Secure Radar-Communication Systems with Malicious Targets: Integrating Radar, Communications and Jamming Functionalities

Nanchi Su; Fan Liu; Christos Masouros

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Secure Radar-Communication Systems with Malicious Targets: Integrating Radar, Communications and Jamming Functionalities

Nanchi Su, Fan Liu, Christos Masouros

arXiv:1909.03873v1Sep 9, 2019eess.SP

TL;DR

The paper studies how to secure MIMO DFRC transmissions when radar targets may eavesdrop legitimate users. It uses artificial-noise-aided optimization to suppress target SINR while meeting user requirements, extending the design to target-location uncertainty and instantaneous or statistical CSI errors. Simulations show feasible robust designs and increasing secrecy rate with wider target-location uncertainty intervals.

Problem
Radar targets in DFRC systems may eavesdrop communication information embedded in shared probing waveforms, while existing secure-transmission work largely assumes precisely known CSI.
Method
The paper uses spatially focused artificial noise and optimization-based beamforming to minimize target SINR while satisfying legitimate-user SINR constraints under perfect or uncertain location and CSI information.
Results
Simulation results show feasible beamforming designs with instantaneous and statistical CSI errors, while secrecy rate increases as the target-location uncertainty interval grows.
Takeaways & Limitations
Secure DFRC beamforming can jointly address information leakage, radar target-location uncertainty, and imperfect CSI within the studied optimization framework.

Abstract

from arXiv · show

This paper studies the physical layer security in a multiple-input-multiple-output (MIMO) dual-functional radar-communication (DFRC) system, which communicates with downlink cellular users and tracks radar targets simultaneously. Here, the radar targets are considered as potential eavesdroppers which might eavesdrop the information from the communication transmitter to legitimate users. To ensure the transmission secrecy, we employ artificial noise (AN) at the transmitter and formulate optimization problems by minimizing the signal-to-interference-plus-noise ratio (SINR) received at radar targets, while guaranteeing the SINR requirement at legitimate users. We first consider the ideal case where both the target angle and the channel state information (CSI) are precisely known. The scenario is further extended to more general cases with target location uncertainty and CSI errors, where we propose robust optimization approaches to guarantee the worst-case performances. Accordingly, the computational complexity is analyzed for each proposed method. Our numerical results show the feasibility of the algorithms with the existence of instantaneous and statistical CSI error. In addition, the secrecy rate of secure DFRC system grows with the increasing angular interval of location uncertainty.

I. INTRODUCTION

The paper addresses secrecy in DFRC systems where radar targets may eavesdrop communications, using artificial noise and robust beamforming under location and CSI uncertainty.

Motivation: Spectrum sharing motivates DFRC systems, but shared probing waveforms can leak communication information to radar targets acting as potential eavesdroppers.DFRC combines radar and communication functions through a common probing waveform, creating information-security concerns.
System objective: The proposed MIMO DFRC design minimizes target SINR while maintaining SINR requirements for legitimate users through spatially focused artificial noise.The system serves multiple legitimate users while detecting targets treated as potential eavesdroppers.
Perfect-information design: The ideal case assumes perfect CSI and precise target location, reformulates the beampattern problem as fractional programming, and solves it using SDR.The beampattern approaches a given benchmark radar beampattern.
Location uncertainty: Target-location uncertainty is handled by designing a beampattern over an angular interval covering possible target directions.The uncertain target may fall anywhere within the specified interval.
CSI uncertainty: Imperfect instantaneous and statistical CSI are incorporated through worst-case optimization with bounded errors, while S-procedure, Lagrange duality, and SDR support reformulation.Statistical CSI reduces feedback requirements, and the paper derives computational complexity for its proposed algorithms.

B. Metrics

The paper evaluates legitimate-user and target SINR, achievable rates, transmit power, and secrecy rate to characterize secure DFRC performance.

SINR metrics: The legitimate-user SINR is defined from the received signal model, including artificial-noise interference from the transmitter.The paper also gives a simplified form of this metric.
Rate metrics: The achievable transmission rates of legitimate users and Eve are defined from their respective SINR expressions.Eve denotes the potential eavesdropper represented by the radar target.
Resource metric: Transmit power is included as a system resource metric alongside user and eavesdropper performance.
Security metric: The achievable secrecy rate is defined from the transmission rates of legitimate users and Eve.

III. MINIMIZING SINR OF EVE WITH PREMISE OF PERFECT CSI AND TARGET DIRECTION

Under perfect CSI and a precisely known target direction, the paper minimizes Eve’s SINR while satisfying legitimate-user SINR, power, and radar-beampattern constraints.

The optimization assumes perfect communication CSI and precise target direction at the transmitter.
The design minimizes Eve’s SINR while enforcing legitimate-user SINR, transmit-power, and desired-radar-beampattern requirements.
The desired radar covariance matrix is constructed from an angular grid, steering vectors, and ideal beampattern gains.
The formulation constrains the covariance mismatch using γbp and each legitimate user’s SINR using γb.
Semidefinite relaxation drops the rank-one constraints, but the resulting problem remains non-convex because of its fractional objective.

B. Efficient Solver

The perfect-CSI solver applies Dinkelbach’s transform to convert the single-ratio problem into sequential SDPs, then uses SDR-based recovery to obtain an approximate beamforming solution.

Dinkelbach’s transform solves the single-ratio FP problem through a sequence of SDPs with an auxiliary scaling variable c.
The target direction is precisely available because the radar tracks targets after an initial search mode.
The SINR denominator includes artificial-noise covariance, steering-vector response, propagation loss, and noise power.
The iterative algorithm updates c and solves an SDP until the iteration threshold is met.
SDR relaxes the rank-one constraint, so eigenvalue decomposition or Gaussian randomization produces a suboptimal or approximate solution.
The complexity analysis accounts for interior-point SDP iterations, SOC constraints, and eigenvalue decomposition, with highest-order terms summarized asymptotically.

IV. EVE’S SINR MINIMIZATION WITH UNCERTAINTY IN THE TARGET DIRECTION AND PERFECT CSI

With uncertain target direction and perfect CSI, the design covers the possible angular interval using a wider main beam while minimizing sidelobe power and aggregate Eve SINR.

The uncertain target angle is modeled within [θ0 − ∆θ, θ0 + ∆θ], requiring every possible target direction to be considered.
The beampattern design seeks a main-beam width covering the uncertainty interval and minimized sidelobe power in a prescribed region.
The objective sums Eve’s SINR across all possible target locations under the angular uncertainty model.
Φ denotes the wide main-beam region, Ω the sidelobe region of interest, and γs the sidelobe-power bound.
The resulting sum-of-ratio formulation remains non-convex and requires a fractional-programming solution approach.

B. Efficient Solver

The uncertain-direction solver transforms the sum-of-ratio objective into an equivalent optimization, alternates variable updates with convex optimization, and applies SDR for approximate recovery.

The sum-of-ratio problem is transformed into an equivalent optimization involving auxiliary variables y.
For fixed θm, each ym can be obtained in closed form, enabling iterative updates within the solver.
The algorithm repeatedly solves a convex optimization problem, updates y, and obtains W_i and R_N through SDR.
Eigenvalue decomposition or Gaussian randomization produces approximate solutions after the iterative procedure.
The complexity analysis treats the constraints as LMIs and incorporates eigenvalue decomposition, with complexity expressed using iteration count and problem dimensions.

V. ROBUST BEAMFORMING WITH IMPERFECT CSI AND TARGET DIRECTION UNCERTAINTY

The paper develops robust beamforming for uncertain target directions and imperfect instantaneous CSI, minimizing worst-case target SINR while preserving legitimate-user requirements.

Robust problem formulation: Imperfect CSI is modeled with channel uncertainty bounded in a spherical region, while target uncertainty spans an angular interval.The robust design minimizes worst-case target SINR over possible target locations and channel errors.
Robust problem formulation: The uncertain-direction objective aggregates Eve’s SINR across all possible target locations in the angular interval.A wider beampattern is formulated toward the uncertain interval to avoid missing the target.
Efficient solver: The robust optimization is relaxed through semidefinite relaxation and reformulated using auxiliary variables and a max-min transformation.The SDR drops the rank-1 constraint, while the reformulation introduces z, t, and angle-indexed auxiliary variables.
Efficient solver: The resulting convex problem is solved by alternating quadratic-transform updates of auxiliary variables and primal beamforming variables.Each auxiliary y_m corresponds to a detecting angle in the uncertain main-beam region.
Efficient solver: Approximate solutions are recovered using eigenvalue decomposition or Gaussian randomization after solving the relaxed problem.These procedures address the dropped rank-one constraint.

C. Complexity Analysis

The complexity analysis characterizes Algorithm 3 through its LMI structure and includes the cost of iterative optimization and solution recovery.

C. Complexity Analysis: Algorithm 3 contains 3Φ0 + Ω0 + K + 1 scalar LMIs, 2K + 2 LMIs of size N, and K LMIs of size N + 1.Here, Φ0 and Ω0 denote the cardinalities of the discretized angular domains.
C. Complexity Analysis: The complexity expression for Algorithm 3 includes the interior-point iteration cost and eigenvalue decomposition cost.The paper retains the highest-order computational term in its summarized complexity expression.
C. Complexity Analysis: Algorithm 3 initializes auxiliary variables, repeatedly solves reformulated optimization problems, and updates auxiliary and primal variables until convergence or the iteration limit.The output consists of RN, Wi, ti, and z for all users.
C. Complexity Analysis: Eigenvalue decomposition or Gaussian randomization is used to obtain approximate solutions from the relaxed optimization.This recovery step follows the iterative solver.

VI. ROBUST OPTIMAL BEAMFORMING WITH STATISTICAL CSI AND TARGET DIRECTION UNCERTAINTY

For statistical CSI, the paper models covariance uncertainty and formulates a robust beamforming problem that handles uncertain target directions and worst-case user requirements.

Problem formulation: Rapidly time-varying channels make instantaneous CSI difficult to estimate, so the method uses slowly varying statistical CSI with uncertainty.The statistical CSI is obtained through long-term feedback but remains imperfect.
Problem formulation: The true user channel covariance is modeled as the estimated covariance plus an error matrix bounded in Frobenius norm.For each user, R_hi = R~_hi + Δ_i with ||Δ_i|| ≤ δ_i.
Robust beamforming: The robust design formulates user QoS constraints and minimizes the maximum Eve SINR over the target’s uncertain angular region.The formulation extends the robust beamforming problem to erroneous statistical CSI.
Robust beamforming: The resulting problem is handled with SDR and reformulated into a convex semidefinite program.The rank-one constraint is dropped, and the convex SDP can be solved in polynomial time using interior-point algorithms.

B. Complexity Analysis

The complexity analysis counts the conic constraints in the statistical-CSI formulation and summarizes the resulting per-iteration computational cost.

B. Complexity Analysis: Problem (27) contains K second-order cone constraints of size 1, Ω0 + 3Φ0 + 1 scalar LMIs, and 4K + 2 LMIs of size N.Φ0 and Ω0 are the cardinalities of the angular domains Φ and Ω.
B. Complexity Analysis: The complexity expression gives the computational cost of each iteration, with all proposed optimization complexities summarized in Table 1.The analysis distinguishes the LMI and SOC constraint structure before computing the cost.
B. Complexity Analysis: Figure 3 compares achievable secrecy rate against the legitimate-user SINR threshold for transmission power budgets of 30 dBm and 20 dBm.The figure uses solid lines for P0 = 30 dBm and dashed lines for P0 = 20 dBm, with N = 18, K = 4, and Δθ = 5°.

VII. NUMERICAL RESULTS

Numerical results evaluate beampattern shaping, secrecy-rate behavior, convergence, radar–communication trade-offs, and robustness under location uncertainty and CSI errors. The proposed designs remain feasible across imperfect-CSI scenarios, while secrecy performance varies with uncertainty, user requirements, sidelobe constraints, and error bounds.

Beam Gain And Secrecy Rate Analysis: Wide main-beams preserve power across possible target locations, but increasing angular uncertainty reduces main-beam power gain.The comparison uses uncertainty intervals [−5°, 5°] and [−10°, 10°], with the precise-location beampattern as a benchmark.
Beam Gain And Secrecy Rate Analysis: Secrecy rate increases with legitimate-user SINR threshold and power budget, with the highest rate when target location and CSI are precisely known.The reported settings compare P0 = 20dBm and P0 = 30dBm with sidelobe power threshold γs = 40dB.
Trade-off Between The Performance Of Radar And Communication System: Secrecy rate increases with target uncertainty and rises approximately 0.5bit/s/Hz when the legitimate-user SINR threshold increases by 5dB.The same results show that secrecy rate decreases as sidelobe threshold γs grows, especially above 30dB.
Robust Beamforming Performance: Under norm-bounded CSI errors, secrecy rate eventually decreases with error bound, whereas under statistical CSI errors it keeps increasing; robust designs remain feasible in both scenarios.The results also report higher secrecy rate when location uncertainty is limited in a larger interval.