Dual-Polarized Movable Antennas

• Dual-Polarized Movable Antennas are advanced transceiver arrays that combine mechanical translation/rotation with dual-polarized feeds to achieve adaptive, performance-optimized beamforming.
• They integrate precise MEMS movements and digitally controlled phase shifters to enable continuous polarization agility and spatial diversity in wireless communication.
• Joint optimization algorithms in D-PMA systems, using gradient-based tuning and metaheuristics, significantly improve metrics like gain, MSE reduction, and polarization isolation.

Dual-polarized movable antennas (D-PMA) constitute a paradigm in wireless transceiver array design, leveraging both spatial and polarization degrees of freedom for adaptive, performance-optimized electromagnetic architectures. D-PMA systems merge mechanical movement (translation/rotation) with electronically reconfigurable dual-polarized feed networks, enabling flexible beamforming, polarization agility, and spatial diversity exploitation crucial for advanced mobile communications and distributed wireless function aggregation. The following sections detail the theoretical principles, hardware foundations, electromagnetic modeling, joint optimization algorithms, and application scenarios underpinning D-PMAs in contemporary wireless research.

1. Hardware Architectures of Dual-Polarized Movable Antennas

A D-PMA element integrates mechanical, electrical, and control subsystems to realize six electromagnetic-domain degrees of freedom. Mechanically, a three-axis motorized stage or MEMS-slide assembly provides continuous translation $(x, y, z)$, typically restricted to a compact region ($\text{cube side} \approx \lambda/2 - \lambda$), while a two-axis rotary stage (using stepper-motors or MEMS gimbals) enables tilt $(\theta)$ and azimuthal rotation $(\phi)$. The total mechanical configuration thus comprises three translations and two rotations; yaw may remain fixed by the array mounting or grid arrangement (Zhu et al., 15 Oct 2025).

Electrically, the dual-polarization feed network consists of two orthogonal ports to excite vertical and horizontal linear polarizations. Each feed incorporates digitally programmable phase shifters $(\Delta\psi_1, \Delta\psi_2)$ and PIN diodes for on/off switching. Advanced configurations may deploy $90^\circ$ hybrid couplers or Wilkinson splitters to achieve arbitrary linear or circular polarization states.

Integration is supported by microcontrollers or FPGAs, which issue motor driver and polarization network commands. Position and orientation sensors (optical encoders, Hall-effect) furnish sub-$0.1^\circ$ angular and sub-$0.1$mm translational feedback for closed-loop manipulation. For user terminals, hybrid architectures (MEMS slide for micro-movements, rotary MEMS for polarization angle change, PIN diodes for rapid feed switching) are recommended to balance latency and bandwidth constraints (Zhu et al., 15 Oct 2025).

2. Electromagnetic-Domain Degrees of Freedom

D-PMA systems span a six-dimensional design space. The controllable variables are:

• Spatial translation: $(x, y, z)$ subject to a region constraint $R_\text{max} \leq \lambda$.
• Orientation: $(\theta, \phi)$, implemented via mechanical rotation.
• Polarization: Adjustable via relative feed phases $(\Delta\psi)$ and amplitudes $(a_1, a_2)$.

Arbitrary linear polarization is obtained for $\alpha = \arctan(a_2/a_1)$; circular polarization arises when $a_1 = a_2$ and $\Delta\psi = \pm \pi/2$. Switchable polarization ports facilitate direct polarization switching, and the hybrid feed enables fine-grained continuous tuning (Zhu et al., 15 Oct 2025). Stackable multidimensional control establishes the basis for advanced polarforming (electronic polarization tuning) and creates spatial-polarization joint channel diversity.

3. Mathematical Modeling and Channel Representation

The radiated far-field by a D-PMA at pose $(\mathbf{p}, \mathbf{R}, \Delta\psi, a_1, a_2)$ is given by

$$E(\theta_e, \phi_e;\mathbf{p}, \mathbf{R}, \Delta\psi) = a_1 F_1(\theta_e, \phi_e;\mathbf{p}, \mathbf{R}) + a_2 e^{j\Delta\psi} F_2(\theta_e, \phi_e;\mathbf{p}, \mathbf{R})$$

where $F_1, F_2$ are embedded element patterns under the current mechanical configuration (Zhu et al., 15 Oct 2025). Polarization purity is measured by cross-polarization discrimination (XPD):

$$\operatorname{XPD}(\theta_e, \phi_e) = 20 \log_{10} \left| \frac{E_{co}(\theta_e, \phi_e)}{E_{cross}(\theta_e, \phi_e)} \right|$$

where $E_{co}$ and $E_{cross}$ are co- and cross-polarized field components, respectively.

At the channel level, the joint spatial-polarization transfer function for a single-cell downlink with $N$ D-PMAs is (Shao et al., 4 Jun 2025):

$$\mathbf{h}_k(\mathbf{u}, \mathbf{w}_k, \mathbf{v}) = \mathbf{h}_k^{\rm LoS}(\mathbf{u}) \left[\mathbf{v}^H \mathbf{A}_k(\mathbf{u}, \mathbf{u}_k^{\rm r}) \mathbf{w}_k\right] \in \mathbb{C}^{N \times 1}$$

where $\mathbf{A}_k$ encodes transceiver polarization, $\mathbf{v}$ and $\mathbf{w}_k$ are BS/user polarforming vectors, and $\mathbf{u}$ is the 3D rotation. This representation enables end-to-end channel modeling accounting for both mechanical and electronic DoFs.

4. Joint Optimization Algorithms

Optimal exploitation of D-PMA resources requires high-dimensional, nonconvex joint optimization over mechanical pose and electronic feed states. Established methodologies include:

• Gradient-based joint tuning: Evaluation of cost function gradients $$(\nabla_{\mathbf{p}} J, \nabla_{[\theta, \phi]} J, \partial J/\partial \Delta\psi)$$ followed by stepwise variable updates via line search. This approach leverages field derivative measurements and adjoint EM solvers (Zhu et al., 15 Oct 2025).
• Metaheuristics: Chromosome encoding of all DoFs. Fitness defined as negative of cost function $J$. Genetic crossover and mutation evolve toward high-gain, high-XPD designs.
• Successive Convex Approximation (SCA): Linearization of nonconvex regions, solving convex surrogates for continuous variable refinement.

For multiuser systems, joint optimization is decomposed into two timescales (Shao et al., 4 Jun 2025): slow (mechanical rotation based on statistical CSI) and fast (polarforming and digital precoding based on instantaneous CSI). Algorithms such as penalty dual decomposition (PDD) and block coordinate descent (BCD) efficiently update discrete and continuous polarforming vectors in parallel.

In multi-cell AirComp (Hu et al., 14 Jan 2026), block-coordinate alternating minimization is employed for mean squared error (MSE) reduction, with closed-form updates for combiners and power coefficients, SCA/SDR for polarization, and gradient descent for antenna positions. Statistical-channel-based schemes further adapt the solution in high-mobility contexts.

5. Performance Metrics and Experimental Evidence

Simulation and prototype evaluations of D-PMA systems demonstrate:

• Radiation gain: $G_{\rm peak} \approx 8$ dBi per port at $f_0 = 3.5$ GHz; beam-steering over $\pm 60^\circ$ with $<1$ dB gain drop (Zhu et al., 15 Oct 2025).
• Polarization isolation: XPD $\geq$ 30 dB in a $\pm 45^\circ$ sector; cross-pol $\leq -25$ dB across $3.4-3.8$ GHz.
• S-parameter isolation: $|S_{12}|, |S_{21}| \leq -25$ dB at tuned settings.
• Polarization efficiency: $\eta_{\rm pol} \geq 92\%$ over main beam for all steering angles.
• Switching latencies: Mechanical slide (<20 ms), MEMS rotation (<1 ms), PIN-diode phase switching (<50 ns).
• Multiuser rate improvements: For $N=64$, $K=30$, 24 GHz, joint polarforming + rotation yields up to 100% sum-rate improvement vs. conventional fixed array (Shao et al., 4 Jun 2025).
• Distributed AirComp MSE: D-PMA yields $\sim20\%$ lower MSE than movable single-polarized (MA) and up to $22\%$ improvement with increased antenna count (Hu et al., 14 Jan 2026).

Metric	D-PMA Value	Reference
Peak gain per port	$\approx 8$ dBi	(Zhu et al., 15 Oct 2025)
Beam range	$\pm 60^\circ$	(Zhu et al., 15 Oct 2025)
XPD	$\geq 30$ dB	(Zhu et al., 15 Oct 2025)
MSE (AirComp, $M=10$)	$2.2 \times 10^{-2}$	(Hu et al., 14 Jan 2026)

6. Implementation Trade-Offs and Practical Guidelines

Key trade-offs in D-PMA deployment involve:

• Movement complexity vs. latency: Full six mechanical DoFs afford maximal spatial flexibility but introduce $\sim10-20$ ms latency. Hybrid approaches (coarse mechanical, fine electronic) decrease repositioning time.
• Polarization agility vs. bandwidth: PIN-diode phase shifters permit nanosecond switching but are typically narrowband ($\sim20-30\%$ fractional BW). Mechanical wideband mechanisms (full 360° rotation) retain $>40\%$ BW at the cost of millisecond-scale delays.
• Isolation vs. aperture: Increasing $R_{\rm max}$ can cause excessive coupling; optimal isolation retained for $R_{\rm max} \leq 0.5\lambda$.

Recommended architectures for 6G terminals include MEMS slides for micromovements, rotary MEMS for rapid polarization tuning, and PIN diodes for port switching. This ensures latency below 10 ms and supports multi-gigabit polar-diverse links (Zhu et al., 15 Oct 2025).

7. Applications and Emerging Directions

D-PMA technology underpins:

• 6G mobile systems: Adaptive spatial-polarization optimization for base stations and user terminals; high spectral efficiency via joint polarforming and rotation (Shao et al., 4 Jun 2025).
• Distributed AirComp: MSE-constrained over-the-air analog aggregation networks; D-PMA arrays facilitate low-error wireless optimization (Hu et al., 14 Jan 2026).
• Robust operation: Results indicate that D-PMA systems retain significant gains under both instantaneous and statistical channel state information, confirming suitability in dynamic, high-mobility environments (Hu et al., 14 Jan 2026).

A plausible implication is that future ultra-dense networks and cooperative wireless function computation will increasingly employ D-PMA arrays to exploit multidimensional channel state adaptation, with research converging on low-latency, multi-timescale optimization protocols for robust, scalable deployment.