Movable Antenna Empowered Covert Dual-Functional Radar-Communication

Movable antenna (MA) has emerged as a promising technology to flexibly reconfigure wireless channels by adjusting antenna placement. In this paper, we study a secured dual-functional radar-communication (DFRC) system aided by movable antennas. To enhance the communication security, we aim to maximize the achievable sum rate by jointly optimizing the transmitter beamforming vectors, receiving filter, and antenna placement, subject to radar signal-to-noise ratio (SINR) and transmission covertness constraints. We consider multiple Willies operating in both non-colluding and colluding modes. For noncolluding Willies, we first employ a Lagrangian dual transformation procedure to reformulate the challenging optimization problem into a more tractable form. Subsequently, we develop an efficient block coordinate descent (BCD) algorithm that integrates semidefinite relaxation (SDR), projected gradient descent (PGD), Dinkelbach transformation, and successive convex approximation (SCA) techniques to tackle the resulting problem. For colluding Willies, we first derive the minimum detection error probability (DEP) by characterizing the optimal detection statistic, which is proven to follow the generalized Erlang distribution. Then, we develop a minimum mean square error (MMSE)-based algorithm to address the colluding detection problem. We further provide a comprehensive complexity analysis on the unified design framework. Simulation results demonstrate that the proposed method can significantly improve the covert sum rate, and achieve a superior balance between communication and radar performance compared with existing benchmark schemes.

💡 Research Summary

This paper investigates a secured dual‑functional radar‑communication (DFRC) system empowered by movable antennas (MAs). By allowing each antenna element to be physically repositioned within a one‑dimensional interval, the authors exploit spatial freedom to reconfigure both the communication and radar channels, thereby alleviating the inherent conflict between sensing and data transmission directions that plagues conventional fixed‑position antenna (FPA) arrays.

The system consists of a base station equipped with two separate MA‑based uniform linear arrays (ULAs): one for transmission and one for reception, each comprising N antennas. The transmit array sends a superposition of K users’ data symbols (beamformed by vectors wₖ) and a dedicated radar probing signal r(m) with covariance R₀. The receive array processes the reflected radar echoes from W point‑like targets (which are also malicious Willies) using linear filters u_{w,i}. The communication channels follow a far‑field geometric model with Lₖ propagation paths per user, while the radar channels are modeled as line‑of‑sight (LoS) with known azimuth angles.

Security is modeled through two adversarial scenarios. In the non‑colluding case, each Willie independently performs a binary hypothesis test (H₀: no covert transmission, H₁: covert transmission) based on the received energy ‖y_w‖². The optimal test reduces to a simple energy detector with a threshold that depends on the received signal power under each hypothesis (η_{w,0}, η_{w,1}). The detection error probability (DEP) ξ_w = P_{MD}+P_{FA} is derived analytically. In the colluding case, multiple Willies share their observations and jointly perform a multivariate test. The authors prove that the optimal test statistic follows a generalized Erlang distribution, and they employ the Woodbury matrix identity together with Pinsker’s inequality to obtain a closed‑form lower bound on DEP.

The design objective is to maximize the achievable sum rate Σₖ log₂(1+γₖ) (where γₖ is the SINR of user k) while satisfying: (i) a minimum radar SINR constraint for each target, (ii) a DEP constraint (different for non‑colluding and colluding Willies), (iii) a total transmit power budget, and (iv) ordering constraints on the antenna positions (0 ≤ t₁ ≤ … ≤ t_N ≤ D and similarly for r). This yields a highly non‑convex problem involving beamforming vectors, MA placement vectors, and radar receive filters.

To tackle the problem, the authors first apply a Lagrangian dual transformation, converting the original formulation into a more tractable dual problem. They then adopt a block coordinate descent (BCD) framework, alternating among four variable blocks: (a) beamforming matrix W, (b) transmit MA positions t, (c) receive MA positions r, and (d) radar filters u_{w,i}. Specific solution techniques for each block are as follows:

• Beamforming (W): Semidefinite relaxation (SDR) is used to lift the quadratic constraints, followed by Gaussian randomization to obtain feasible rank‑one solutions.
• MA placement (t, r): Projected gradient descent (PGD) handles the box constraints, while successive convex approximation (SCA) linearizes the non‑convex terms (e.g., products of steering vectors and beamformers). The ordering constraints are enforced by simple projection onto the feasible simplex.
• Radar filters (u_{w,i}): Dinkelbach’s fractional programming transforms the radar SINR ratio into a sequence of convex subproblems with closed‑form updates.
• DEP constraints: For non‑colluding Willies, the energy‑detector threshold is expressed as a convex function of the design variables, allowing direct incorporation into the BCD subproblems. For colluding Willies, an MMSE‑based algorithm is devised: the optimal MMSE estimator of the joint Willie observation is derived, and the resulting MSE expression is linked to the DEP bound, yielding a convex surrogate that can be minimized within the BCD loop.

Complexity analysis shows that each subproblem can be solved in polynomial time (dominant cost O(N³) due to SDR), and the overall BCD algorithm converges within a few tens of iterations in practice.

Numerical results consider a scenario with N=8 antennas, K=4 users, W=3 Willies, and a movement interval D=10λ. Key findings include:

1. MA advantage: Optimizing antenna positions yields up to 30 % higher covert sum rate compared with a fixed‑position baseline, confirming that spatial reconfiguration effectively mitigates the radar‑communication trade‑off.
2. Non‑colluding vs. colluding: While colluding Willies impose a stricter detection capability, the proposed MMSE‑based design still achieves a 10–15 % higher covert rate than the non‑colluding benchmark under the same DEP target (e.g., ξ_max = 0.1).
3. Radar performance: The radar SINR constraints (e.g., Γ_w,i ≥ 10 dB) are satisfied throughout, demonstrating that security enhancements do not sacrifice sensing quality.
4. Convergence: The algorithm typically converges within 15–20 BCD iterations, and the runtime scales modestly with N and K.

In summary, the paper presents a comprehensive framework that leverages movable antennas to jointly optimize beamforming, antenna placement, and radar filtering under stringent security and sensing constraints. By integrating advanced optimization tools—Lagrangian duality, BCD, SDR, PGD, Dinkelbach transformation, SCA, and MMSE theory—the authors provide a practically implementable solution that significantly improves covert communication throughput while preserving radar functionality. The work opens avenues for further research on multi‑dimensional MA arrays, real‑time position control, and experimental validation on hardware testbeds.