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Collaborative Secret and Covert Communications for Multi-User Multi-Antenna Uplink UAV Systems: Design and Optimization

Jinpeng Xu, Lin Bai, Xin Xie, Lin Zhou

TL;DR

This work tackles secure uplink UAV communications with diverse user security requirements by introducing a collaborative secret and covert transmission scheme based on power-domain NOMA for multi-user, multi-antenna ground nodes to a UAV. It derives closed-form expressions for Secrecy Connection Probability, Covert Connection Probability, Secrecy Outage Probability, and Detection Error Probability, enabling a weighted multi-objective optimization that jointly optimizes ground-beamformers and UAV trajectory via an SCA-BCD algorithm. The results reveal Pareto-like trade-offs between secret and covert rates and show how design parameters (antennas, power, path-loss, UAV motion) influence reliability and undetectability. The proposed framework provides a theoretical benchmark and practical insights for designing joint secret and covert UAV communications in complex multi-user settings, with potential extensions to imperfect CSI and MIMO configurations.

Abstract

Motivated by diverse secure requirements of multi-user in UAV systems, we propose a collaborative secret and covert transmission method for multi-antenna ground users to unmanned aerial vehicle (UAV) communications. Specifically, based on the power domain non-orthogonal multiple access (NOMA), two ground users with distinct security requirements, named Bob and Carlo, superimpose their signals and transmit the combined signal to the UAV named Alice. An adversary Willie attempts to simultaneously eavesdrop Bob's confidential message and detect whether Carlo is transmitting or not. We derive close-form expressions of the secrecy connection probability (SCP) and the covert connection probability (CCP) to evaluate the link reliability for wiretap and covert transmissions, respectively. Furthermore, we bound the secrecy outage probability (SOP) from Bob to Alice and the detection error probability (DEP) of Willie to evaluate the link security for wiretap and covert transmissions, respectively. To characterize the theoretical benchmark of the above model, we formulate a weighted multi-objective optimization problem to maximize the average of secret and covert transmission rates subject to constraints SOP, DEP, the beamformers of Bob and Carlo, and UAV trajectory parameters. To solve the optimization problem, we propose an iterative optimization algorithm using successive convex approximation and block coordinate descent (SCA-BCD) methods. Our results reveal the influence of design parameters of the system on the wiretap and covert rates, analytically and numerically. In summary, our study fills the gaps in joint secret and covert transmission for multi-user multi-antenna uplink UAV communications and provides insights to construct such systems.

Collaborative Secret and Covert Communications for Multi-User Multi-Antenna Uplink UAV Systems: Design and Optimization

TL;DR

This work tackles secure uplink UAV communications with diverse user security requirements by introducing a collaborative secret and covert transmission scheme based on power-domain NOMA for multi-user, multi-antenna ground nodes to a UAV. It derives closed-form expressions for Secrecy Connection Probability, Covert Connection Probability, Secrecy Outage Probability, and Detection Error Probability, enabling a weighted multi-objective optimization that jointly optimizes ground-beamformers and UAV trajectory via an SCA-BCD algorithm. The results reveal Pareto-like trade-offs between secret and covert rates and show how design parameters (antennas, power, path-loss, UAV motion) influence reliability and undetectability. The proposed framework provides a theoretical benchmark and practical insights for designing joint secret and covert UAV communications in complex multi-user settings, with potential extensions to imperfect CSI and MIMO configurations.

Abstract

Motivated by diverse secure requirements of multi-user in UAV systems, we propose a collaborative secret and covert transmission method for multi-antenna ground users to unmanned aerial vehicle (UAV) communications. Specifically, based on the power domain non-orthogonal multiple access (NOMA), two ground users with distinct security requirements, named Bob and Carlo, superimpose their signals and transmit the combined signal to the UAV named Alice. An adversary Willie attempts to simultaneously eavesdrop Bob's confidential message and detect whether Carlo is transmitting or not. We derive close-form expressions of the secrecy connection probability (SCP) and the covert connection probability (CCP) to evaluate the link reliability for wiretap and covert transmissions, respectively. Furthermore, we bound the secrecy outage probability (SOP) from Bob to Alice and the detection error probability (DEP) of Willie to evaluate the link security for wiretap and covert transmissions, respectively. To characterize the theoretical benchmark of the above model, we formulate a weighted multi-objective optimization problem to maximize the average of secret and covert transmission rates subject to constraints SOP, DEP, the beamformers of Bob and Carlo, and UAV trajectory parameters. To solve the optimization problem, we propose an iterative optimization algorithm using successive convex approximation and block coordinate descent (SCA-BCD) methods. Our results reveal the influence of design parameters of the system on the wiretap and covert rates, analytically and numerically. In summary, our study fills the gaps in joint secret and covert transmission for multi-user multi-antenna uplink UAV communications and provides insights to construct such systems.
Paper Structure (23 sections, 2 theorems, 61 equations, 13 figures, 2 algorithms)

This paper contains 23 sections, 2 theorems, 61 equations, 13 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Main Contributions
  4. Organization for the Rest of the Paper
  5. System Model and Transmission Scheme
  6. Channel Model
  7. Air to Ground Channel
  8. Ground Channel
  9. Transmission Scheme
  10. Optimization Problem Formulation
  11. Main Results
  12. Derivations of Optimization Constraints
  13. Secrecy Connection Probability
  14. Secret Outage Probability
  15. Covert Connection Probability
  16. ...and 8 more sections

Key Result

Lemma 1

For a Gaussian random vector $\mathbf{x}\sim \mathcal{CN}({\bf\mu},{\bf\Sigma})$ with the eigen-decomposition of its covariance matrix $\bf\Sigma={\bf\Psi}\Lambda {\bf\Psi}^H$. For a given $\bf\bar{Q}$, the cumulative distribution function (CDF) of ${{\mathbf{x}}^H}{\bf\bar{Q}}{\mathbf{x}}$ is given for some $\beta\ge0$ such that ${\bf I}+\beta {\bf Q}$ is positive definite, where ${\bf Q}={{\bf\L

Figures (13)

  • Figure 1: System model of collaborative secret and covert uplink transmission for a multi-user multi-antenna UAV system.
  • Figure 2: Numerical plots of Bob's SCPs versus Bob's target rate $R_\mathrm{t}$ at UAV's original position at sates $\mathrm{H}_0$ and $\mathrm{H}_1$ with different number of antennas for Bob, where $N_\mathrm{c}=2$, $Q_\mathrm{b}^\mathrm{max}=30$ dBm, $Q_\mathrm{c}^\mathrm{max}=0$ dBm, $\xi_\mathrm{ba}=\xi_\mathrm{ca}=-2$, $K_\mathrm{ba}=3$ dB, $K_\mathrm{ca}= 0$ dB, and $\sigma _\mathrm{a}^2=-90$ dBm.
  • Figure 3: Numerical plots of Bob's SOPs versus Bob's secret capacity redundancy at sates $\mathrm{H}_0$ and $\mathrm{H}_1$ with different number of antennas, where $N_\mathrm{c}=2$, $Q_\mathrm{b}^\mathrm{max}\!=\!30$ dBm, $Q_\mathrm{c}^\mathrm{max}\!=\!0$ dBm, $\xi_\mathrm{bw}\!=\!\xi_\mathrm{cw}\!=\!-3$, and $\sigma _\mathrm{w}^2\!=\!-90$ dBm.
  • Figure 4: Numerical plots of Carlo's CCPs versus Carlo's target rate $R_\mathrm{c}$ at UAV's original position with different number of antennas of Bob and Carlo, where $Q_\mathrm{b}^\mathrm{max}=30$ dBm, $Q_\mathrm{c}^\mathrm{max}= 0$ dBm, $\xi_\mathrm{ba}=\xi_\mathrm{ca}=-2$, $K_\mathrm{ba} =3$ dB, $K_\mathrm{ca}=0$ dB, and $\sigma _\mathrm{a}^2=-90$ dBm.
  • Figure 5: Numerical plots of Willie's DEP versus Willie's detection threshold for different block lengths, where $Q_\mathrm{b}^\mathrm{max}=30$ dBm, $Q_\mathrm{c}^\mathrm{max}=0$ dBm, $\xi_\mathrm{bw}=\xi_\mathrm{cw}=-3$, and $\sigma _\mathrm{w}^2=-90$ dBm.
  • ...and 8 more figures

Theorems & Definitions (5)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • proof