PaperlayerView exact revision on arXiv

Source-linked AI summary

Flexible-Duplex Cell-Free Architecture for Secure Uplink Communications in Low-Altitude Wireless Networks

Wei Shi, Wei Xu, Yongming Huang, Jiacheng Yao, Wenhao Hu, Dongming Wang

arXiv:2601.04011v1cs.ITeess.SPmath.IT

TL;DR

UAV uplinks in low-altitude networks are vulnerable to interception, while secure cell-free research has given limited attention to the distinctive low-altitude setting. The paper uses flexible-duplex APs for reception or cooperative jamming and reports higher secrecy performance than fixed-role cell-free baselines, with a lower-complexity scheme retaining over 90% of joint optimization performance.

  • Problem

    Low-altitude UAV links face interception risks, and systematic investigation of secure cell-free strategies tailored to their line-of-sight-dominant, dynamic setting remains limited.

    Source: §I · pp. 1–2

  • Method

    The paper assigns cell-free APs dynamically to receive UAV uplinks or transmit artificial noise, and develops joint and sequential optimization schemes.

    Source: §I · pp. 2–3

  • Results

    The joint optimization achieves the highest secrecy rate, while the low-complexity heuristic maintains over 90% of its performance as UAV transmit power increases from 10 to 30 dBm.

    Source: §V · p. 12

  • Takeaways & Limitations

    Simulations report substantial secrecy-rate gains over fixed-role cell-free baselines and describe the low-complexity scheme as an effective performance–complexity tradeoff for large-scale deployments.

    Source: §I · p. 3, §VI · p. 13

Abstract

from arXiv · show

Low-altitude wireless networks (LAWNs) are expected to play a central role in future 6G infrastructures, yet uplink transmissions of uncrewed aerial vehicles (UAVs) remain vulnerable to eavesdropping due to their limited transmit power, constrained antenna resources, and highly exposed air-ground propagation conditions. To address this fundamental bottleneck, we propose a flexible-duplex cell-free (CF) architecture in which each distributed access point (AP) can dynamically operate either as a receive AP for UAV uplink collection or as a transmit AP that generates cooperative artificial noise (AN) for secrecy enhancement. Such AP-level duplex flexibility introduces an additional spatial degree of freedom that enables distributed and adaptive protection against wiretapping in LAWNs. Building upon this architecture, we formulate a max-min secrecy-rate problem that jointly optimizes AP mode selection, receive combining, and AN covariance design. This tightly coupled and nonconvex optimization is tackled by first deriving the optimal receive combiners in closed form, followed by developing a penalty dual decomposition (PDD) algorithm with guaranteed convergence to a stationary solution. To further reduce computational burden, we propose a low-complexity sequential scheme that determines AP modes via a heuristic metric and then updates the AN covariance matrices through closed-form iterations embedded in the PDD framework. Simulation results show that the proposed flexible-duplex architecture yields substantial secrecy-rate gains over CF systems with fixed AP roles. The joint optimization method attains the highest secrecy performance, while the low-complexity approach achieves over 90% of the optimal performance with an order-of-magnitude lower computational complexity, offering a practical solution for secure uplink communications in LAWNs.

I. Introduction

The introduction motivates secure UAV uplinks in LAWNs and proposes flexible-duplex cell-free APs that receive UAV data or transmit artificial noise. The system model describes these AP roles and the uplink signal components used for centralized processing.

I. Introduction

  • Prior secure cell-free work largely focused on terrestrial users, while systematic study of low-altitude UAV networks and cooperative AP protection remains limited.The introduction cites UAV links’ strong line-of-sight propagation, limited onboard resources, and high mobility as distinct vulnerabilities.Source: §I · p. 2
  • Flexible-duplex APs receive UAV uplinks or transmit artificial noise, adding a spatial degree of freedom for distributed secrecy enhancement.The paper formulates joint AP-mode, receive-combiner, and AN-covariance optimization, alongside a lower-complexity sequential scheme.Source: §I · pp. 2–3

II. System Model

  • Each AP operates in receive mode to collect UAV uplinks or transmit mode to emit artificial noise against the eavesdropper.Distributed APs connect to a CPU for joint signal processing and coordination.Source: §II · p. 3

A. Uplink Signal and SINR Model

  • The uplink model includes UAV data signals, channels from transmit APs to receive APs, and additive white Gaussian noise in the signals forwarded to the CPU.The model also defines AN covariance matrices that determine spatial structure and power allocation.Source: A. Uplink Signal and SINR Model · pp. 3–4

B. Eavesdropper Signal and SINR Model

The paper models an eavesdropper’s reception and defines UAV secrecy rates from legitimate and eavesdropping rates. It then formulates an optimization that maximizes the minimum secrecy rate across UAVs.

B. Eavesdropper Signal and SINR Model

  • Eve is modeled with multiple antennas and a linear combiner for detecting each UAV’s transmission.The model specifies channels from UAVs and APs to Eve, as well as Eve’s receiver noise.Source: B. Eavesdropper Signal and SINR Model · p. 4

C. Achievable Rate and Secrecy Rate

  • UAV secrecy rate is based on the difference between its achievable CPU rate and Eve’s eavesdropping rate, clipped below at zero.The paper motivates instantaneous secrecy rates for fast time-varying channels and dynamic network topologies.Source: C. Achievable Rate and Secrecy Rate · p. 4

D. Optimization Problem Formulation

  • The optimization maximizes the minimum secrecy rate among UAVs by jointly coordinating AP reception and jamming modes.The formulation enforces mutually exclusive AP modes and limits each AP’s artificial-noise power.Source: D. Optimization Problem Formulation · p. 4

III. Proposed Joint Optimization Algorithm

The section reduces the joint design by deriving optimal receive combiners in closed form, then applies PDD to optimize AP modes and AN covariance matrices. The PDD formulation uses auxiliary variables to decouple coupled constraints and enable alternating optimization.

A. Closed-Form Solutions to Receive Combining

  • Closed-form optimal receive combiners simplify the original problem before AP mode selection and AN covariance optimization.For fixed AP modes and AN, each combiner maximizes its UAV's uplink SINR without affecting other UAVs or eavesdropping performance.Source: §III · p. 4, A. Closed-Form Solutions to Receive… · p. 5

B. PDD Framework for AP Mode and AN Optimization

  • The joint design is reformulated with slack variables to handle complicated fractional terms and constraints linking the AP modes and AN design.The resulting augmented Lagrangian problem is the basis for the subsequent iterative solution.Source: B. PDD Framework for AP Mode and AN… · pp. 5–6
  • PDD addresses the challenging equality constraint by introducing auxiliary variables, decoupling variables to facilitate alternating optimization.The section then optimizes AP modes and AN covariance matrices within this framework.Source: B. PDD Framework for AP Mode and AN… · p. 5

C. BCD Method for Solving Problem (17)

The method solves problem (17) with block coordinate descent in inner iterations and dual-variable and penalty updates in outer iterations. Successive convex approximation handles remaining nonconvex constraints, and the iterative procedure converges to a KKT point of problem (19).

C. BCD Method for Solving Problem (17)

  • The BCD inner iterations update three variable blocks, while outer iterations update the dual variables and penalty parameter.The method alternates between these inner and outer updates.Source: C. BCD Method for Solving Problem (17) · p. 6
  • SCA approximates the remaining nonconvex constraints C1 and C4 with convex surrogates for the next iteration.The approximation parameter ϖ controls accuracy, with smaller values yielding higher accuracy.Source: 1) Updating {yC m} · p. 6
  • The iterative procedure is guaranteed to converge to a KKT point of problem (19).After solving (22), the method updates V_m^(t) and χ^(t) using the obtained optimal solutions before proceeding to the next iteration.Source: 1) Updating {yC m} · p. 6

2) Updating Bk:

The B_k update uses an MM-based method because the objective's fourth-order term prevents directly characterizing convexity or concavity. The iterations construct convex surrogate problems and converge to a stationary point of problem (25).

2) Updating Bk:

  • The B_k subproblem is convex, and its optimal solution can be derived directly.The section then addresses nonconvexity in constraint C3 with a lower bound and MM-based processing of the mode variables.Source: 2) Updating Bk · p. 6, 3) Updating  · pp. 6–7
  • The fourth-order objective term involving x_m^C motivates simplification and an MM upper bound because its matrix term's definiteness is undetermined.The resulting convex surrogate is iterated until convergence.Source: 3) Updating  · pp. 6–7
  • The iterative process converges to a stationary point of problem (25).The PDD method's dominant computational burden arises from updating B_k and V_m, with the stated complexity on the order of O(LK^3.5M^6.5N^6.5a).Source: 3) Updating  · p. 7

IV. Low-Complexity Algorithm

The low-complexity scheme first selects AP modes heuristically, then optimizes AN covariance through closed-form iterative updates within PDD. Its sequential heuristic evaluates candidate receive APs against only the still-unassigned APs that may transmit AN.

IV. Low-Complexity Algorithm

  • The low-complexity algorithm selects AP modes with a heuristic rule before applying a closed-form iterative procedure to optimize AN.The remaining nonconvex AN optimization is handled using the PDD framework.Source: §IV · p. 7

A. Heuristic AP Mode Selection

  • When selecting the n-th R-AP, the heuristic considers only unassigned APs as potential T-APs.This evaluates interference vulnerability against the APs that may actually transmit AN at that stage, avoiding interference overestimation and yielding more adaptive mode decisions.Source: A. Heuristic AP Mode Selection · p. 8

1) Metric Definitions:

The section defines reception and jamming metrics for assessing candidate AP roles, combines them in a sequential priority score, and uses that score to assign AP modes.

1) Metric Definitions:

  • Reception gain measures aggregated UAV signal strength, while the other metrics assess AN interference at candidate and selected R-APs and an AP’s ability to jam Eve.The jamming-gain metric is larger for APs better suited to T-AP operation.Source: 1) Metric Definitions · p. 8

2) Sequential Priority Score:

  • The priority score favors strong reception and low AN susceptibility, while penalizing APs with high jamming potential or strong leakage to selected R-APs.The parameter β adjusts preference for preserving strong jammers as T-APs, and ϵ > 0 ensures numerical stability.Source: 2) Sequential Priority Score · p. 8

3) Greedy Assignment Procedure:

  • The greedy procedure selects the required number of R-APs iteratively, then assigns the remaining APs to T-AP operation.The resulting assignment reflects the asymmetric reception and jamming roles and initializes subsequent AN covariance optimization.Source: 3) Greedy Assignment Procedure · p. 8

B. AN Optimization with Fixed AP Allocation

With AP roles fixed, the section updates effective channels and optimizes AN covariance matrices using reformulations and PDD-based variable decomposition.

B. AN Optimization with Fixed AP Allocation

  • For fixed AP allocation, the AN optimization remains highly nonconvex, so the method continues using PDD for variable decoupling and problem decomposition.The effective channel vector removes the zero component corresponding to an AP operating in jamming mode.Source: B. AN Optimization with Fixed AP… · pp. 8–9
  • The reformulation introduces τk and χk to decompose fractional terms, Qk to substitute for a matrix inverse, and eVm and uk as auxiliary replicas.These replicas facilitate closed-form solutions for corresponding subproblems, with BCD updating variables in inner iterations.Source: B. AN Optimization with Fixed AP… · p. 9
  • The Qk subproblem is unconstrained and convex; vectorization reformulates its objective, from which the optimal solution is derived.The effective inter-AP channel matrix is also updated before rewriting the AN optimization problem.Source: 1) Updating Qk: The subproblem… · p. 9, B. AN Optimization with Fixed AP… · p. 9

2) Updating Vm:

The section derives optimal updates for Vm and its auxiliary variable eVm through reformulated subproblems, including a convex update characterized by singular values and eigenvalues.

2) Updating Vm:

  • Reformulations using vectorized Vm and Υm,k yield the optimal solution to the Vm subproblem.The preceding Vm subproblem is formulated before these transformations.Source: 2) Updating Vm · pp. 9–10
  • The eVm subproblem is convex, and Proposition 2 gives its optimal solution using a singular matrix and an optimal eigenvalue.The passage identifies ym,n as an eigenvalue used in that solution.Source: 2) Updating Vm · p. 10

4) Updating {τk,

The section gives update procedures for the sequential optimization and reports simulation comparisons across AN power, AP count, UAV transmit power, receiver assumptions, and UAV fairness. The PDD-based joint method leads in secrecy performance, while the low-complexity method retains strong performance and improves balance across UAVs.

4) Updating {τk,

  • The τ_k update is reduced to a convex problem whose KKT-based solution uses a bisection search and enumeration of candidate indices.For χ_k, the single-variable problem is solved with Newton’s method.Source: 4) Updating {τk · p. 10

V. Numerical Results

  • Across the AN-power range, joint optimization achieves the highest secrecy rate, while the sequential scheme closely follows and both outperform the baselines.A fixed AP split can cause AN leakage and harm secrecy when mode selection is not jointly optimized.Source: Figure 3 · p. 11, §V · pp. 11–12
  • As AP count rises, secrecy rates increase for all schemes, and the proposed schemes’ gain over Baseline 2 grows from less than 2 bps/Hz at M = 4 to nearly 3 bps/Hz at M = 8.The passage attributes the trend to greater reception diversity and more APs available for AN transmission.Source: Figure 4 · p. 11, §V · p. 12
  • With higher UAV transmit power, all schemes improve; PDD achieves the highest secrecy rate and the low-complexity heuristic retains over 90% of its performance.The performance gap over baselines widens as transmit power increases.Source: Figure 5 · p. 12, §V · p. 12
  • Under receiver mismatch, the ZF Eve case achieves a higher secrecy rate than the matched MMSE case, and the proposed AN design continues suppressing Eve’s reception.The text attributes the difference partly to ZF’s susceptibility to noise amplification and recommends assuming MMSE for worst-case secrecy optimization.Source: Figure 6 · p. 12, §V · p. 12
  • The PDD method significantly improves secrecy rates for all UAVs, while the low-complexity scheme yields a narrower best-to-worst UAV gap.The max-min secrecy-rate criterion is associated with a more balanced distribution across UAVs.Source: Figure 7 · p. 12, §V · pp. 12–13

VI. Conclusion

The paper proposes flexible-duplex cell-free architecture for secure UAV uplinks and develops joint and sequential optimization strategies. Simulations show improved secrecy rates over baselines, with the sequential scheme offering a performance–complexity tradeoff.

  • Flexible-duplex cell-free architecture lets each access point operate in reception or jamming mode for secure uplink communications.Source: §VI · p. 13
  • The joint strategy uses closed-form combiners and a PDD-based algorithm, while a sequential low-complexity scheme targets scalability.Source: §VI · p. 13
  • Simulations show significantly improved secrecy rates over baselines, while the low-complexity scheme offers a performance–complexity tradeoff for large-scale deployments.Source: §VI · p. 13
Loading 2601.04011v1…