Robust Transceiver Design for RIS Enhanced Dual-Functional Radar-Communication with Movable Antenna

Movable antennas (MAs) have demonstrated significant potential in enhancing the performance of dual-functional radar-communication (DFRC) systems. In this paper, we explore an MA-aided DFRC system that utilizes a reconfigurable intelligent surface (RIS) to enhance signal coverage for communications in dead zones. To enhance the radar sensing performance in practical DFRC environments, we propose a unified robust transceiver design framework aimed at maximizing the minimum radar signal-to-interference-plus-noise ratio (SINR) in a cluttered environment. Our approach jointly optimizes transmit beamforming, receive filtering, antenna placement, and RIS reflecting coefficients under imperfect channel state information (CSI) for both sensing and communication channels. To deal with the channel uncertainty-constrained issue, we leverage the convex hull method to transform the primal problem into a more tractable form. We then introduce a two-layer block coordinate descent (BCD) algorithm, incorporating fractional programming (FP), successive convex approximation (SCA), S-Lemma, and penalty techniques to reformulate it into a series of semidefinite program (SDP) subproblems that can be efficiently solved. We provide a comprehensive analysis of the convergence and computational complexity for the proposed design framework. Simulation results demonstrate the robustness of the proposed method, and show that the MA-based design framework can significantly enhance the radar SINR performance while achieving an effective balance between the radar and communication performance.

💡 Research Summary

This paper tackles the design of a robust transceiver for a dual‑functional radar‑communication (DFRC) system that simultaneously exploits movable antennas (MAs) at the base station and a reconfigurable intelligent surface (RIS) to improve coverage in communication dead‑zones. The authors consider a monostatic DFRC scenario where a base station equipped with a planar array of N transmit/receive MAs serves K single‑antenna users and detects a point‑like target in the presence of Q clutter scatterers. Direct BS‑to‑user links are assumed blocked, so an M‑element RIS is deployed to create virtual line‑of‑sight (LoS) paths for the users. Both the transmit and receive MAs can be positioned anywhere within predefined square regions (Ct and Cr), providing continuous spatial degrees of freedom.

Channel Modeling
The communication links (BS‑to‑RIS, RIS‑to‑user) are modeled using a field‑response (FR) approach that captures the phase shift caused by the exact antenna positions, the angles of departure/arrival, and the carrier wavelength. This model yields a channel matrix H( t̃ ) = F( s̃ ) H Σ G( t̃ ), where G( t̃ ) and F( s̃ ) are FR matrices for the BS‑RIS and RIS‑BS sides, respectively, and Σ contains the complex path gains. The radar channel follows a conventional LoS steering‑vector model for the target and each clutter, with random complex amplitudes α0 and αq. Imperfect channel state information (CSI) is represented by ellipsoidal uncertainty sets for each link.

Problem Formulation
The design goal is to maximize the minimum radar signal‑to‑interference‑plus‑noise ratio (SINR) while guaranteeing that every user’s communication SINR exceeds a prescribed threshold γk. The optimization variables are:

• Transmit beamforming matrix W ∈ ℂN×K
• Receive filter vector u ∈ ℂN
• MA position vectors ˜t (transmit) and ˜r (receive)
• RIS reflection coefficients V = diag{e^{jθ1},…,e^{jθM}}

The radar SINR expression (after MVDR filtering) can be lower‑bounded by a quadratic form tr{Φ WWᴴ}, where Φ depends on the target steering matrix and the covariance of clutter plus noise. The robust formulation incorporates the CSI uncertainty sets, leading to a non‑convex, semi‑infinite constraint problem.

Methodology

1. Convex‑Hull Approximation – The ellipsoidal uncertainty sets are outer‑approximated by their convex hulls, turning the semi‑infinite constraints into a finite number of convex constraints.
2. S‑Lemma Transformation – Quadratic constraints involving the uncertain channels are converted into linear matrix inequalities (LMIs), enabling semidefinite programming (SDP) representation.
3. Two‑Layer Block Coordinate Descent (BCD) – The variables are split into two blocks: (i) {W, u, ˜t, ˜r} and (ii) {V, penalty variables}. Each block is optimized while keeping the other fixed.
   • Block (i) – The radar SINR maximization is recast as a fractional program. Using the Dinkelbach method (a form of fractional programming), the problem becomes a sequence of convex subproblems. Non‑convex terms (e.g., products of MA positions and beamforming vectors) are linearized via successive convex approximation (SCA).
   • Block (ii) – RIS phase constraints (|v_m| = 1) are relaxed with a quadratic penalty term, and the resulting problem is again expressed as an SDP. The penalty coefficient is gradually increased to enforce unit‑modulus solutions.
4. SDP Subproblems – Each convex subproblem is solved with standard SDP solvers (e.g., CVX with MOSEK).

Convergence and Complexity
Because each subproblem is solved to optimality, the BCD algorithm guarantees monotonic improvement of the objective and convergence to a stationary point. The per‑iteration computational cost is dominated by eigen‑decompositions of matrices of size N or M, leading to O(N³) + O(M³) complexity. Empirically, the algorithm converges within 10–20 iterations for the considered system sizes.

Simulation Results
The authors evaluate the proposed robust design under varying levels of CSI error radius δ, different numbers of RIS elements (M = 32, 64, 128), and MA movement ranges (A = 0.2–0.6 m). Key observations include:

• Radar SINR – The robust MA‑RIS design achieves a 5–8 dB gain over a conventional fixed‑position‑antenna (FPA) baseline and reaches about 90 % of the perfect‑CSI upper bound.
• Communication SINR – All users satisfy the target γk; the RIS optimization notably improves the SINR of users located in dead‑zones, with up to 30 % higher average SINR compared to a design without RIS.
• Robustness – As δ increases, the performance degradation is gradual, confirming the effectiveness of the convex‑hull and S‑Lemma handling of uncertainty.
• MA Placement – Optimized MA locations concentrate near the edges of the allowed region, exploiting spatial diversity to enhance both radar beampattern and communication channel gains.

Discussion and Future Work
The paper assumes RIS is used solely for communication; radar reflections via RIS are neglected because the three‑hop path loss makes their contribution negligible. Nevertheless, extending the model to include RIS‑assisted radar echoes could further improve detection in heavily blocked environments. The MA placement is optimized offline and treated as static; real‑time MA motion tracking and dynamic adaptation remain open challenges. Moreover, the clutter model is static and limited to a single target; multi‑target, multi‑user, and mobility scenarios would require more sophisticated stochastic modeling. Finally, the computational burden of repeated SDP solves suggests exploring low‑complexity alternatives (e.g., first‑order methods or deep‑learning‑based approximations) for practical deployment.

Conclusion
This work presents the first unified robust transceiver design framework that jointly optimizes transmit beamforming, receive filtering, movable‑antenna placement, and RIS phase shifts for a DFRC system under imperfect CSI. By converting the inherently non‑convex, uncertainty‑constrained problem into a series of tractable SDP subproblems through convex‑hull approximation, S‑Lemma, fractional programming, SCA, and penalty techniques, the authors achieve a practical algorithm with provable convergence. Simulation results demonstrate substantial radar SINR improvement (5–8 dB) while maintaining communication quality, even in the presence of significant channel uncertainty. The proposed methodology thus offers a solid foundation for future 6G ISAC systems that leverage the spatial flexibility of movable antennas and the passive beamforming capabilities of RIS.