Movable Antenna: Enhancing Near-Field ISAC

• Movable Antenna (MA) is a paradigm that introduces adjustable degrees of freedom via mechanical repositioning, enabling enhanced near-field channel probing and fine spatial sampling.
• It employs advanced techniques such as Newtonized Orthogonal Matching Pursuit and subregion clustering (LSRC) for high-resolution angle estimation and robust geometric localization.
• The MA framework significantly improves integrated sensing and communication (ISAC) performance, offering up to 2–5 dB NMSE improvements over baseline methods in multi-scatterer environments.

Movable Antenna (MA) introduces adjustable physical degrees of freedom to future wireless communication systems via mechanized repositioning of antenna ports. This paradigm shift facilitates transmission and sensing in the near-field regime, enhancing channel estimation, localization, and integrated sensing and communication (ISAC) capabilities. MA’s adaptive movement enables fine spatial sampling and manipulation of EM field patterns for multi-stage signal acquisition, estimation, and geometric inference. A recent MA-assisted broadband near-field ISAC framework applies structured subregion partitioning, high-resolution angle estimation (via Newtonized Orthogonal Matching Pursuit, NOMP), and a geometric clustering/localization pipeline termed LSRC (Localization via Subregion Ray Clustering), yielding notable performance improvements in multi-scatterer environments (Sun et al., 13 Jan 2026).

1. Mathematical Model of Movable Antenna Systems

The MA system consists of a base station (BS) equipped with $N$ movable antenna ports, each located at $\mathbf r_n=[x_n,0,z_n]^T \in \mathbb R^3$, forming the set $\mathcal{R} = \{\mathbf r_n\}_{n=1}^{N}$. The environment contains $L$ dominant scatterers, with each scatterer’s position encoded in spherical coordinates as $\mathbf p_l=[r_l, \theta_l, \phi_l]^T$, and its Cartesian counterpart $\mathbf s_l = [r_l\sin\theta_l\cos\phi_l$, $r_l\sin\theta_l\sin\phi_l$, $r_l\cos\theta_l]^T$.

The frequency-selective channel vector on subcarrier $k$ $(f_k)$ is

$$\mathbf h_k = \sum_{l=1}^{L} \beta_l\, \mathbf a(\mathbf p_l)\, e^{-j2\pi f_k \tau_l},$$

with $\beta_l$ the complex gain, $\tau_l$ the path delay, and the near-field steering vector

$$[\mathbf a(\mathbf p_l)]_n = \exp\left[-j\frac{2\pi}{\lambda} \left(\|\mathbf r_n-\mathbf s_l\|_2 - r_l\right)\right].$$

Stacking across $K$ subcarriers produces the composite measurement $$\mathbf H = [\mathbf h_1,\dots,\mathbf h_K] \in \mathbb C^{N\times K}$$, decomposable as

$\mathbf H = \mathbf A\, \mathbf B\, \mathbf F^T,$

where $$\mathbf A = [\mathbf a(\mathbf p_1), \dots, \mathbf a(\mathbf p_L)]$$, $\mathbf B = \mathrm{diag}(\beta_1, \dots, \beta_L)$, and the delay vector $$\mathbf f(\tau) = [e^{-j2\pi f_1 \tau}, \dots, e^{-j2\pi f_K \tau}]^T$$.

2. Subregion Partitioning and Signal Acquisition

MA spatial sampling is structured by partitioning the $N$ ports into $Q$ disjoint subregions, each visiting $N_T$ ports indexed by $\mathcal I_q$ ($\cup_{q=1}^Q \mathcal I_q = \{1,\ldots,N\}$). Signal acquisition in subregion $q$ on a pilot set of $K_c$ subcarriers ($\mathcal J \subset \{1,\dots,K\}$) is

$$\mathbf Y^{(q)} = \mathbf S_q^{\rm pos}\, \mathbf H\, \mathbf S^{\rm sc} + \mathbf Z^{(q)},$$

where $\mathbf S_q^{\rm pos}$ extracts rows in $\mathcal I_q$, $\mathbf S^{\rm sc}$ selects pilot subcarriers, and $\mathbf Z^{(q)}$ models AWGN.

3. High-Precision Angle Estimation via Newtonized OMP

To circumvent near-field atom correlation in the full $(r,\theta,\phi)$ dictionary, angle estimation exploits an angular-only grid: reference distance $r_{\rm fix}$ is selected, and grid points are assigned via

$$\bar\theta_{g_1} = \frac{\pi}{6} + \frac{2\pi}{3}\frac{g_1}{G_\theta}, \quad \bar\phi_{g_2} = \frac{\pi}{6} + \frac{2\pi}{3}\frac{g_2}{G_\phi},$$

for $g_1=1,\dots,G_\theta$, $g_2=1,\dots,G_\phi$ ($G=G_\theta G_\phi$). The dictionary $$\bar{\mathbf A}=[\mathbf a(\bar{\mathbf p}_1),\dots,\mathbf a(\bar{\mathbf p}_G)]$$ with $$\bar{\mathbf p}_g = [r_{\rm fix}, \bar\theta_{g_1}, \bar\phi_{g_2}]^T$$ supports sparse recovery via the MMV-CS problem: $$\min_{\bar{\mathbf X}} \|\mathbf Y^{(q)} - \mathbf S_q^{\rm pos}\, \bar{\mathbf A}\, \bar{\mathbf X}\, \mathbf S^{\rm sc}\|_F^2, \quad \text{s.t. common support of size } L_{\text{pre}}.$$

Newtonized Orthogonal Matching Pursuit (NOMP) refines detected angular atoms off-grid, iteratively applying coarse correlation (argmax), Newton optimization of the quadratic form $J(\mathbf p)$, and residual updating. This yields angle estimates $$\{\hat\theta_q^{(\tilde\ell)}, \hat\phi_q^{(\tilde\ell)}\}$$ for each subregion $q$.

4. Subregion Ray Clustering and Geometric Localization

Candidate rays are constructed as unit direction vectors (DVs)

$$\tilde{\mathbf v}_q^{(\tilde\ell)} = [\sin\hat\theta_q^{(\tilde\ell)}\cos\hat\phi_q^{(\tilde\ell)},\, \sin\hat\theta_q^{(\tilde\ell)}\sin\hat\phi_q^{(\tilde\ell)},\, \cos\hat\theta_q^{(\tilde\ell)}]^T,$$

formally collected into the set $\mathcal V_{\tilde\ell}$ as indexed by angle candidates across subregions.

Clustering proceeds under the angular consistency criterion (Condition 1), where a set $\mathcal S$ is accepted if

$$\arccos(\mathbf v_i^T \mathbf v_j) < \alpha_{\rm th}$$

for all $\mathbf v_i, \mathbf v_j \in \mathcal S$, with threshold $\alpha_{\rm th}$ (e.g., $10^\circ$). Greedy growth produces clusters $\mathcal C_i$ of $\ge2$ rays, each interpreted as originating from one scatterer.

Least-squares localization of cluster $i$ solves

$$E_{\rm loc}(\mathbf s) = \sum_{c=1}^{C_i} \|(\mathbf I_3 - \mathbf v_{i,c} \mathbf v_{i,c}^T)(\mathbf s - \mathbf o_{i,c})\|_2^2,$$

where $\mathbf o_{i,c}$ is the subregion center of ray $c$. Setting the gradient to zero yields

$$\boxed{\mathbf s_i = \mathbf\Gamma_i^{-1} \boldsymbol\gamma_i},$$

with

$$\mathbf\Gamma_i = \sum_c (\mathbf I - \mathbf v_{i,c} \mathbf v_{i,c}^T), \quad \boldsymbol\gamma_i = \sum_c (\mathbf I - \mathbf v_{i,c} \mathbf v_{i,c}^T)\, \mathbf o_{i,c}.$$

Algorithmic steps are summarized in Algorithm 2, encompassing clustering, labeling, solving for $\mathbf s_i$, and conversion to $(r_i, \theta_i, \phi_i)$ coordinates.

5. Sensing-Assisted Near-Field Channel Estimation

Recovered scatterer positions $$\left\{(\hat r_i, \hat\theta_i, \hat\phi_i)\right\}$$ facilitate enhanced channel modeling. The refined dictionary $\hat{\mathbf A}$ is constructed from estimated positions. Aggregated pilot measurements from all subregions yield

$$\mathbf Y = \mathbf\Psi\, \mathbf X_{\text{sam}} + \mathbf Z$$

with $$\mathbf\Psi = \mathbf S^{\text{pos}}\, \hat{\mathbf A}$$, and

$$\hat{\mathbf X}_{\text{sam}} = \left(\Psi^H \Psi\right)^{-1} \Psi^H \mathbf Y$$

producing path gains. Delay and gain estimation refine channel parameters via delay-domain gridding and MMV least-squares, followed by path pruning and final channel synthesis

$$\hat{\mathbf H} = \hat{\mathbf A}\, \mathrm{diag}(\hat\beta_i)\, \hat{\mathbf F}^T.$$

This closed-loop refinement improves the NMSE by $2$–$5$ dB over baseline methods.

6. Computational Complexity and Empirical Performance

The computational complexity analysis yields:

• NOMP per subregion: $O(L_{\rm pre}\, G\, N_T\, K_c)$ for correlation, with $O(R\, L_{\rm pre}\, N_T\, K_c)$ per Newton refinement. Multiplied by $Q$ subregions;
• Ray clustering: $O(L_{\rm pre}\, Q^2)$ (worst case);
• Position LS per cluster: $O(N_{\rm clu}\, 27)$.

Total operational complexity approximates $$O(Q\, L_{\rm pre}\, G\, N_T\, K_c + L_{\rm pre}\, Q^2 + N_{\rm clu})$$. Simulation results demonstrate that angle MAE and radial-distance MAE are typically halved compared to full-region OMP for SNR $\geq 10$ dB, and that the NMSE of reconstructed channels achieves $-20$ dB at $20$ dB SNR (versus $-15$ dB baseline). Optimal sensing has been observed for a $2\times2$ subregion grid ($Q=4$), with port measurement compression ratio $M/N$ exerting greater influence than pilot subcarrier ratio $K_c/K$.

7. Significance and Implications for ISAC

The movable antenna paradigm provides a substantive new degree of freedom for future ISAC systems: by leveraging large-range mechanical movement, near-field channel structure can be adaptively probed, revealing detailed geometric and electromagnetic scattering properties. The LSRC methodology demonstrates an efficient pipeline for fusing sparse multi-region angle estimates into robust 3D localization and refined channel estimation. This technique enables higher sensing resolution and augments communication reliability in multi-scatterer, near-field environments, supporting future broadband, location-aware wireless networks (Sun et al., 13 Jan 2026). A plausible implication is that further refinement of MA movement and sensing protocols could extend practical ISAC capabilities in urban or dense multipath scenarios.