Algorithms for Globally-Optimal Secure Signaling over Gaussian MIMO Wiretap Channels Under Interference Constraints

TL;DR

This paper introduces algorithms that globally optimize the secrecy rate in Gaussian MIMO wiretap channels with interference constraints, proving convergence and addressing singular cases for power-efficient secure communication.

Contribution

It presents novel algorithms that guarantee convergence to the global optimum in MIMO scenarios, including singular cases, improving secure signaling strategies under interference constraints.

Findings

Algorithms converge rapidly with few Newton steps.

Proven to reach the global secrecy capacity in general MIMO channels.

Addresses singular cases for optimal power-efficient signaling.

Abstract

Multi-user Gaussian MIMO wiretap channel is considered under interference power constraints (IPC), in addition to the total transmit power constraint (TPC). Algorithms for \textit{global} maximization of its secrecy rate are proposed. Their convergence to the secrecy capacity is rigorously proved and a number of properties are established analytically. Unlike known algorithms, the proposed ones are not limited to the MISO case and are proved to converge to a \textit{global} rather than local optimum in the general MIMO case, even when the channel is not degraded. In practice, the convergence is fast as only a small to moderate number of Newton steps is required to achieve a high precision level. The interplay of TPC and IPC is shown to result in an unusual property when an optimal point of the max-min problem does not provide an optimal transmit covariance matrix in some (singular) cases. To address this issue, an algorithm is developed to compute an optimal transmit covariance matrix in those singular cases. It is shown that this algorithm also solves the dual (nonconvex) problems of \textit{globally} minimizing the total transmit power subject to the secrecy and interference constraints; it provides the minimum transmit power and respective signaling strategy needed to achieve the secrecy capacity, hence allowing power savings.