Artificial Noise Aided Secrecy Information and Power Transfer in OFDMA Systems

• OFDMA provides flexible resource allocation, while SWIPT lets users harvest energy and decode information from the same received signal.Source: §I · p. 1
• Prior secure SWIPT studies – leave AN-aided OFDMA-based SWIPT with secrecy constraints uninvestigated.Energy receivers can eavesdrop on information receivers, and artificial noise can also supply energy.Source: §I · pp. 1–2
• The proposed method adds independent artificial noise on each subcarrier, canceled by the assigned information receiver using a key before decoding.The optimization maximizes weighted sum secrecy rate for information receivers subject to minimum harvested-power requirements for energy receivers.Source: §I · p. 2
• The problem is mixed-integer and non-convex; a Lagrange-duality algorithm is asymptotically optimal as the number of subcarriers grows, alongside a lower-complexity suboptimal algorithm.The algorithms address the weighted secrecy-rate objective under individual energy-harvesting constraints.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

• The BS selects secret AN sequences per allocated subcarrier; the intended IR knows the sequence and can cancel AN, while other receivers do not.The paper describes securely refreshing and transmitting the sequence keys to intended IRs.Source: §II · pp. 2–3
• In the considered SISO system, traditional AN without cancellation at intended IRs cannot achieve a higher secrecy rate than transmission without AN.The paper refers to this as the traditional AN scheme without AN cancellation.Source: §II · p. 3
• ERs harvest energy from both the information signal and AN, while AN does not interfere with the intended IR but does interfere with other receivers.The system assumes separate IRs and ERs, and treats every other receiver as a potential eavesdropper.Source: §II · pp. 2–3
• The objective jointly optimizes transmit power, subcarrier allocation, and AN power splitting to maximize weighted IR secrecy rate subject to each ER’s harvested-power constraint.Each subcarrier is assigned to at most one IR, while ERs can harvest energy from all subcarriers.Source: §II · pp. 3–4

III. OPTIMAL SOLUTION

• As the number of subcarriers grows, the zero duality gap under the time-sharing condition makes the Lagrange-duality solution asymptotically optimal for the mixed-integer, NP-hard, non-convex problem.The method forms a Lagrangian with dual variables for ER harvested-power constraints and the total transmit-power constraint, then decomposes its maximization into independent subcarrier subproblems.Source: §III · p. 4

A. Joint Optimization of Power Allocation and Transmit Power Splitting Ratio

• The algorithm chooses the feasible power and AN-splitting candidate that maximizes the subcarrier Lagrangian.It evaluates candidates across the feasible regions after deriving an optimal splitting ratio for fixed power.Source: 1) Region I (pk,n > [Xk,n(αk,n)]+) · pp. 5–6
• When the intended channel is weaker than the strongest eavesdropper channel, the low-power region has zero secrecy rate; its feasibility and the other region depend on channel gains and peak power.The paper divides the search into regions and subregions, with feasible candidates determined by channel conditions and the peak-power limit.Source: 1) Region I (pk,n > [Xk,n(αk,n)]+) · pp. 5–6
• The five illustrated cases distinguish which regions or subregions are feasible under different channel-gain orderings and peak-power thresholds.For equal channel gains, the paper states that only subregion i in Region I is feasible.Source: 1) Region I (pk,n > [Xk,n(αk,n)]+) · p. 5, Figure 4 · p. 6

B. Subcarrier Allocation

• The allocation indicator is set to one when the associated value is positive and zero otherwise.This rule is applied after substituting the optimized power and AN-splitting ratio.Source: B. Subcarrier Allocation · p. 6

C. Dual Update

• The dual problem is convex, allowing the subgradient method to update its variables iteratively.Source: C. Dual Update · pp. 6–7
• Algorithm 2 performs subcarrier allocation, updates λ and γ, and repeats until both dual variables converge.Source: C. Dual Update · p. 7
• The update uses iteration index t and positive step sizes ξ1,...,ξK2 and ν.Source: C. Dual Update · p. 7
• The authors state that the proposed algorithm's convergence and optimality are guaranteed by its direct application of the subgradient method.Source: C. Dual Update · p. 7

D. Complexity

• O(KN) computations are needed per iteration because optimization is independent across subcarriers.Each subcarrier requires O(K2) computations to solve Ωn and O(K1) to search for the best IR.Source: D. Complexity · p. 7
• The subgradient-based dual updates have complexity polynomial in the number of dual variables, K2 + 1.Source: D. Complexity · p. 7
• The overall complexity is O((K2 + 1)^qKN), where q is a positive constant, and is polynomial.Source: D. Complexity · p. 7

IV. SUBOPTIMAL SOLUTION

• The optimal algorithm's complexity rises with K1, K2, and/or N, mainly because it updates the Lagrange multipliers λ and γ.The suboptimal method eliminates these dual updates.Source: §IV · p. 7
• With equal power allocation, stage one repeatedly assigns an ER its highest-gain unassigned subcarrier and gives it to the highest-gain IR.Source: §IV · p. 7
• After stage one satisfies ER constraints, stage two chooses optimal power-splitting ratios and greedily assigns each remaining subcarrier to the IR with the largest weighted secrecy rate.ERs can also harvest additional energy from subcarriers assigned to IRs in stage two.Source: §IV · p. 7
• O(K2N1 + K1N2) is the two-stage algorithm's total complexity, upper-bounded by O(KN) and much lower than Algorithm 2.Source: §IV · p. 7

V. NUMERICAL RESULTS

• At N = 64, the duality gap is below 1 × 10^-5 bps/Hz and is considered negligible.The gap becomes smaller as the number of subcarriers increases.Source: Figure 5 · p. 8, §V · p. 8
• At Pmax = 37 dBm, allocated power is almost uniform across subcarriers, and the information source uses approximately half the power on each subcarrier.The reported optimal power split is αk,n ≈ 0.5.Source: Figure 6 · p. 8, §V · p. 8
• At Pmax = 37 dBm and N = 64, the suboptimal algorithm loses at most 30% secrecy rate versus the optimal algorithm and both outperform FSA and NoAN as harvested-power requirements vary.The α = 0.5 scheme also performs closely to the optimal algorithm.Source: Figure 7 · p. 8, §V · p. 8
• With AN, all considered schemes achieve significant rate-energy gains over NoAN, whose sum secrecy rate is almost zero even without a harvested-power requirement.In this setup, ERs have much better channel gains than IRs, so without effective AN, no secrecy information can be transmitted.Source: §V · pp. 8–9
• With Q̄ = 100 µW and N = 64, both proposed algorithms outperform FSA and NoAN as Pmax varies, while α = 0.5 performs very closely to optimal.The suboptimal algorithm approaches the optimal algorithm more closely as total transmit power increases.Source: Figure 8 · p. 9, §V · p. 9
• As the number of ERs increases, all schemes’ sum secrecy rates decrease, and FSA becomes infeasible above 55 ERs while the proposed algorithms retain noticeably higher rates.The paper attributes the decline to stronger eavesdropping channels and additional power allocated to meet ER requirements.Source: §V · p. 9

VI. CONCLUSION

• The proposed frequency-domain AN generation and removal method supports secrecy-constrained resource allocation in OFDMA-based SWIPT.The study maximizes IR weighted sum secrecy rate subject to individual ER harvested-power constraints.Source: §VI · p. 9
• The optimization jointly selects transmit power, subcarrier allocation, and AN transmit-power splitting ratios.The objective is weighted sum secrecy rate for IRs under individual harvested-power constraints for ERs.Source: §VI · p. 9
• The Lagrange-duality algorithm has polynomial-time complexity, and the lower-complexity suboptimal algorithm also outperforms the heuristic schemes in simulations.The comparisons include schemes with and without AN.Source: §VI · p. 9

APPENDIX A PROOF OF LEMMA 1

• R^s_k,n>0 exactly when p_k,n>[X_k,n(α_k,n)]+, covering both channel-gain orderings and α_k,n=0.When |h_k,n|²≥|β_k,n|² there is one zero root; when |h_k,n|²<|β_k,n|² there is also a root at X_k,n(α_k,n).Source: Appendix A · pp. 9–10

TRADITIONAL AN SCHEME

• Without receiver cancellation, α*_k,n=0 is always optimal, so traditional AN performs no better than transmission without AN.This conclusion holds across the two cases defined by the relative channel gains.Source: TRADITIONAL AN SCHEME · p. 10

APPENDIX C PROOF OF LEMMA 2

• For fixed p_k,n, the Appendix C proof applies KKT conditions and separates the optimal α_k,n derivation by the ordering of |h_k,n|² and |β_k,n|².The proof then rewrites the optimal α*_k,n for the given power.Source: Appendix C · p. 10