Efficient Numerical Methods for Secrecy Capacity of Gaussian MIMO Wiretap Channel

Mukherjee, Anshu; Ottersten, Björn; Tran, Le-Nam

doi:10.1109/vtc2021-spring51267.2021.9448796

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…For the non-degraded case, we implement the barrier method [10, Alg. 3] and [13,Alg. 3], both of which can find the secrecy capacity but are based on the equivalent convex-concave reformulation.…”

Section: Numerical Resultsmentioning

confidence: 99%

On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

Mukherjee¹,

Kumar²,

Jorswieck³

et al. 2021

Preprint

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To achieve perfect secrecy in a multiple-input multiple-output (MIMO) Gaussian wiretap channel (WTC), we need to find its secrecy capacity and optimal signaling, which involves solving a difference of convex functions program known to be non-convex for the non-degraded case. To deal with this, a class of existing solutions have been developed but only local optimality is guaranteed by standard convergence analysis. Interestingly, our extensive numerical experiments have shown that these local optimization methods indeed achieve global optimality. In this paper, we provide an analytical proof for this observation. To achieve this, we show that the Karush-Kuhn-Tucker (KKT) conditions of the secrecy rate maximization problem admit a unique solution for both degraded and nondegraded cases. Motivated by this, we also propose a lowcomplexity algorithm to find a stationary point. Numerical results are presented to verify the theoretical analysis.

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Section: Numerical Resultsmentioning

confidence: 99%

On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

Mukherjee¹,

Kumar²,

Jorswieck³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

Mukherjee

Kumar

Jorswieck

et al. 2022

IEEE Wireless Commun. Lett.

View full text Add to dashboard Cite

To achieve perfect secrecy in a multiple-input multiple-output (MIMO) Gaussian wiretap channel (WTC), we need to find its secrecy capacity and optimal signaling, which involves solving a difference of convex functions program known to be non-convex for the non-degraded case. To deal with this, a class of existing solutions have been developed but only local optimality is guaranteed by standard convergence analysis. Interestingly, our extensive numerical experiments have shown that these local optimization methods indeed achieve global optimality. In this letter, we provide an analytical proof for this observation. To achieve this, we show that the Karush-Kuhn-Tucker (KKT) conditions of the secrecy rate maximization problem admit a unique solution for both degraded and non-degraded cases. Motivated by this, we also propose a low-complexity algorithm to find a stationary point. Numerical results are presented to verify the theoretical analysis.

show abstract

Comparison of Optimization Criteria for Preprocessing for Physical-Layer Security in Multi-Carrier-THz-MIMO Systems

Schulz,

Fischer

2024

2024 27th International Workshop on Smart Antennas (WSA)

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Efficient Numerical Methods for Secrecy Capacity of Gaussian MIMO Wiretap Channel

Cited by 3 publications

References 16 publications

On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

Comparison of Optimization Criteria for Preprocessing for Physical-Layer Security in Multi-Carrier-THz-MIMO Systems

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