(\mathbf{r})$ are transmit and receive field-response vectors, and $\mathbf{\Sigma}$ is the path-response matrix (PRM) (Zhu et al., 2022). Under the far-field assumption used throughout the MA literature, path amplitudes and angles remain approximately unchanged over the movement region, while antenna motion changes path-dependent phases. This same principle appears in later formulations for multiuser MIMO, secure transmission, multicast, ISAC, and trajectory-aware MA systems (Zheng et al., 2024, Cheng et al., 2023, Cheng et al., 2024, Jiang et al., 2 Jan 2025, Li et al., 5 May 2026).

The immediate consequence is that channel power becomes a spatial function over the movement region. In deterministic few-path settings, this function can be periodic, with local peaks produced by constructive superposition and local nulls produced by destructive superposition. In the two-path case, the received power is explicitly oscillatory in position; in richer scattering, the pattern becomes less visually periodic but still exhibits substantial local variation (Zhu et al., 2022, Zhu et al., 2023). The 2024 prototype paper further uses the small-scale channel power gain

$$g(\mathbf{r})\triangleq\left|\sum_{l=1}^{L}\alpha_l\exp\left(-j2\pi\left(\frac{d_l(\mathbf{r})}{\lambda}+f_c\tau_l\right)\right)\right|^2$$

as the quantity optimized through movement, making explicit that MA operation amounts to searching the spatial channel field for favorable phase alignment (Dong et al., 2024).

For MIMO, the same concept lifts to matrix-valued channels. A point-to-point MA-enabled MIMO channel is commonly written as

$$\mathbf{H}(\tilde{\mathbf{t}},\tilde{\mathbf{r}})=\mathbf{F}(\tilde{\mathbf{r}})^H\mathbf{\Sigma}\mathbf{G}(\tilde{\mathbf{t}}),$$

with transmit and receive field-response matrices assembled from per-element position-dependent responses (Ma et al., 2022). This formulation underlies capacity analysis, joint covariance-position optimization, and later extensions that incorporate mutual coupling explicitly into the effective channel (Liao et al., 13 Mar 2026).

2. Architectures, movement spaces, and hardware realizations

MA architectures are differentiated primarily by the dimensionality of motion and by whether movement is element-wise or structured. The ISAC survey classifies MA systems into 1D MA, 2D MA, 3D MA, and 6D MA. In 1D MA, antennas move along a line segment; in 2D MA, they move over a rectangular plane; in 3D MA, motion is allowed in a cuboid; and in 6D MA, the array panel itself can translate and rotate in three dimensions, yielding 3D translation plus 3D rotation (Li et al., 2024). The tutorial adopts a consistent viewpoint, treating 6DMA as the general case in which both position and orientation are controllable variables (Zhu et al., 25 Feb 2025).

The basic hardware architecture described in the survey literature has two main modules: a communication module and an antenna positioning module. The latter commonly uses a 3D mechanical slide, step motors or stepping motors, flexible cables connecting movable radiators to RF chains, and CPU control for joint signal processing and position control (Zhu et al., 2023, Li et al., 2024, Zhu et al., 25 Feb 2025). Alternative realizations explicitly listed in the literature include MEMS-based mechanisms, rotation along circular tracks, vehicle-assisted movement for large antennas, MEMS-integrated antennas, and liquid antennas or fluid antennas (Zhu et al., 2023, Zhu et al., 25 Feb 2025).

Movement can be modeled either continuously or discretely. Continuous models dominate the foundational field-response papers and several later optimization studies, with antenna coordinates constrained to bounded spatial regions and separated by minimum distances to avoid coupling or collision (Zhu et al., 2022, Ma et al., 2022). Discrete models appear when actuator resolution or grid-based movement is emphasized. In the discrete multiuser downlink formulation, each movable antenna selects exactly one point from a finite candidate set

$$\mathcal{P}=\{\mathbf{p}_1,\mathbf{p}_2,\ldots,\mathbf{p}_N\},$$

with neighboring positions separated by a fixed step size and binary variables encoding the selected location (Wu et al., 2023). The same discrete philosophy is used in multicast communication (Cheng et al., 2024) and in the general discrete-sampling framework that converts continuous MA placement into a finite point-selection problem (Liu et al., 25 Sep 2025).

A further architectural development is the two-layer movable antenna (TL-MA) array, introduced as a practical alternative to fully element-wise single-layer MA (SL-MA). In TL-MA, motion is split into coarse subarray relocation and fine intra-subarray tuning, so the absolute position of antenna $a$ in subarray $\mathbf{r}$0 is

$\mathbf{r}$1

where $\mathbf{r}$2 is the subarray starting point and $\mathbf{r}$3 is the local relative displacement (Yao et al., 19 Nov 2025). This hierarchical design is motivated by the observation that independent motion of every element entails high control complexity and hardware cost.

A persistent clarification in the literature is that MA is not equivalent to antenna selection. Antenna selection chooses among many pre-mounted fixed antennas; MA physically moves a smaller number of antennas within a region and thus can exploit the full spatial degrees of freedom of that region (Zhu et al., 2023, Wu et al., 2023, Zhu et al., 25 Feb 2025).

3. Optimization formulations and algorithmic methods

Most MA design problems are posed as joint optimization over antenna positions and conventional communication variables such as beamformers, transmit covariance matrices, combining vectors, or user powers. Because the channel depends nonlinearly on positions through complex exponentials or near-field distances, these problems are typically nonconvex even before discrete constraints, spacing constraints, or movement-delay effects are added (Ma et al., 2022, Wu et al., 2023, Zhu et al., 25 Feb 2025).

In point-to-point MIMO capacity maximization, the canonical objective is

$\mathbf{r}$4

subject to movement-region, minimum-spacing, and power constraints (Ma et al., 2022). The standard solution pattern is alternating optimization (AO): optimize the transmit covariance by water-filling for fixed positions, then update one transmit or receive antenna at a time while keeping the others fixed. Successive convex approximation (SCA) is then used to replace the position-dependent nonconvex objective by a tractable local surrogate (Ma et al., 2022).

In multiuser settings, joint beamforming-position design is typically driven by QoS, power, or sum-rate objectives. The 2023 discrete-positioning paper formulates transmit-power minimization subject to per-user SINR constraints, the bilinear coupling $\mathbf{r}$5, binary location variables, and minimum-distance constraints, yielding an NP-hard mixed-integer nonconvex program. It is solved globally by generalized Bender’s decomposition (GBD), with a convex continuous subproblem and a MILP master problem, and the authors explicitly state finite-step convergence to the global optimum for any prescribed tolerance (Wu et al., 2023).

Later work broadens the algorithmic toolbox. The two-timescale MU-MIMO framework optimizes MA positions from statistical CSI on a large timescale and beamforming vectors from instantaneous CSI on a small timescale, using AO together with SCA and majorization-minimization (MM) for MRT and ZF designs (Zheng et al., 2024). The general discrete-sampling framework uniformly discretizes the movement region into $\mathbf{r}$6 points, updates antenna positions sequentially, and inserts a Gibbs sampling phase between rounds to escape poor local optima; its stated complexity is linear in the number of antennas and sampling points (Liu et al., 25 Sep 2025). For TL-MA, AO is combined with particle swarm optimization (PSO), while receive beamforming is updated in closed form by the MMSE/max-SINR solution (Yao et al., 19 Nov 2025).

Several application-specific formulations admit sharper structure. In MA-enabled symbiotic radio, MRT toward the primary user fixes the beamformer, and the remaining degree of freedom is the antenna-position vector $\mathbf{r}$7. The secondary-rate maximization reduces to maximizing the beam gain

$\mathbf{r}$8

with one optimal design given by

$\mathbf{r}$9

which yields $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$0 under the paper’s assumptions (Zhou et al., 2024). In the two-user multicast case, a closed-form optimal beamformer is derived for fixed MA placement, after which a greedy location search and a branch-and-bound algorithm for LoS channels are constructed (Cheng et al., 2024).

A more recent refinement is the explicit treatment of mutual coupling as a designable quantity. The 2026 circuit-theoretic MA-MIMO model introduces transmit and receive coupling matrices $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$1 and $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$2, producing the effective channel

$$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$3

Because derivatives of matrix inverse square roots are analytically intractable in closed form, the position update is handled by a trust region method (TRM), with the required derivatives obtained through Sylvester equations (Liao et al., 13 Mar 2026).

4. Communication, sensing, and security roles

The MA literature spans a broad set of physical-layer tasks. In conventional communications, the reported advantages are signal power improvement, interference mitigation, flexible beamforming, spatial multiplexing, and reduced transmit power for given QoS targets (Zhu et al., 2023). Early analyses show that MA can substantially improve the maximum channel gain relative to FPA in stochastic multipath channels, with higher gains as the number of channel paths increases (Zhu et al., 2022). In MA-enabled MIMO, joint Tx/Rx position optimization increases capacity over FPA baselines and benchmark schemes across a range of SNRs and scattering conditions (Ma et al., 2022).

Multiuser transmission is one of the main application classes. The discrete multiuser MISO formulation demonstrates that joint beamforming and discrete MA positioning can reduce BS transmit power and the number of antenna elements needed to meet user SINR constraints relative to fixed random placement, antenna selection, and suboptimal AO designs (Wu et al., 2023). The two-timescale MU-MIMO framework further shows that MA with ZF consistently outperforms MA with MRT in ergodic sum rate, particularly under moderate Rician factors and high user density, while MA with MRT is positioned as a simpler alternative under strong LoS conditions (Zheng et al., 2024).

MA also changes classic multi-link tradeoffs. In symbiotic radio, the proposed MA-enabled architecture is explicitly framed as an opportunity for “mutualism”: MRT guarantees the highest primary rate at the primary user, while optimized MA positions maximize beam gain toward the backscatter device, allowing simultaneous enhancement of both primary and secondary transmissions under the paper’s model (Zhou et al., 2024). In multicast, discrete MA placement is used to improve the worst-user common-message rate, with AO-SCA, greedy search, and branch-and-bound formulations depending on the regime (Cheng et al., 2024).

Physical-layer security forms another major branch. In the wiretap-style model with a multi-antenna MA transmitter, the secrecy rate is

$$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$4

and both power minimization under secrecy constraints and secrecy-rate maximization under power constraints are studied via alternating optimization and gradient descent (Cheng et al., 2023). The reported outcome is that MA-based secure transmission substantially improves physical-layer security over FPA and antenna-selection benchmarks.

Integrated sensing and communication (ISAC) is an especially active domain for MA. Two complementary lines appear in the literature. One is system-level exposition, emphasizing higher spectral efficiency, flexible and precise beamforming, adjustable coverage, lower transmit power for given performance, and stronger sensing accuracy (Li et al., 2024). The other is optimization-driven. In MA-assisted bistatic ISAC, transmit and receive MA positions are jointly optimized with transmit and receive beamforming to maximize sensing SINR while meeting minimum communication SINR constraints (Jiang et al., 2 Jan 2025). In the full-duplex ISAC case discussed in the survey, a BPSO-based design over discrete candidate positions is combined with DC programming and SCA, and the MA-enabled design requires lower total transmit power than fixed antennas and random placements across sensing SINR thresholds (Li et al., 2024).

A security controversy arises because the same spatial reconfigurability that improves legitimate links can also strengthen attacks. The 2024 jamming study considers a malicious jammer equipped with $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$5 movable antennas in a downlink multi-user MISO/SDMA system. Under the reported simulation setup, MA-based jamming reduces the system sum rate by about $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$6 more effectively than FPAs, increases outage probability by about $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$7, and raises the number of users experiencing outages by about $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$8 (Maghrebi et al., 2024). This establishes MA not only as a communication enabler but also as a new physical-layer attack surface.

5. Measurement, prototyping, and empirical evidence

A notable feature of the MA field is the unusually rapid emergence of hardware prototypes alongside theory. The 3.5/27.5 GHz prototype uses a USRP-X410, a host computer, a fixed transmitter, and an MA receiver mounted on high-precision slide tracks. The system includes a feedback loop in which movement commands are issued, position feedback is returned, and measurement is triggered only after the antenna reaches the designated coordinate, ensuring that each power sample is taken after mechanical settling (Dong et al., 2024).

This prototype reports strong spatial power variation over very small regions. At 3.5 GHz, the MA moves along a one-dimensional horizontal line of range 500 mm with 1 mm step size, corresponding to about $$h(\mathbf{t},\mathbf{r})=\mathbf{f}(\mathbf{r})^{H}\mathbf{\Sigma}\mathbf{g}(\mathbf{t}),$$9 total range and $\mathbf{g}(\mathbf{t})$0 step size. At 27.5 GHz, it moves in a $\mathbf{g}(\mathbf{t})$1 mm $\mathbf{g}(\mathbf{t})$2 $\mathbf{g}(\mathbf{t})$3 mm two-dimensional square region with 0.5 mm step size, corresponding to a $\mathbf{g}(\mathbf{t})$4 region and $\mathbf{g}(\mathbf{t})$5 spacing (Dong et al., 2024). In a mixed LoS/NLoS indoor hall environment, measured power varies by over 40 dB at 3.5 GHz and over 23 dB at 27.5 GHz, while the position of the maximum agrees well with simulations driven by estimated path state information (PSI) (Dong et al., 2024).

A second major experimental line is the 300 GHz measurement campaign. That work develops a broadband THz measurement platform with physical MAs, a movable displacement precision of 0.02 mm, and a $\mathbf{g}(\mathbf{t})$6 planar grid of positions with 1 mm spacing in a small anechoic chamber (Wang et al., 2024). The measured channel exhibits a dominant two-ray structure consisting of a LoS ray and a metal-surface reflected ray. On the basis of this dataset, the paper constructs measurement-parameterized spatially correlated channel models and proposes a uniform-region SINR-maximized position-selection algorithm that achieves about 99% of greedy optimum across several array sizes (Wang et al., 2024).

The 300 GHz results also quantify link-level gains. In the measured channel, spectral efficiency improvement over the worst fixed-position cases reaches 11.48% for a $\mathbf{g}(\mathbf{t})$7 MA selected from $\mathbf{g}(\mathbf{t})$8 ports, with the relative gain decreasing as the number of antennas grows (Wang et al., 2024). The same study notes that because the measured channel varies more strongly along one spatial direction than the other, suitably oriented linear MA configurations can outperform planar ones of the same antenna count in that environment.

The measurements support a broader methodological point: MA performance depends heavily on geometric path information. The 3.5/27.5 GHz prototype explicitly states that power gain relies on estimated PSI, including the number of paths, path delays, elevation and azimuth AoAs, and the power ratio of each path (Dong et al., 2024). This experimentally reinforces the model-based channel-reconstruction perspective emphasized in the tutorial literature (Zhu et al., 25 Feb 2025).

6. Movement cost, misconceptions, and open directions

A recurring misconception is that the best MA position is simply the one that maximizes instantaneous SNR or SINR. The movement-delay literature shows that this is generally false once mechanical motion consumes non-negligible time. In the throughput-maximization formulation for a multiuser downlink with user-side MAs, each user’s effective throughput over a block is

$\mathbf{g}(\mathbf{t})$9

so the design objective becomes a tradeoff between channel improvement and remaining transmission time (Wang et al., 2024). The paper explicitly argues that the best SINR position is not necessarily the best throughput position.

This tradeoff has several sharp consequences. In the single-user case with one path, the optimal decision is to keep the antenna at its initial position, since movement only wastes time (Wang et al., 2024). In the broader 2026 downlink formulation, where the BS first spends $\mathbf{f}(\mathbf{r})$0 seconds repositioning its antennas and then transmits during $\mathbf{f}(\mathbf{r})$1, effective throughput is

$\mathbf{f}(\mathbf{r})$2

The paper derives a closed-form speed threshold

$\mathbf{f}(\mathbf{r})$3

and states that if $\mathbf{f}(\mathbf{r})$4, the optimal strategy is $\mathbf{f}(\mathbf{r})$5, namely to keep antennas stationary throughout the interval (Hu et al., 22 Apr 2026). This directly counters the notion that “more movement is always better.”

A related line studies transmit-while-moving rather than move-then-transmit. For a single-MA SISO system, the trajectory-aware design maximizes the average rate over a block under velocity constraints. In the special two-path case, the optimal trajectory is closed form: move at maximum velocity toward the nearest coherent position and then stay there if reachable; for general multipath channels, space is discretized and the problem is converted into a fixed-hop shortest path problem solvable optimally by dynamic programming (Li et al., 5 May 2026). This suggests that MA trajectory design can be as important as final-position design when movement time is comparable to the coherence interval.

Other practical challenges remain central across the literature. Channel acquisition is harder than in FPA systems because one must reconstruct a channel map over a movement region rather than estimate a channel at a single static geometry (Zhu et al., 2023, Zhu et al., 25 Feb 2025). Mutual coupling, long treated mainly as a constraint motivating minimum-spacing rules, can become either a performance limiter or an additional design resource, depending on whether it is ignored or modeled explicitly (Liao et al., 13 Mar 2026). Hardware and control burdens motivate structured architectures such as TL-MA, two-timescale statistical-CSI designs, and discrete-sampling or grid-based optimization frameworks (Yao et al., 19 Nov 2025, Zheng et al., 2024, Liu et al., 25 Sep 2025).

The current literature therefore presents MA systems neither as a universal replacement for fixed arrays nor as a purely mechanical curiosity. The evidence supports a more precise characterization: MA turns antenna placement into a controllable variable that can enlarge the effective spatial degrees of freedom of communication and sensing systems, but its value depends critically on channel structure, movement constraints, CSI availability, and security context (Zhu et al., 25 Feb 2025, Maghrebi et al., 2024). A plausible implication is that future MA deployments will be shaped as much by movement-aware protocols, estimation strategies, and security safeguards as by beamforming theory itself.