PaperlayerView exact revision on arXiv

Source-linked AI summary

Secrecy Sum-Rate Maximization in Finite Blocklength IRS-aided Systems With Perfect and Imperfect CSI

Monir Abughalwa, Nguyen Van Huynh, Diep N. Nguyen, Dinh Thai Hoang, Eryk Dutkiewicz

arXiv:2609.12481v1eess.SP

TL;DR

Short-packet secrecy couples reliability, leakage, and latency, complicating conventional long-blocklength optimization. The paper jointly optimizes beamforming and IRS reflections under finite-blocklength constraints and reports secure communication with imperfect or unavailable Eve CSI.

  • Problem

    Finite-blocklength secrecy couples decoding reliability, information leakage, and latency, creating nonconvex optimization challenges that differ from long-blocklength formulations.

    Source: §II · p. 4

  • Method

    The paper jointly optimizes beamforming vectors and IRS reflective elements for sum secrecy rate under finite-blocklength constraints, using linearization-based algorithms.

    Source: B. Contributions · p. 2

  • Results

    The authors report secure communication under FBR constraints with imperfect CSI, while the power-minimization algorithm maintains secrecy when Eve’s CSI is unavailable.

    Source: §VII · p. 14

  • Takeaways & Limitations

    When Eve’s CSI is unavailable, residual transmit power is used as artificial noise to further degrade Eve’s SINR.

    Source: §VII · p. 14

Abstract

from arXiv · show

The rapid growth of the Internet of Things (IoT) requires efficient and secure communication technologies to enable ultra-reliable low-latency (URLLC) communication applications. Intelligent reflecting surfaces (IRS) have emerged as a promising solution to enhance IoT network secrecy performance by improving signal quality for legitimate devices (Bob), while thwarting the eavesdropper (Eve) interception. However, ensuring secrecy across multiple users, given their diverse channels and locations, is challenging, especially under finite blocklength (FBR) constraints, which are common in IoT networks. This paper investigates the secrecy performance of IRS-aided URLLC systems under three channel state information (CSI) scenarios: perfect CSI, imperfect CSI, and unknown eavesdropper's CSI. We first formulate a non-convex optimization problem to maximize the system's sum secrecy rate (SSR) by jointly optimizing the transmitter's beamforming and the IRS's passive reflective elements, while maintaining FBR-related latency and transmission duration constraints. For imperfect CSI, the semi-infinite uncertainty constraints are transformed into finite linear matrix inequalities (LMIs) via a successive convex approximation (SCA)-based approach, and the proposed algorithm is proven to converge to a locally optimal solution with low computational complexity.

I. INTRODUCTION

The section motivates IRS-aided multi-user secrecy for IoT URLLC, where finite-blocklength constraints complicate existing approaches, and introduces joint optimization under multiple CSI conditions.

A. Related Works and Motivations

  • Most existing FBR-IRS secrecy studies focus on single-user systems, and assuming Eve’s CSI is available is impractical.These limits motivate considering multiple users and imperfect or unavailable eavesdropper CSI.Source: A. Related Works and Motivations · p. 2

B. Contributions

  • The proposed framework maximizes users’ sum secrecy rate by jointly optimizing beamforming and IRS elements subject to FBR latency and transmission-duration constraints.The IRS is designed to enhance users’ SINR while thwarting Eve’s SINR.Source: B. Contributions · p. 2
  • With available CSI, linearized approximations and direct optimization of IRS element arguments yield a computationally efficient algorithm proved locally optimal.The argument-based approach is presented as a lower-complexity alternative to conventional SDR and as scalable to large IRSs.Source: B. Contributions · p. 2
  • For imperfect CSI, SCA transforms semi-infinite uncertainty constraints into finite LMIs, with the proposed algorithm proved locally optimal and low-complexity.The closed-form linearization is described as supporting scalability to large IRS deployments.Source: B. Contributions · p. 2
  • When Eve’s CSI is unavailable, the design minimizes transmit power subject to user QoS and FBR constraints, then uses residual power as artificial noise.The artificial noise is intended to decrease Eve’s SINR.Source: B. Contributions · pp. 2–3
  • Simulations report secure communication for all users under FBR constraints even with imperfect CSI, and evaluate the impact of reflected-channel CSI imperfection.The results use practical settings, as described by the authors.Source: B. Contributions · p. 3

II. SYSTEM MODEL

  • The system has a blocked direct link, bounded uncertainty in reflected channels to users and Eve, and an FBR secrecy rate coupling reliability, leakage, and latency.The model considers perfect or imperfect CSI, and also the case where Eve’s CSI is unknown.Source: §II · pp. 3–4

III. SSR MAXIMIZATION UNDER PERFECT CSI IN FBR

Under perfect CSI, the paper formulates an FBR sum-secrecy-rate maximization problem and proposes tractable linearization to address its nonconvexity and the computational burden of alternating optimization.

III. SSR MAXIMIZATION UNDER PERFECT CSI IN FBR

  • Setting the CSI error to zero defines the perfect-CSI case addressed by the section.The paper defines imperfect CSI through nonzero channel-estimation error in the bounded uncertainty model.Source: §III · p. 5
  • The perfect-CSI problem maximizes sum secrecy rate under a transmit-power budget and IRS unit-modulus constraints, with FBR constraints embedded in the objective.The dispersion terms make the formulation nonconvex and more difficult than its long-blocklength counterpart.Source: §III · p. 5
  • The objective is nonconcave and the IRS unit-modulus constraint is nonconvex, motivating an alternating-optimization approach.That approach alternates between optimizing the beamforming vector with fixed IRS phases and optimizing IRS phases with fixed beamforming.Source: §III · p. 5
  • The proposed linearization uses tractable approximation functions to reduce the computational burden of alternating-optimization subproblems, especially for large IRSs.The paper positions this approach as computationally efficient for many passive reflective elements.Source: §III · p. 5

1) Sub-Problem for Optimizing the Beamforming Vectors:

The beamforming and IRS phase-shift subproblems are handled by constructing tractable approximations of the finite-blocklength secrecy rate. The resulting procedure converges to a locally optimal solution, and setting the dispersion factors to zero reduces the problem to the LBR case.

1) Sub-Problem for Optimizing the Beamforming Vectors:

  • The beamforming subproblem linearizes user and eavesdropper rates and dispersion factors, then forms a convex problem solvable with standard solvers.The surrogate FBR-SR function is substituted into the subproblem before solving for the beamforming vectors.Source: 1) Sub-Problem for Optimizing the… · pp. 5–6

2) Sub-Problem for Optimizing the PREs:

3) Complexity Analysis:

Algorithm 1 decouples beamforming-vector and IRS phase-shift optimization into two subproblems. Their computational complexities are O(M^3) and O(N^3), respectively.

3) Complexity Analysis:

  • Algorithm 1 decouples optimization into beamforming and IRS phase-shift subproblems, solved with a convex solver and a closed-form solution, respectively.The stated complexity estimates depend on the sizes of the optimization variables.Source: 3) Complexity Analysis · p. 7
  • O(M^3) is the computational complexity of obtaining the beamforming vectors for a given IRS phase vector.Source: 3) Complexity Analysis · p. 7
  • O(N^3) is the computational complexity of obtaining the IRS phase vector for given beamforming vectors.Source: 3) Complexity Analysis · p. 7

IV. SSR MAXIMIZATION UNDER IMPERFECT CSI WITH FBR SYSTEMS

Under imperfect CSI, FBR dispersion terms and semi-infinite uncertainty constraints make SSR maximization nonconvex and more restrictive than its LBR counterpart. The proposed approach uses convex surrogates and converges to a locally optimal solution satisfying secrecy and FBR requirements.

IV. SSR MAXIMIZATION UNDER IMPERFECT CSI WITH FBR SYSTEMS

  • Imperfect CSI and dispersion factors embedded in the FBR-SSR objective make the problem nonconvex and more challenging than its LBR counterpart.The dispersion terms also couple the beamforming vectors and IRS PREs, tightening the feasible region.Source: §IV · pp. 7–8
  • The proposed approximation method targets the computational burden of alternating optimization when IRSs have many PREs.The resulting algorithm is described as computationally efficient for large numbers of PREs.Source: §IV · p. 7
  • The AO-based algorithm maintains feasible iterations and converges to a locally optimal solution satisfying secrecy and FBR requirements.Each iteration uses a feasible convex surrogate, and the final solution satisfies the FBR feasible set.Source: §IV · p. 8
  • Slack variables decouple beamforming and IRS PREs, while SCA and the S-procedure convert semi-infinite constraints into finite LMIs and PCCP handles the unit-modulus constraint.Source: §IV · p. 8

1) Sub-Problem for Optimizing the Beamforming Vectors:

The imperfect-CSI beamforming subproblem is transformed into tractable LMIs through uncertainty handling and successive approximations. Additional matrix transformations and linearizations yield an SDP solvable with standard methods.

1) Sub-Problem for Optimizing the Beamforming Vectors:

  • The S-procedure transforms semi-infinite uncertainty constraints into LMIs, while a first-order Taylor approximation convexifies the remaining bilinear term.Slack variables and auxiliary interference-plus-noise functions are introduced in the reformulation.Source: 1) Sub-Problem for Optimizing the… · p. 8
  • Schur’s complement and Nemirovski’s Lemma recast additional constraints, while SCA linearizes another nonconvex term in the transformed problem.Source: 1) Sub-Problem for Optimizing the… · pp. 8–9
  • After the nonlinear constraints are linearized as LMIs, the resulting problem is an SDP that can be solved with standard solvers.The passage names the interior-point method and CVX toolbox as examples.Source: 1) Sub-Problem for Optimizing the… · p. 10

2) Sub-Problem for Optimizing the PREs:

The PRE subproblem uses PCCP to handle the IRS unit-modulus constraint, and the alternating-optimization algorithm is stated to converge to a locally optimal solution. The method also provides a feasible point for problem (P2.5).

2) Sub-Problem for Optimizing the PREs:

3) Complexity Analysis:

The complexity analysis describes the interior-point solution costs for the convex subproblems in terms of variable counts and LMI sizes. The algorithm alternates beamforming and IRS-phase updates until convergence.

3) Complexity Analysis:

  • The convex problems (P2.1) and (P2.2) are solved by the interior-point method, with complexity characterized using variable counts and LMI sizes.For (P2.1), the variable count is 2M; listed LMI sizes include MN+M+1 and 2M+1.Source: 3) Complexity Analysis · p. 10
  • The algorithm initializes beamforming, IRS phases, power bounds, and a convergence tolerance, then alternates updates until convergence.The listed update step solves (P2.2) for beamforming and uses PCCP for the IRS phases.Source: 3) Complexity Analysis · p. 11

V. DEALING WITH EVE’S UNKNOWN CSI

When Alice lacks Eve’s CSI, the formulation minimizes transmit power subject to a QoS constraint and uses remaining power as artificial noise. It considers an FBR setting rather than the LBR setting of the cited prior works.

V. DEALING WITH EVE’S UNKNOWN CSI

  • Without Eve’s CSI, the design minimizes transmit power while requiring the user’s QoS, γ_k ≥ γ_e.Remaining transmit power is used as artificial noise to further degrade Eve’s SINR.Source: §V · p. 11
  • The formulation differs from cited works, by considering finite blocklength rather than their long blocklength setting.The paper characterizes FBR by low latency and short transmission duration.Source: §V · p. 11
  • Artificial noise is projected into the user-channel null space, satisfying h_k(θ)V = 0.The projection matrix V is the null space of the user’s channel, and r is the artificial-noise vector.Source: §V · p. 11
  • Coupling between beamforming w and IRS phases θ in constraint (70b) makes problem (P3) nonconvex.Source: §V · p. 11

1) Sub-Problem for Optimizing the Beamforming Vectors:

The simulations show how secrecy-rate performance varies with antenna count, transmit power, CSI uncertainty, and transmission duration, while comparing finite- and long-blocklength regimes. For unknown Eve CSI, an alternating-optimization procedure updates beamforming and IRS phases and is proven locally optimal.

1) Sub-Problem for Optimizing the Beamforming Vectors:

  • For unknown CSI, alternating optimization iteratively updates the beamforming vector and IRS phases, with convex beamforming subproblems solved using CVX.The beamforming constraints are recast as LMIs.Source: 1) Sub-Problem for Optimizing the… · p. 11

2) Sub-Problem for Optimizing the PREs:

3) Complexity Analysis:

  • The algorithm’s complexity is similar to Algorithm 3 and is characterized through its linear constraints and LMIs.Source: 3) Complexity Analysis · p. 11

A. Parameter Setting

  • Simulations randomly place users in a 60 m × 60 m area and Eve outside it; CSI uncertainty and a 0.1 ms transmission duration are among the settings.If Eve is too close to a user, positive secrecy rates for all users may be impossible; encryption or friendly jamming can provide secrecy in that case.Source: A. Parameter Setting · pp. 11–12

B. Performance Evaluation

  • The FBR SSR algorithm converges in fewer iterations than the perfect-CSI SSR method, while the power-minimization algorithm converges monotonically and requires more power under FBR.The FBR SSR algorithm uses the LBR local optimum as its initial feasible point; dispersion factors add secrecy constraints in FBR.Source: Figure 2 · p. 12, B. Performance Evaluation · pp. 12–13, Figure 7 · p. 13
  • The arithmetic mean increases with transmission power and decreases with CSI uncertainty, yet the algorithms retain system secrecy under high uncertainty.Source: B. Performance Evaluation · p. 13
  • The secrecy-rate arithmetic mean rises with antenna count and transmission duration, while the LBR secrecy rate upper-bounds its FBR counterpart.The LBR comparison assumes transmission duration T = ∞.Source: B. Performance Evaluation · pp. 12–13
  • The LBR secrecy-rate CDF lies consistently to the right of the FBR CDF; under FBR, power is concentrated on users with favorable channels.Source: B. Performance Evaluation · p. 14

VII. CONCLUSIONS

The paper develops IRS-aided secure communication methods for IoT URLLC under finite blocklength constraints and multiple CSI conditions. Simulations show secrecy is maintained with imperfect CSI, while power minimization supports secrecy when Eve’s CSI is unknown.

VII. CONCLUSIONS

  • The framework maximizes sum secrecy rate under FBR constraints with perfect or imperfect user CSI and perfect, imperfect, or unknown Eve CSI.When Eve’s CSI is unknown, the framework instead uses power minimization.Source: §VII · p. 14
  • The FBR-SR model accounts for decoding error probability and information leakage when ensuring confidentiality.Beamforming vectors and IRS reflective coefficients are jointly optimized to minimize Eve’s ability to decode while satisfying user QoS constraints.Source: §VII · p. 14
  • When Eve is too close to a legitimate user, secrecy for all users may be infeasible, and cryptography-based or friendly-jamming countermeasures may be needed.The paper identifies multi-IRS optimization and spatially correlated channel evaluation as future work.Source: §VII · p. 14

APPENDIX A PROOF OF THEOREM 1

The appendices justify the SCA surrogate and local-optimality claims for the optimization algorithms, and provide an inequality used in a lemma. They establish nondecreasing objective sequences and KKT conditions for the relevant problems.

APPENDIX A PROOF OF THEOREM 1

  • First-order Taylor expansions of the smooth functions yield a bounded linearization error for the dispersion term, supporting the SCA surrogate.The functions are stated to have Lipschitz-continuous gradients.Source: Appendix A · p. 14
  • The algorithm’s alternating beamforming and IRS-phase updates produce a nondecreasing objective sequence that converges to a point satisfying the KKT conditions of (P1).The proof also verifies that the surrogate in (21) satisfies the stated SCA conditions.Source: Appendix A · pp. 14–15

APPENDIX B PROOF OF LEMMA 1

  • For scalar complex q, with a(i) the fixed point obtained at iteration (i), substituting q with (u_k Φ_GAR)w_k yields (41), concluding the proof.The inequality is stated to hold for q, with citation.Source: Appendix B · p. 15

APPENDIX C PROOF OF THEOREM 2

  • For Theorem 2, the objective sequence is nondecreasing and the converged point is locally optimal for the stated problems.The proof describes this result as analogous to Theorem 1.Source: Appendix C · p. 15

APPENDIX D INEQUALITIES

  • Appendix D assembles inequalities from cited results and properties of concave logarithmic and square-root functions.It also states an inequality for vectors and positive scalar parameters.Source: Appendix D · p. 15
Loading 2609.12481v1…