RIS-Enhanced DFRC with Movable Antennas

• RIS-enhanced DFRC with movable antennas is an advanced joint sensing and communication system that leverages adaptive beamforming and dynamic antenna positioning.
• The system employs block coordinate descent with techniques like SDR and SCA to jointly optimize beamforming, RIS phase control, and antenna placement under non-convex constraints.
• Performance gains include 4–6 dB radar SINR improvement and 20–40% communication rate increase while ensuring robust operation against channel uncertainties and eavesdropping.

Reconfigurable intelligent surfaces (RIS)–enhanced dual-functional radar-communication (DFRC) with movable antennas (MAs) is an emerging paradigm for joint wireless sensing and communications in scenarios with challenging propagation (e.g., dead zones, security threats, or multipath). By combining the spatial degrees of freedom afforded by position-adjustable antennas and programmable RIS, these systems enable highly flexible beamforming, stronger separation of communication/user channels, enhanced radar beampattern control, and resilient operation under channel uncertainty and eavesdropping.

1. System Architecture and Channel Modeling

RIS-enhanced DFRC systems with movable antennas typically comprise a base station (BS) equipped with $N$ transmit/receive MAs, a planar passive RIS with $M$ reflecting elements, and $K$ single-antenna user terminals (possibly with movable antennas themselves). The RIS provides reconfigurable phase control to assist in both line-of-sight (LoS) restoration and spatial beam shaping, especially in dead zones where the direct BS-to-user link is blocked (Wu et al., 2024, Yang et al., 13 Feb 2025, Yang et al., 9 Jun 2025, Ma et al., 2024).

Antenna geometry is defined as follows: the $n$th MA is at $$\mathbf t_n = [x_n, y_n]^T \in \mathcal C_t \subset \mathbb R^2$$ (or $\mathbf p_m$ in some notations), with spatial constraints—including minimum inter-antenna spacing $D$ for mutual coupling avoidance and bounded movement region $\mathcal C_t$. The RIS elements $\mathbf s_m$ are usually placed on a fixed equispaced planar array.

Channel modeling adopts a geometric far-field field-response approach, characterizing each path by angle-of-departure/arrival and path gain. The BS-to-RIS channel, for example, is given by:

$$H(\tilde{\mathbf t}) = F(\tilde{\mathbf s})^H \Sigma G(\tilde{\mathbf t}) \in \mathbb C^{M \times N}$$

where $G(\tilde{\mathbf t})$ and $F(\tilde{\mathbf s})$ collect the field response vectors at the MAs/RIS for all paths, and $\Sigma$ is the diagonal path-gain matrix (Yang et al., 9 Jun 2025, Yang et al., 13 Feb 2025). The cascaded BS-RIS-user channels and monostatic radar return channels are modeled with analogous structure, incorporating the phase and amplitude changes controlled by both MA positions and RIS phases.

2. Optimization Problem Formulation

The central transceiver and array configuration problem in RIS-enhanced DFRC with MAs is to maximize the worst-case radar beampattern gain or radar SINR, while guaranteeing strict quality-of-service (QoS) constraints for each communication user, and obeying hardware (power, phase), spatial, and security constraints. In robust implementations, the optimization is conducted over sets of possible channel/angle uncertainty (Wu et al., 2024, Yang et al., 9 Jun 2025).

A representative formulation is: $$\begin{align*} \max_{R, \Phi, p} \quad & \min_{l \in \{1,...,L\}} a(\theta_l)^\dagger \Phi H(p) R H(p)^\dagger \Phi^\dagger a(\theta_l) \ \text{s.t.} \quad & \mathrm{SINR}_k(R, \Phi, p) \ge \Gamma_k,\quad k = 1..K \ & \mathrm{Tr}(R) \le P_{\max}, \quad R \succeq 0,\ \mathrm{rank}(R_k) = 1 \ & |\phi_n| = 1,\ n=1..N \ & p_m \in \mathcal C,\ \|p_m - p_q\| \ge D,\ \forall m \neq q \end{align*}$$ with compatible extensions for joint robust beamforming, receive filtering, and secrecy constraints (e.g., bounding eavesdropper SINR) (Ma et al., 2024).

The problem is a non-convex max–min with coupled matrix variables ($R$), nonconvex constraints (unit-modulus, phase, placement), and continuous variables (antenna positions).

3. Joint Transceiver and Array Optimization Methods

Solving RIS-enhanced DFRC with MAs requires jointly optimizing over three distinct but intertwined variable blocks: (i) transmit and receive beamformers ($W$, $u$), (ii) RIS reflection coefficients/phases ($\Phi$ or $V$), and (iii) positions of the movable antennas ($p$). The state-of-the-art methodology is block coordinate descent (BCD)—also termed alternating optimization (AO)—augmented by problem-specific convex relaxation and successive convex approximation (SCA) strategies (Wu et al., 2024, Yang et al., 9 Jun 2025, Yang et al., 13 Feb 2025). The major steps involve:

• Beamformer update: With RIS phases and MA positions fixed, semidefinite relaxation (SDR) or SCA is applied to drop rank-1 constraints and linearize SINR (communication) or quadratic beampattern (radar) constraints, reducing to SDPs or SOCPs solvable via CVX.
• RIS phase update: With beamformers and MA positions fixed, replace unit-modulus (nonconvex) constraints with a sequence of linear penalty surrogates or liftings (e.g., sequential rank-one constraint relaxation, SRCR), and use MM or SCA to yield convex surrogates.
• Movable antenna placement: With beamformers and RIS fixed, antenna positions are updated one at a time by constructing second-order convex lower (for radar) or upper (for SINR) surrogates (via Taylor expansion and bounding of Hessians), and linearizing minimum spacing constraints.

Robust designs incorporate angle/CSI uncertainty by convex hull approximation (angle discretization), S-Lemma and Nemirovski’s lemma for uncertain quadratic forms, and penalty methods for unit-modulus constraints (Yang et al., 9 Jun 2025). Fractional programming (FP) is used to linearize and decouple the trace-inverse terms in radar SINR, and auxiliary variables help manage complicated coupling across the variables.

4. Robustness, Security, and Practical Constraints

Recent robust designs directly address channel and angle uncertainty (e.g., uncertain AoA/AoD, imperfect user CSI), formulating worst-case max–min objectives. Convex-hull sampling discretizes the angle uncertainty region, and S-Lemma–based relaxations capture the worst-case SINR constraints for user channels within norm-bounded CSI error sets. Penalty and approximation methods are used to make the array placement and phase control tractable within these robustified formulations (Yang et al., 9 Jun 2025).

When secrecy or physical layer security is required (e.g., presence of an eavesdropping target), the joint design enforces additional SINR upper bounds for unauthorized users, typically via additional auxiliary variables and convex quadratic constraints (Ma et al., 2024). Null-steering via coordinated MA and RIS phase optimization can substantially suppress leakage to eavesdroppers without sacrificing communication or radar performance for legitimate users.

5. Performance Gains and Trade-offs

Numerical studies demonstrate that jointly optimized RIS and movable antenna arrays significantly outperform fixed-antenna + RIS baselines in coherent DFRC regimes:

Scheme	Radar SINR Gain	Comm. Rate Gain	Outage/Robustness
MA+RIS (optimal)	+4–6 dB	+20–40%	0% under robust
FPA+RIS	baseline	baseline	Up to 30% outage
Random placement	−2–5 dB	lower	---

For moderate values of $N$ (e.g., $N=4$–$8$) and $M=16$ RIS elements, radar SINR gain is 4–6 dB compared to fixed planar arrays; increasing region size or RIS elements further increases SNR, but with diminishing returns beyond movement regions of $A \approx 2\lambda$ (Yang et al., 9 Jun 2025, Wu et al., 2024, Yang et al., 13 Feb 2025). Communication rate gains are similarly significant—joint MA+RIS design yields 20–40% higher sum-rate and expands the Pareto frontier between comm and radar objectives. Robust transceiver design closes the performance gap to ideal (perfect-CSI) operation to within 0.5 dB, and is resilient to up to 20° steering or 5% CSI error, with zero communication outage (Yang et al., 9 Jun 2025).

Trade-offs between radar and communication needs are managed by tuning SINR/SNR thresholds in the optimization: increasing the radar requirement reduces sum-rate, but the loss is sublinear (1.5 dB SINR loss for 10 dB comm QoS change). Practical design should limit MA travel to a few wavelengths and can use quantized RIS phases (3–4 bits) without substantial loss.

6. Algorithmic Complexity and Convergence

The alternating BCD/AO frameworks are algorithmically tractable: each block update solves a convex subproblem (SDP, SOCP, or QCQP), with complexity scaling as $O((NK)^3)$ (beamforming), $O(N^{3.5})$ (RIS phase), and $O(T_2 T_1 N^{3.5})$ (outer-inner iteration total), where $N$ is the number of antennas/reflectors and $T_1,T_2$ are iteration counts (Wu et al., 2024, Yang et al., 9 Jun 2025, Yang et al., 13 Feb 2025). Empirically, convergence is rapid (≤6 AO/BCD steps), with monotonic improvement and convergence to a stationary point provably guaranteed for convex surrogates and convex hull–based robustifications.

7. Physical Insights and Design Guidelines

Movable antennas jointly with intelligent surfaces enable adaptive two-dimensional spatial shaping of the beampattern, which can be dynamically tuned for tradeoffs between radar and communication, security, and robustness. Key design insights include:

• Most MA gain is achieved for movement ranges of $2\lambda$–$5\lambda$; further extension provides modest improvement (Ma et al., 2024).
• RIS settings primarily benefit communication links (QoS, interference mitigation), while MA positions more strongly affect radar beampattern and multi-user separation (Yang et al., 13 Feb 2025, Wu et al., 2024).
• Secrecy performance can be flexibly tuned by balancing eavesdropper SINR constraints and comm/radar requirements, with only moderate sum-rate penalty.
• The integration of SCA, SDR, SRCR, FP, and penalty approaches in the AO/BCD framework is essential for tractable optimization.

These results establish a comprehensive theoretical and algorithmic framework for RIS-enhanced DFRC with MAs, supporting resilient, efficient, and secure joint communication–sensing in the presence of adverse propagation and eavesdropping (Wu et al., 2024, Yang et al., 13 Feb 2025, Yang et al., 9 Jun 2025, Ma et al., 2024).