Source-linked AI summary
Secure Dual-Functional Radar-Communication Transmission: Exploiting Interference for Resilience Against Target Eavesdropping
Nanchi Su, Fan Liu, Zhongxiang Wei, Ya-Feng Liu, Christos Masouros
TL;DR
DFRC systems must support radar sensing and downlink communication while preventing the radar target from eavesdropping on information carried by the probing signal. The paper jointly designs waveform and receive beamforming with constructive and destructive interference constraints, and reports secure transmission with improved performance against benchmark DFRC techniques.
Problem
Radar targets in DFRC systems can surveil information sent from the base station to communication users through the radar probing signal.
Method
The paper jointly designs transmit waveforms and receive beamformers using directional modulation, constructive interference for users, and destructive interference at the target.
Results
Numerical results show that the proposed fractional-programming algorithms outperform benchmark algorithms, while destructive-interference constraints deteriorate the target's symbol-error-rate performance.
Takeaways & Limitations
Secure DFRC transmission can exploit multiuser interference constructively for communication users while disrupting information reception at the radar target.
Abstract
from arXiv · showhide
We study security solutions for dual-functional radar communication (DFRC) systems, which detect the radar target and communicate with downlink cellular users in millimeter-wave (mmWave) wireless networks simultaneously. Uniquely for such scenarios, the radar target is regarded as a potential eavesdropper which might surveil the information sent from the base station (BS) to communication users (CUs), that is carried by the radar probing signal. Transmit waveform and receive beamforming are jointly designed to maximize the signal-to-interference-plus-noise ratio (SINR) of the radar under the security and power budget constraints. We apply a Directional Modulation (DM) approach to exploit constructive interference (CI), where the known multiuser interference (MUI) can be exploited as a source of useful signal. Moreover, to further deteriorate the eavesdropping signal at the radar target, we utilize destructive interference (DI) by pushing the received symbols at the target towards the destructive region of the signal constellation. Our numerical results verify the effectiveness of the proposed design showing a secure transmission with enhanced performance against benchmark DFRC techniques.
I. INTRODUCTION
DFRC systems share radar and communication functions, but their probing signals can expose downlink information to radar targets acting as eavesdroppers. This paper develops secure CI-based waveform and beamformer designs, including uncertainty handling and destructive interference at the target.
- Motivation: DFRC shares spectrum or hardware between radar sensing and wireless communication, using waveforms designed for both functions.The overlap of radar and communication resources motivates dual-functional operation.
- Security challenge: Radar targets can intercept information carried by probing signals intended for legitimate communication users.This creates a need for physical-layer security solutions tailored to dual-functional operation.
- Research gap: Existing DFRC security studies primarily maximize secrecy rate under Gaussian signaling and perfect or imperfect channel-state information.The paper motivates CI-based designs because multiuser interference can become useful signal power rather than only a detrimental effect.
- Approach: The paper jointly designs transmit waveforms and receive beamformers using directional modulation, power constraints, and constructive-interference security constraints.The objective is to maximize radar receive SINR while supporting secure communication.
- Optimization: Fractional-programming algorithms are compared with semidefinite-relaxation and successive-QCQP alternatives for radar SINR maximization.The study also considers target-location uncertainty by maximizing minimum radar SINR over a possible angular interval.
- Enhanced security: An advanced design makes multiuser interference constructive for communication users but destructive at the potential eavesdropping target.The target signal is pushed toward the destructive constellation region to increase its symbol error rate.
II. SYSTEM MODEL
The system is a MIMO DFRC base station that serves single-antenna users while detecting a point-like target amid clutter and noise. Its transmit waveform and receive beamformer determine the target return and radar output SINR, while the target also receives an eavesdropping signal.
- System configuration: The DFRC base station uses NT transmit and NR receive antennas to serve K single-antenna users and detect a point-like target simultaneously.The target may intercept information sent to legitimate users.
- Radar observation: The radar receiver observes the target return together with I signal-dependent clutter sources and additive white Gaussian noise.The target and clutter are characterized by complex amplitudes and angular locations.
- Signal model: The transmit signal vector x is mapped through array responses determined by target and clutter angles.The model uses uniform linear arrays with half-wavelength antenna spacing.
- Beamforming and security: A receive beamforming vector w filters the received waveform, producing an output whose SINR is optimized in the secure DFRC design.The same transmitted information signal can also be received at the target as an eavesdropping signal.
B. Communication Signal Model
The communication model serves multiple single-antenna users over slow time-varying block Rician channels while the BS simultaneously detects a target and accounts for clutter and noise. It uses M-PSK symbols and considers precise target-location knowledge for joint secure waveform design.
- System and channel model: The BS serves K single-antenna users while transmitting and receiving through a DFRC MIMO architecture.The communication channels are modeled as narrowband, slow time-varying block Rician fading channels.
- System and channel model: Each user channel combines a deterministic strongest line-of-sight component with a multipath scattered component.The scattering component is described through propagation paths, complex path gains, and angles of departure.
- Communication symbols: The intended symbols are M-PSK modulated and vary symbol by symbol in constructive-interference precoding.The symbol alphabet is determined by the modulation order M.
- Secure waveform design: With precise target-location knowledge, the transmit waveform and receive beamformer are designed toward a specific direction while enforcing physical-layer security.The paper presents successive QCQP and FP solvers, with SDR used to analyze an upper-bound performance.
A. Problem Formulation
The formulation uses relaxed-phase constructive interference to exploit multiuser interference at legitimate users while optimizing radar SINR under power and communication constraints. It then develops an SQ-based iterative solver for the resulting signal-dependent, non-convex problem.
- A. Problem Formulation: Relaxed-phase DM places each received user symbol inside a constructive region rather than constraining it to the constellation point.This preserves more waveform design degrees of freedom than strict phase matching.
- A. Problem Formulation: Constructive-interference precoding converts known multiuser interference into useful received power by moving symbols away from M-PSK decision boundaries.The formulation uses channel information, user data, target and clutter locations, a transmit-power budget P0, SNR thresholds Γk, and a phase threshold ξ.
- A. Problem Formulation: For QPSK, the constructive region is illustrated geometrically by rotating the noise-free received signal and projecting it onto the real and imaginary axes.The rotated representation supports the constructive-region constraints used in the recast radar-SINR maximization problem.
- B. Solve (12) by SQ Approach: The SQ approach treats the optimizing waveform as appearing in both the numerator and denominator and views the problem as MVDR beamforming with respect to the receive vector.The resulting signal-dependent SINR matrix Φ(x) is positive semidefinite and is held fixed during each sequential optimization iteration.
- B. Solve (12) by SQ Approach: With Φ fixed, the method converts the problem into a convex QCQP by shifting Φ with λI so that Q=(Φ−λI) is negative semidefinite.The concave objective can then be solved efficiently, after which the waveform and receive beamformer are updated iteratively.
- B. Solve (12) by SQ Approach: The SQ reformulation relaxes the original objective because the power constraint does not make x^Hx constant in the shifted quadratic term.The paper therefore characterizes the SQ output as a suboptimal solution rather than an exact solution to the original formulation.
- B. Solve (12) by SQ Approach: Algorithm 1 initializes a positive-semidefinite matrix, repeatedly solves the reformulated problem for x, updates Φ, transforms it into Q, and stops at convergence or a maximum iteration count.The procedure outputs the optimized waveform x.
C. Solve (12) by FP Approach
The FP approach addresses the remaining non-concavity by transforming the fractional objective and replacing its difficult term with a first-order Taylor approximation. Each iteration solves a convex problem, updates the waveform, receive beamformer, and auxiliary variable, and relies on a non-increasing objective sequence for convergence.
- FP reformulation: The original radar-SINR maximization is reformulated with Dinkelbach’s transform, leaving non-convexity only in the objective while retaining a convex feasible region.The transformed problem is then handled through linear iteration schemes.
- First-order approximation: The first term remains non-concave, so the FP method defines f(x) and approximates it at x′ within the feasible region D using a first-order Taylor expansion.The gradient provides the linearized objective used in the next optimization step.
- Convex subproblem: Each FP iteration solves the resulting convex optimization problem subject to the original constraints.The linearized formulation omits the constant term f(x′) without affecting the optimization variable.
- Iterative updates: After solving for waveform x_m, the algorithm obtains receive beamformer w_m from x_m and updates the auxiliary variable u iteratively.The update sequence follows the reformulated FP objective.
- Convergence and implementation: The algorithm converges under the stated non-increasing property of y during each iteration.Algorithm 2 initializes x0 randomly in D and repeats the convex solve, beamformer update, and u update until the stopping condition or maximum iteration count.
D. Upper Bound Performance
The upper-bound analysis relaxes the radar-SINR problem into a semidefinite program by lifting x x^H and dropping a rank-one constraint. The resulting convex problem is solvable optimally, but its objective value is an upper bound rather than an achievable SINR.
- Upper-bound relaxation: The analysis first relaxes the objective using [Σ(x)+I]^-1 ⪯ I, producing an upper-bound optimization problem.This bound follows because Σ(x)+I is greater than or equal to I in the positive-semidefinite ordering.
- Semidefinite relaxation: The relaxed problem is an inhomogeneous QCQP that is lifted by defining X=xx^H and then recast into a matrix optimization problem.The lifted formulation enables application of semidefinite relaxation.
- Semidefinite relaxation: Dropping the rank-one constraint yields a convex problem that can be solved optimally by SDR.The resulting X* and x* are treated as approximate solutions to the relaxed problem.
- Interpretation of the bound: Because the relaxation imposes X ⪰ xx^H, its objective value is larger than the achievable radar SINR.The paper therefore reports this value as an upper bound for simulation comparisons.
IV. SINRrad MAXIMIZATION WITH TARGET LOCATION UNCERTAINTY
The design maximizes the minimum radar SINR across an uncertain target-angle interval while respecting waveform constraints and power limits. An iterative fractional-programming procedure solves the resulting non-convex worst-case problem.
- Problem formulation: The target is modeled within an uncertain angular interval, and the objective maximizes the minimum SINRrad over all possible locations.The interval is Ψ = [θ0 − ∆θ, θ0 + ∆θ], with each possible angle included in the worst-case formulation.
- Problem formulation: The optimization problem is non-convex because it contains a pointwise maximum of concave functions.A quadratic transformation is used because a straightforward Dinkelbach extension does not guarantee equivalence for this max-min ratio problem.
- Optimization method: The formulation is rewritten in epigraph form by introducing a real-valued variable a and a collection of ratio variables {u1, · · · , uP}.The resulting non-convex constraint is approximated using a first-order Taylor expansion at the previous iterate.
- Modeling assumption: Because the objective is independent of the amplitude coefficient α0, uncertainty in amplitude is neglected when the target location is imperfectly known.The formulation therefore models angular uncertainty without adding amplitude uncertainty.
- Optimization method: At each iteration, the method solves for the waveform, obtains the receive beamformer, and updates u until the stopping condition or maximum iteration count is reached.Problem (31) is solved with interior-point methods, and the procedure is summarized in Algorithm 3.
V. CI PRECODING WITH DESTRUCTIVE INTERFERENCE TO THE RADAR RECEIVER
The paper frames the radar target as a potential eavesdropper and designs secure DFRC transmission around that threat. The design maximizes radar-receiver SINR while forcing the target’s received signal into a destructive constellation region, for both perfect and imperfect target-location knowledge.
- Security objective: The secure DFRC design treats legitimate communication users separately from the radar target, which may surveil information carried by the probing signal.The target-location cases considered are perfect knowledge and imperfect knowledge.
- Security objective: The optimization maximizes radar-receiver SINR while confining the target’s received signal to the destructive region of the signal constellation.This combines radar performance optimization with a physical-layer security constraint.
A. With Knowledge of Precise Target Location
With precise target-location knowledge, the design protects DFRC transmission by preserving constructive-interference benefits for communication users while steering the target’s received signal into a destructive region. The resulting problem is transformed into convex subproblems whose best radar-SINR solution is selected.
- Motivation: Prior DM designs scramble symbols at unintended directions but do not explicitly guarantee physical-layer security against the target.For QPSK, interception probability can increase when the target and communication-user channels are correlated.
- Destructive-interference design: The method restricts the potential eavesdropper’s received signal to the destructive region, defined as the area outside the constructive region.The destructive region is divided into three zones, and any one of the corresponding constraints can satisfy the condition.
- Destructive-interference design: The target’s desired maximum SNR is represented by ΓT, which corresponds to γe in the constructive/destructive-region illustration.The DI constraints describe how the target signal is placed in the destructive area.
- Optimization method: Because the constraints are linear, the reformulated problem is solved through three convex subproblems, producing candidate waveforms x∗1, x∗2, and x∗3.The candidate yielding the maximum SINRrad is selected as the final solution.
B. With Target Location Uncertainty
With uncertain target location, the design imposes destructive-region constraints at every possible angle in the interval. Binary variables encode the either-or constraints, and successive convex approximation combined with iterative fractional programming obtains the waveform.
- Uncertain-location formulation: For an uncertain target angle βp within Ψ = [θ0 − ∆θ, θ0 + ∆θ], the received signal must lie in the destructive area at every possible angle.This extends the precise-location security design to all candidate target directions.
- Constraint reformulation: The non-convex either-or destructive-region constraints are represented with binary variables ηp ∈ {0, 1} and a sufficiently large constant Ω.ηp = 0 activates one constraint, while ηp = 1 activates the alternative constraint.
- Constraint reformulation: The reformulated problem is a mixed-integer optimization problem without polynomial-time computational complexity, motivating a lower-complexity equivalent formulation.The resulting formulation retains the waveform, epigraph, and binary-variable constraints.
- Optimization method: Successive convex approximation first obtains the optimal ηp, after which x and a are updated iteratively using fractional programming.The variables ηp are updated until convergence, and the waveform is then obtained through iterative updates of up.
- Optimization method: Algorithm 4 initializes ηp and x randomly, repeatedly solves the reformulated problem, updates the receive beamformer and u, and stops at convergence or the iteration limit.The algorithm is designed for the mixed-integer problem under target-location uncertainty.
VI. NUMERICAL RESULTS
The numerical evaluation uses Monte Carlo simulations under specified channel, array, power-budget, and target settings, with benchmark beampattern results reported for varying DFRC BS antenna counts.
- Simulation setup: The simulations assume standard Complex Gaussian channel entries and uniform linear arrays with half-wavelength antenna spacing.Both the DFRC BS and radar receiver use the same number of array elements.
- Simulation setup: The power budget is set to P0 = 30dBm and the Rician coefficient is vk = 1.
- Beampattern evaluation: Fig. 4 evaluates optimized beampatterns for different numbers of DFRC BS antennas with K = 5.The beamformer design approach proposed in [49] is used as the benchmark.
A. The Resultant Beampattern
The proposed DFRC-CI design produces radar beampatterns with clear clutter nulls and improved radar-oriented performance, while target-location uncertainty reduces main-beam power. Its DI extension further degrades the target’s ability to decode communication data.
- Resultant beampattern: Clear nulls appear at clutter-source locations, and DFRC-CI improves the beampattern from the radar viewpoint relative to the DFRC-PD benchmark.The communication-user SNR threshold is fixed at 15 dB in this evaluation.
- Resultant beampattern: Power gain in the main beam decreases as the target-location uncertainty interval expands.This evaluates beampattern robustness when the base station lacks perfect knowledge of the radar target location.
- Convergence and SINR: The proposed algorithm converges in 5 iterations with precise target-location knowledge and around 9 iterations under target-location uncertainty.The convergence analysis compares the two target-location knowledge conditions.
- Convergence and SINR: Radar SINR reflects a tradeoff with target uncertainty, but is only slightly affected by CU location when the CU–target angle difference exceeds 15°.The evaluation varies the angular uncertainty interval and angle difference between the CU and target.
- Secure transmission: DI constraints push target-received symbols into the destructive region and raise target SER close to 1 as angular separation increases.With CI alone, target decode probability converges to 0.75 as angular separation increases; the paper concludes that DI efficiently prevents eavesdropping.