Abstract
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 <i>indeed achieve global optimality</i>. 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 <i>both degraded and non-degraded cases</i>. Motivated by this, we also propose a low-complexity algorithm to find a stationary point. Numerical results are presented to verify the theoretical analysis.
Highlights
W ITH the advent of new wireless communication applications including social networking, financial transactions, and military-related communications, there has been an ever increasing demand for privacy-preserving communication services
Wyner in his seminal work introduced an information-theoretic paradigm of physical layer security (PLS) for discrete memoryless wiretap channel (WTC) [1]
We give a rigorous analytical proof that there exists a unique Karush–Kuhn–Tucker (KKT) point for the secrecy capacity problem for both degraded and non-degraded Gaussian multiple-input multiple-output (MIMO) WTC. This interesting result establishes that existing local optimization methods such as [8] for the secrecy problem yield the globallyoptimal solution. Motivated by this result, we propose an accelerated gradient projection algorithm with adaptive momentum parameters that solves the secrecy capacity problem directly, rather than the equivalent convex-concave form
Summary
W ITH the advent of new wireless communication applications including social networking, financial transactions, and military-related communications, there has been an ever increasing demand for privacy-preserving communication services. The equivalent convexconcave reformulation of the secrecy capacity problem has been used to find the optimal signaling for the non-degraded MIMO WTC [6], [10] Against this background, the main contributions in this letter are as follows:. We give a rigorous analytical proof that there exists a unique Karush–Kuhn–Tucker (KKT) point for the secrecy capacity problem for both degraded and non-degraded Gaussian MIMO WTC. This interesting result establishes that existing local optimization methods such as [8] for the secrecy problem yield the globallyoptimal solution.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
