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Aerial Intelligent Reflecting Surface Enabled Terahertz Covert Communications in Beyond-5G Internet of Things

Milad Tatar Mamaghani, Yi Hong

arXiv:2111.11650v2cs.ITcs.ETcs.NIeess.SPmath.IT

TL;DR

The paper addresses covert THz communication from an access point to scheduled IoT users when unscheduled users may detect transmissions. It proposes a multi-UAV IRS-and-jammer design optimized for energy efficiency, and reports that the joint scheme outperforms its benchmarks in mAEE and mACT. Practical THz channel modeling and imperfect IRS design remain future-work topics.

Abstract

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Unmanned aerial vehicles (UAVs) are envisioned to be extensively employed for assisting wireless communications in Internet of Things (IoT) applications. On the other hand, terahertz (THz) enabled intelligent reflecting surface (IRS) is expected to be one of the core enabling technologies for forthcoming beyond-5G wireless communications that promise a broad range of data-demand applications. In this paper, we propose a UAV-mounted IRS (UIRS) communication system over THz bands for confidential data dissemination from an access point (AP) towards multiple ground user equipments (UEs) in IoT networks. Specifically, the AP intends to send data to the scheduled UE, while unscheduled UEs may pose potential adversaries. To protect information messages and the privacy of the scheduled UE, we aim to devise an energy-efficient multi-UAV covert communication scheme, where the UIRS is for reliable data transmissions, and an extra UAV is utilized as a cooperative jammer generating artificial noise (AN) to degrade unscheduled UEs detection. We then formulate a novel minimum average energy efficiency (mAEE) optimization problem, targetting to improve the covert throughput and reduce UAVs' propulsion energy consumption subject to the covertness requirement, which is determined analytically. Since the optimization problem is non-convex, we tackle it via the block successive convex approximation (BSCA) approach to iteratively solve a sequence of approximated convex sub-problems, designing the binary user scheduling, AP's power allocation, maximum AN jamming power, IRS beamforming, and both UAVs' trajectory planning. Finally, we present a low-complex overall algorithm for system performance enhancement with complexity and convergence analysis. Numerical results are provided to verify our analysis and demonstrate significant outperformance of our design over other existing benchmark schemes.

I INTRODUCTION

The paper motivates combining UAV mobility, THz links, and aerial IRSs for IoT data delivery, while covert communication addresses the need to hide transmissions from potential wardens. It proposes a two-UAV design and energy-efficient optimization for scheduled-UE communication in the presence of untrusted unscheduled UEs.

A UAV-IoT Communications

  • UAVs offer flexible deployment and LoS air-ground links, while THz bands provide spectrum opportunities but bring frequency selectivity, distance-related path loss, and water-vapor absorption.The paper identifies THz designs as a response to spectrum congestion in sub-6 GHz UAV communications.Source: A UAV-IoT Communications · p. 2, B THz and IRS Technologies · p. 2

B THz and IRS Technologies

  • Aerial IRSs can provide flexible three-dimensional deployment and full-angle reflection, whereas fixed IRSs face installation and reflection-coverage constraints.IRSs are reconfigurable scatterers that adjust signal amplitude and phase before reflecting it.Source: B THz and IRS Technologies · p. 2

C Secure and Covert Communications

  • Covert communication hides the existence of wireless transmissions, complementing information-theoretic secrecy, which protects message content from eavesdroppers.The paper notes that revealing a legitimate transmission may attract a warden's attention.Source: C Secure and Covert Communications · p. 2

D Our Contributions

  • The proposed scheme uses a THz UAV-mounted IRS for scheduled-UE data delivery and a cooperative-jammer UAV that generates artificial noise to impair unscheduled UEs' detection.The system assumes no direct AP-to-UE path because of environmental blockage.Source: D Our Contributions · p. 3, A Multi-UAV Covert Communication System · p. 4
  • The paper derives unscheduled-UE missed-detection and false-alarm measures and a tight lower bound on average covert data rate.Source: D Our Contributions · p. 3
  • The mAEE objective relates lower-bound covert throughput to UAV propulsion power, and the paper uses BSCA to solve the nonconvex design through approximated convex subproblems.The designed variables include user scheduling, power allocation, IRS beamforming, and both UAVs' trajectories and velocities.Source: D Our Contributions · p. 3

B System Setting Assumptions

C UAVs’ Flight Power Model and Mission Requirements

The system models propulsion energy and imposes periodic-flight and mobility constraints on both UAVs. It uses time-division scheduling and models THz links with distance- and atmosphere-dependent attenuation, while noting that practical THz channel modeling remains incomplete.

C UAVs’ Flight Power Model and Mission Requirements

  • Network power is modeled as dominated by the rotary-wing UAVs' mechanical propulsion consumption, which depends on their instantaneous velocities.Hovering power is not necessarily the minimum, so remaining stationary may not be energy efficient.Source: C UAVs’ Flight Power Model and Mission… · p. 4
  • Both UAVs have periodic-flight, permitted-region, speed, and acceleration constraints, and must maintain a minimum separation to avoid collision.The UIRS returns to its initial location by the final time slot.Source: C UAVs’ Flight Power Model and Mission… · pp. 4–5

D Transmission Strategy

  • The TDMA strategy schedules at most one UE per time slot; unscheduled UEs act as adversaries attempting to detect whether communication is present.The binary scheduling variable is one for a scheduled UE and zero otherwise.Source: D Transmission Strategy · p. 5

E Channel Modeling

  • THz channel modeling accounts for distance-related attenuation and water-vapor molecular absorption, with absorption dependent on carrier frequency, distance, and atmospheric conditions.The cited path-loss model is reported accurate for links up to 1 km under standard atmospheric conditions; practical channel modeling and design remain future work.Source: E Channel Modeling · pp. 5–6
  • The IRS is modeled as a uniform planar array parallel to the ground, with an L-by-L beamforming matrix whose diagonal entries represent element amplitude and phase shifts; amplitudes lie in [0,1] and phases in [0,2π].Source: E Channel Modeling · p. 6

F Signals Representation

The signal model uses Gaussian AP signaling and a cooperative jammer with random artificial-noise power. This randomness creates received-power ambiguity for unscheduled UEs, under a conservative assumption that they know the jammer-power distribution and noise variance.

F Signals Representation

  • The AP uses zero-mean Gaussian signaling with transmit power p_a[n], and each message is completed within one time slot while channel properties remain constant.Source: F Signals Representation · p. 6
  • The cooperative jammer's artificial-noise power is uniform from zero to its peak value in each slot, and unscheduled UEs are assumed to know its distribution and their noise variances.This is treated as a worst-case assumption for covertness analysis.Source: F Signals Representation · pp. 6–7
  • Randomizing jammer power creates ambiguity in Willies' received power to assist covert transmissions to the scheduled UE.Source: F Signals Representation · p. 7

G Covert Communication Requirement and Analysis

The section models unscheduled UEs as independent Willies that use radiometer tests to detect transmissions to the scheduled UE, then analytically derives the minimum detection error and covertness condition. It links covertness to a throughput–energy-efficiency design optimized through BSCA.

G Covert Communication Requirement and Analysis

  • Covertness requires each Willie’s minimum detection error to satisfy ζ⋆m,k[n] ≥ 1 − ε in every time slot.ε is the small, non-negative covertness requirement.Source: Missed Detection Rate · p. 8
  • The optimal Willie threshold lies in χ1 ≤ τm[n] ≤ χ2, where the detection error is minimized.The error rate decreases below χ1, increases above χ2, and is constant between them.Source: Missed Detection Rate · p. 8
  • Increasing AP power or downlink channel quality reduces minimum detection error but increases covert throughput, creating a covertness–rate trade-off.Increasing UCJ peak AN power or interference-link quality has the reverse effects on detection error and covert throughput.Source: Missed Detection Rate · pp. 8–9
  • The optimization targets minimum average energy efficiency, balancing lower-bound throughput against the UAVs’ total propulsion power consumption.The nonconvex problem is divided into user scheduling, power allocation, beamforming, and both UAVs’ trajectory and velocity blocks for iterative BSCA solution.Source: Missed Detection Rate · p. 9

A Sub-problem I: User Scheduling Optimization

The user-scheduling subproblem relaxes binary scheduling into a continuous formulation while seeking a feasible, tractable solution. A penalty-SCA procedure handles the resulting nonconvexity and progressively enforces binary decisions.

A Sub-problem I: User Scheduling Optimization

  • The binary user-scheduling problem is challenging because its scheduling constraint is nonconvex and coupled with the other optimization variables.UAV mechanical propulsion power is described as dominant over communication-related power consumption.Source: A Sub-problem I: User Scheduling… · p. 9
  • A first-order restrictive approximation upper-bounds the nonconvex linear-minus-quadratic constraint after relaxing scheduling to continuous variables.The paired constraints are intended to enforce αk[n] ∈ {0, 1}.Source: A Sub-problem I: User Scheduling… · p. 9
  • Penalty-SCA adds the difficult constraint as a penalty term, enabling iterative SCA while temporarily allowing violations of binary scheduling.Increasing the penalty parameter drives slack η toward zero; η = 0 recovers feasibility for the original problem.Source: A Sub-problem I: User Scheduling… · pp. 9–10

B Sub-problem II: Joint Power Allocation Optimization

The power-allocation and beamforming blocks are converted into tractable approximations while other variable blocks are held fixed. Beamforming uses rank-aware semidefinite optimization, with a lower-complexity phase-alignment alternative that is suboptimal.

B Sub-problem II: Joint Power Allocation Optimization

  • AP transmit power and UCJ peak AN power are jointly optimized, with slack variables and convex lower-bound approximations used to address nonconvexity.The resulting conic convex formulation can be solved using CVX.Source: B Sub-problem II: Joint Power… · p. 10

C Sub-problem III: Beamforming optimization

  • The beamforming formulation uses semidefinite relaxation, but dropping the rank-one constraint may yield only a lower bound unless the solution is rank one.RP-SCA penalizes the smaller eigenvalues to iteratively seek rank-one matrices for recovery of the IRS beamforming vector.Source: C Sub-problem III: Beamforming… · pp. 11–12
  • The low-complexity beamforming alternative aligns path phases to improve Bob’s received signal while degrading leakage to Willies.It fixes each IRS reflected-beam magnitude to unity, although increasing the magnitude could further improve mAEE, making the design suboptimal.Source: C Sub-problem III: Beamforming… · p. 12

D Sub-problem IV: Joint UCJ’s Trajectory and Velocity Optimization

The UCJ trajectory and velocity subproblem is cast as a fractional program and approximated with convex bounds. Alternating updates and successive convex approximation provide an approximate solution with stated convergence guarantees.

D Sub-problem IV: Joint UCJ’s Trajectory and Velocity Optimization

  • The UCJ trajectory subproblem jointly optimizes its position and velocity while holding powers, UIRS beamforming, and scheduling fixed.The formulation is a minimum of sum-of-fractional nonlinear terms.Source: D Sub-problem IV: Joint UCJ’s… · pp. 12–13
  • The fractional-programming approach uses concave lower bounds for numerators and convex upper bounds for denominators to construct a convex approximation.Slack variables are introduced to represent the ratio terms.Source: D Sub-problem IV: Joint UCJ’s… · p. 13
  • The iterative fractional-programming procedure is reported to converge to an approximate solution of the original subproblem.The method alternately updates the auxiliary parameter and optimization variables from a feasible point.Source: D Sub-problem IV: Joint UCJ’s… · p. 13
  • Restrictive Taylor approximations replace remaining nonconvex constraints, yielding a convex formulation solved by SCA with alternating updates.The cited formulation is described as an equivalent convex approximate representation for fixed auxiliary variables.Source: D Sub-problem IV: Joint UCJ’s… · p. 14

E Sub-problem V: Joint UIRS’s Trajectory and Velocity Optimization

This subproblem optimizes the UIRS trajectory and velocity while other variables are fixed. It uses fractional-programming conversion and convex approximations to obtain an efficiently solvable approximation.

E Sub-problem V: Joint UIRS’s Trajectory and Velocity Optimization

  • P5 optimizes the UIRS trajectory and velocity with the other variables fixed, and its convex approximation can be solved by an interior-point method using CVX.The resulting solution is approximate.Source: E Sub-problem V: Joint UIRS’s… · pp. 14–15
  • P5 is a nonconvex min-of-sum-of-fractional-nonlinear problem, which the method tackles by converting fractional programming to a quadratic subtraction form.The reformulation introduces nonconvex constraints that are replaced by convex approximations.Source: E Sub-problem V: Joint UIRS’s… · pp. 14–15
  • Slack variables and lemmas reformulate P5, while a first-order Taylor approximation provides a global lower bound at the given local point.The approximation relies on the stated convexity of the function Υ.Source: E Sub-problem V: Joint UIRS’s… · pp. 14–15

F Overall Algorithm

The overall iterative algorithm combines the subproblem solutions to improve mAEE subject to the covertness requirement. It stops when the fractional increase in mAEE falls below a threshold.

F Overall Algorithm

  • Algorithm 4 combines the subsolutions in a low-complexity sequential procedure to improve mAEE subject to the covertness requirement.The algorithm updates scheduling and power allocation, solves P4 and the trajectory-and-velocity subproblem, then calculates mAEE.Source: F Overall Algorithm · pp. 15–16
  • The outer loop terminates when the fractional increase in mAEE falls below the threshold εo.The algorithm recalculates mAEE at each iteration.Source: F Overall Algorithm · p. 16

G Complexity and Convergence Analysis

The proposed BSCA-based algorithm is guaranteed to converge from any feasible initialization, and its overall complexity is polynomial-time.

G Complexity and Convergence Analysis

  • Both the inner fractional-programming optimization and outer alternating optimization converge from any feasible initialization, with non-decreasing objective values bounded above.The feasible solution set is compact, and the overall algorithm has polynomial-time complexity.Source: G Complexity and Convergence Analysis · p. 16

IV NUMERICAL RESULTS AND DISCUSSION

The simulations show that the proposed JTCD scheme outperforms the benchmarks, while its objective improves across iterations. Trajectory, resource-allocation, covertness, IRS-size, and carrier-frequency results illustrate the trade-offs shaping mAEE.

IV NUMERICAL RESULTS AND DISCUSSION

V CONCLUSIONS

The paper designs a THz multi-UAV system for covert data delivery, using a UAV-mounted IRS for relaying and another UAV for artificial-noise injection. Its proposed JTCD scheme significantly outperforms other schemes in mAEE and mACT.

V CONCLUSIONS

  • The UIRS passively relays AP data to the scheduled UE, while a cooperative UAV injects artificial noise to degrade unscheduled UEs’ detection.The system targets covert data dissemination in a THz-operated B5G UAV-IoT network.Source: V CONCLUSIONS · p. 19
  • The authors derive analytical expressions for evaluating the transmission-detection performance of unscheduled UEs.The paper’s conclusion also identifies practical THz channel modeling and imperfect IRS phase-shift and amplitude design as future work.Source: V CONCLUSIONS · pp. 19–20
  • The proposed JTCD scheme significantly outperforms other schemes in both mAEE and mACT.The design jointly optimizes user scheduling, network transmission power, IRS beamforming, and UAV trajectories subject to covertness.Source: V CONCLUSIONS · p. 20

APPENDIX A JOINT DESIGN OF NETWORK POWER ALLOCATION AND

Appendix A reformulates joint network-power and user-scheduling design using slack variables, then uses local bounds and scheduling reformulation to obtain a convex problem. Appendix B proves that a complex square PSD matrix is Hermitian with nonnegative real eigenvalues.

APPENDIX A JOINT DESIGN OF NETWORK POWER ALLOCATION AND

  • The joint design optimizes network transmission powers and user-scheduling variables, with slack variables used to represent the problem equivalently.The slack variables are w, v, and r, indexed by users and time slots.Source: Appendix A · p. 20
  • Problem (f P3) remains nonconvex because constraints (A.1a), (A.1b), (A.1c), and (A.1e) are nonconvex, although (A.1d) is convex.The stated convexity of (A.1d) follows from quadratic-over-linear convexity and the convexity of the maximum of convex functions.Source: Appendix A · p. 20
  • Lemma 4 bounds the product xy at a given point using difference-of-quadratics reformulation and first-order approximations.The bounds are used with the binary user-scheduling treatment to reformulate (f P3) as a convex optimization problem.Source: Appendix A · p. 20
  • The appendix cautions that obtaining the convex problem (g P3.1) uses too many approximations.The passage identifies the local points as given but does not specify a quantitative effect of the approximations.Source: Appendix A · p. 20

APPENDIX B PROOF OF LEMMA 1

  • A complex square PSD matrix has a unique decomposition into Hermitian real and imaginary components, and is itself Hermitian with nonnegative real eigenvalues.The proof uses the PSD condition on eigenvectors to show the imaginary Hermitian component must vanish.Source: Appendix B · pp. 20–21
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