A Covariance-Surrogate Framework for Movable-Antenna Enabled Anti-Jamming with Unknown Jammers

In this paper, we investigate a movable antenna (MA) enabled anti-jamming optimization problem, where a legitimate uplink system is exposed to multiple jammers with unknown jamming channels. To enhance the anti-jamming capability of the considered system, an MA array is deployed at the receiver, and the antenna positions and the minimum-variance distortionless-response (MVDR) receive beamformer are jointly optimized to maximize the output signal-to-interference-plus-noise ratio (SINR). The main challenge arises from the fact that the interference covariance matrix is unknown and nonlinearly dependent on the antenna positions. To overcome these issues, we propose a surrogate objective by replacing the unknown covariance with the sample covariance evaluated at the current antenna position anchor. Under a two-timescale framework, the surrogate objective is updated once per block (contains multiple snapshots) at the current anchor position, while the MVDR beamformer is adapted on a per-snapshot basis. We establish a local bound on the discrepancy between the surrogate and the true objective by leveraging matrix concentration inequalities, and further prove that a natural historical-averaging surrogate suffers from a non-vanishing geometric bias. Building on these insights, we develop a low-complexity projected trust-region (TR) surrogate optimization (PTRSO) algorithm that maintains the locality of each iteration via TR constraints and enforces feasibility through projection, which is guaranteed to converge to a stationary point near the anchor. Numerical results verify the effectiveness and robustness of the proposed PTRSO algorithm, which consistently achieves higher output SINR than existing baselines.

Antenna Position and Beamforming Optimization for Movable Antenna Enabled ISAC: Optimal Solutions and Efficient Algorithms

In this paper, we propose an integrated sensing and communication (ISAC) system enabled by movable antennas (MAs), which can dynamically adjust antenna positions to enhance both sensing and communication performance for future wireless networks. To characterize the benefits of MA-enabled ISAC systems, we first derive the Cram\'er-Rao bound (CRB) for angle estimation error, which is then minimized for optimizing the antenna position vector (APV) and beamforming design, subject to a pre-defined signal-to-noise ratio (SNR) constraint to ensure the communication performance. In particular, for the case with receive MAs only, we provide a closed-form optimal antenna position solution, and show that employing MAs over conventional fixed-position antennas (FPAs) can achieve a sensing performance gain upper-bounded by 4.77 dB. On the other hand, for the case with transmit MAs only, we develop a boundary traversal breadth-first search (BT-BFS) algorithm to obtain the global optimal solution in the line-of-sight (LoS) channel scenario, along with a lower-complexity boundary traversal depth-first search (BT-DFS) algorithm to find a local optimal solution efficiently. While in the scenario with non-LoS (NLoS) channels, a majorization-minimization (MM) based Rosen's gradient projection (RGP) algorithm with an efficient initialization method is proposed to obtain stationary solutions for the considered problem, which can be extended to the general case with both transmit and receive MAs. Extensive numerical results are presented to verify the effectiveness of the proposed algorithms, and demonstrate the superiority of the considered MA-enabled ISAC system over conventional ISAC systems with FPAs in terms of sensing and communication performance trade-off.