Resource Allocation for Secure URLLC in Mission-Critical IoT Scenario

Motivation

• URLLC's stringent reliability and latency targets conflict: longer redundant codewords aid reliability but increase latency, while shorter packets reduce reliability.The introduction gives illustrative targets of 1 −10−9 reliability and 1 ms latency.Source: §I · p. 2

Finite-blocklength URLLC

• Short-blocklength decoding errors remain nonzero, so Shannon-capacity design can underestimate reliability and latency and fail to guarantee QoS.The paper notes that Shannon capacity relies on assumptions unsuitable for short-packet transmission.Source: §I · p. 2

Security motivation

• Wireless IoT secrecy is vulnerable to eavesdropping, while upper-layer key exchange needs additional channel uses that are problematic under URLLC's limited blocklength.The paper motivates physical-layer security as avoiding the complicated key-exchange procedure.Source: §I · p. 3

Research gap

• The paper studies resource allocation for secure mission-critical IoT using finite-blocklength secrecy capacity, addressing a gap left by prior work on secrecy rates and system performance.Prior work had analyzed secure short-packet communications, but resource allocation based on the finite-blocklength result had not been studied.Source: §I · p. 3

Weighted sum throughput maximization

• For weighted sum throughput, the method jointly allocates bandwidth units and power under total-power and bandwidth constraints, using BCD, SCA, and greedy discretization.The problem is described as non-convex mixed-integer; the paper also provides convergence and complexity analyses.Source: §I · pp. 3–4

Total transmit-power minimization

• For total transmit-power minimization, the method relaxes blocklength allocation to continuous variables and uses a sufficient convexity condition followed by greedy discretization.The paper states that typical URLLC scenarios satisfy the condition.Source: §I · p. 4

A. System model

• A downlink access point sends confidential control signals to single-antenna IoT devices while an eavesdropper attempts to intercept them.The devices include examples such as actuators, robots, and automated guided vehicles.Source: A. System model · pp. 4–5
• Devices transmit simultaneously over orthogonal frequency bands, with bandwidth allocated in basic units and total allocation bounded by the channel coherence bandwidth.The paper assumes the coherence bandwidth is divisible by the basic bandwidth unit.Source: A. System model · p. 5
• Each device's channel uses equal its allocated bandwidth times transmission duration, and the short transmission duration makes the channels constant during a transmission.The model specifies channels from the access point to each device and to the eavesdropper.Source: A. System model · p. 5

B. Achievable Secrecy Data Rate Under Finite Blocklength

• Short-blocklength transmission has non-zero decoding error probability and non-negligible information leakage.The paper adopts this regime to support low latency.Source: B. Achievable Secrecy Data Rate Under… · p. 6
• For a given blocklength, decoding-error bound, and leakage constraint, the paper approximates a lower bound on the maximum secrecy communication rate.The constraints are denoted by ε_k and δ_k, respectively, and the blocklength is N_k = B_kT.Source: B. Achievable Secrecy Data Rate Under… · p. 6
• The rate formulation distinguishes finite-blocklength secrecy capacity from its infinite-blocklength maximum and includes channel dispersion and the inverse Q-function.The passage defines dispersion as characterizing channel variability relative to a deterministic channel with the same capacity.Source: B. Achievable Secrecy Data Rate Under… · p. 6
• The subsequent problems jointly allocate power and bandwidth units to maximize weighted sum throughput or minimize total transmit power.The objectives are presented as the goals of the two optimization sections.Source: B. Achievable Secrecy Data Rate Under… · pp. 6–7

A. Problem Formulation

• The formulation maximizes weighted sum throughput while enforcing total power, total bandwidth, and integer bandwidth-allocation constraints.The positive device weights are used to ensure fairness among devices.Source: A. Problem Formulation · p. 7
• Because power and blocklength are coupled, BCD alternately optimizes each variable block while fixing the other.The two subproblems optimize power for given blocklength and blocklength for given power.Source: A. Problem Formulation · p. 8

B. The Solution of (P2-1)

• For fixed blocklength, the power-allocation objective is non-convex but has a difference-of-concave structure, so SCA replaces it iteratively with a convex subproblem.The paper establishes concavity of f_k(p_k) and y_k(p_k), whose difference forms R_k(p_k).Source: B. The Solution of (P2-1) · pp. 8–9

C. The Solution of (P2-2)

• The rate R_k(n_k) is represented as a difference of two concave functions, enabling SCA to form convex subproblems for blocklength allocation.The subproblem's objective is concave and its constraints are affine.Source: C. The Solution of (P2-2) · pp. 10–11
• Lagrangian dual decomposition turns each convex blocklength subproblem into K independent device-level optimization problems for a given dual variable.The paper states the duality gap is zero under the stated convexity and Slater-condition assumptions.Source: C. The Solution of (P2-2) · pp. 11–12
• Bisection finds device blocklength allocations for a given dual variable, and the monotone-decreasing total allocation supports bisection to find that variable.The paper establishes that W(µ) decreases monotonically with µ.Source: C. The Solution of (P2-2) · p. 12

1) Algorithm Description:

• BCD uses an outer iteration over power and bandwidth allocation, with inner SCA iterations solving each subproblem.The SCA inner layer solves the power and channel-blocklength subproblems in turn.Source: 1) Algorithm Description · p. 13

2) Convergence Analysis:

• BCD's throughput values increase monotonically and are bounded above by the power and bandwidth limits, so the algorithm is guaranteed to converge.The SCA algorithm is also stated to converge.Source: 2) Convergence Analysis · p. 13

3) Complexity Analysis:

• The paper gives polynomial-time complexity for BCD to reach a locally optimal solution.Its total complexity is expressed in terms of the BCD and inner SCA iteration counts and the number of devices.Source: 3) Complexity Analysis · p. 14

E. Integer Conversion for n

• Because integer conversion is combinatorial and globally optimal search requires exponential time, the paper uses greedy search to produce a suboptimal allocation.The greedy method assigns each remaining bandwidth unit to the device with the greatest throughput increment, then updates power allocation.Source: E. Integer Conversion for n · p. 14

A. Problem Formulation

• The objective is to minimize total transmit power while meeting each device's minimum throughput and the total bandwidth budget; feasibility is assumed.The integer bandwidth constraint makes the problem mixed-integer and NP-hard.Source: A. Problem Formulation · p. 15

B. Approximation Method

• The method relaxes integer channel blocklengths to continuous values and uses a power function of blocklength to form a convex approximation under a sufficient condition.The paper states that, for typical URLLC parameters, the condition holds when N_k ≤ 572, making p_k(N_k) convex.Source: B. Approximation Method · pp. 16–17
• After solving the continuous problem with Lagrangian dual decomposition, greedy search assigns remaining channel uses to the device with the largest power decrement.The paper notes the discrete conversion is combinatorial and NP-hard; its greedy method converts the continuous solution to discrete values.Source: B. Approximation Method · pp. 17–18

• The simulations evaluate the performance of the proposed algorithms.Source: §V · p. 18
• The figures show BCD convergence and WST versus the total power limit.Source: Figure 2 · p. 19, Figure 3 · p. 19
• The channel-unit bandwidth is 1 KHz, noise power spectral density is -173 dBm/Hz, and channel coherence bandwidth is 0.5 MHz.Source: §V · p. 19
• Default settings include K=4 devices, εk=10^-9, δk=10^-2, and a 1 ms transmission duration.Source: §V · p. 19

A. Weighted Sum Throughput Maximization

• Roughly ten iterations suffice for BCD convergence, although larger device counts slow convergence.Source: A. Weighted Sum Throughput Maximization · p. 19
• BCD outperforms conventional long-packet transmission, with the performance gap increasing as the transmit-power limit rises.WST increases with available transmit power; the paper attributes the widening gap to short-packet penalty terms omitted by the conventional scheme.Source: A. Weighted Sum Throughput Maximization · p. 20
• A lower decoding-error probability requirement brings lower WST in the reported comparison.The passage attributes this to larger penalty terms when δk is large.Source: A. Weighted Sum Throughput Maximization · p. 20
• WST increases with channel coherence bandwidth, approximately linearly, and BCD performs better than conventional long-packet transmission.The paper links higher coherence bandwidth to more channel uses per transmission.Source: A. Weighted Sum Throughput Maximization · p. 20, Figure 4 · p. 20
• The simulations also plot total transmit power against minimum packet size and devices' decoding-error probability requirements.Source: Figure 6 · p. 21, Figure 7 · p. 21
• BCD's WST increases with device count, while the conventional long-packet scheme first increases and then decreases.The paper attributes BCD's trend to multiuser diversity and notes that the conventional scheme does not account for short-packet penalties.Source: Figure 5 · p. 20, A. Weighted Sum Throughput Maximization · p. 21
• The conventional scheme optimizes throughput without short-packet penalty terms, so its solution may not perform well under the short-packet throughput formula.The paper forms this benchmark by setting parameters in the BCD algorithm to zero.Source: A. Weighted Sum Throughput Maximization · pp. 19–21

B. Total Transmit Power Minimization

• The proposed algorithms save power over Equal BU Allocation; for D ≥160 bits, that method is infeasible while the proposed algorithm supports packet sizes up to 200 bits.Continuous Relaxation and Integer Conversion have almost the same performance, indicating marginal loss from greedy integer conversion.Source: B. Total Transmit Power Minimization · p. 22
• Required TTP decreases as the decoding error probability requirement ϵk increases; the proposed algorithms outperform Equal BU Allocation especially when ϵk is extremely small.The paper explains that smaller ϵk requires more power to meet the target data amount.Source: B. Total Transmit Power Minimization · p. 22
• As channel coherence bandwidth increases, TTP decreases; at sufficiently large bandwidth, the proposed algorithms offer negligible advantage over Equal BU Allocation, which is nearly optimal.The paper attributes the decrease to more channel users fitting as coherence bandwidth grows, enhancing throughput.Source: B. Total Transmit Power Minimization · pp. 22–23, Figure 8 · p. 22
• Sum power increases rapidly with device count because fewer bandwidth units per device require more power to transmit the targeted data amount.The evaluation assumes channel coherence bandwidth Wc = 1 MHz.Source: Figure 9 · p. 22, B. Total Transmit Power Minimization · p. 23

VI. CONCLUSIONS

• The paper jointly optimizes bandwidth-unit allocation and power for TTP minimization, deriving a sufficient convexity condition that most typical URLLC applications satisfy.It proposes low-complexity, efficient algorithms to find globally optimal solutions.Source: §VI · p. 23
• The WST problem jointly allocates bandwidth units and power subject to total-power and bandwidth constraints.For WST, the BCD algorithm decouples the coupled optimization problem and solves it iteratively; simulation results report rapid convergence and advantages over conventional long-packet transmission.Source: §VI · p. 23

APPENDIX A PROOF LEMMA 1

• Rk(pk) is expressed as the difference of the concave functions fk(pk) and yk(pk), completing the proof of Lemma 1.The appendix establishes concavity of each component with respect to pk.Source: Appendix A · pp. 23–24

APPENDIX B PROOF THEOREM 1

• Theorem 1’s power solution follows from KKT conditions; when the stated threshold condition holds, pk must be zero.The proof reduces the optimal power to the solution given in Theorem 1.Source: Appendix B · pp. 24–25

APPENDIX C PROOF OF LEMMA 2

• Rk(nk) is the difference of the concave functions Fk(nk) and Gk(nk), completing the proof of Lemma 2.The appendix establishes that both component functions are concave with respect to nk.Source: Appendix C · pp. 25–26

APPENDIX D PROOF OF LEMMA 3

• The Lemma 3 proof compares the optimal bandwidth allocations for two dual-variable values and sums the resulting inequalities across devices.The supplied passage does not state the resulting inequality explicitly.Source: Appendix D · p. 26

APPENDIX E PROOF OF THEOREM 2

• Under inequality (35), pk(Nk) is convex and monotonically decreasing with Nk.The appendix establishes convexity and then derives the monotonicity result under the same condition.Source: Appendix E · pp. 27–28