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IEEE Communications Letters

Comments on “AN-Aided Secrecy Precoding for SWIPT in Cognitive MIMO Broadcast Channels”

Mahdi Khojastehnia, Sergey L. Loyka

Published Jan 10, 2020• 0 citations
Publisher

Abstract

Several gaps and errors in (B. Fanget al.,“AN-aided secrecy precoding for SWIPT in cognitive MIMO broadcast channels,”IEEE Commun. Lett.,vol. 19, no. 9, pp. 1632–1635, Sep. 2015) are identified. Their corrections as well as new results are reported. After these corrections in the analysis, the successive convex approximation algorithm for secrecy rate maximization with artificial noise is shown to generate an increasing, converging sequence of secrecy rates. For a degraded channel, (i) this sequence converges to the maximum secrecy rate of the channel, and (ii) it is optimal to use no artificial noise. For a reversely-degraded channel, the maximum achievable secrecy rate is zero.

DOI
10.1109/lcomm.2020.2965535

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Several gaps and errors in (B. Fanget al.,“AN-aided secrecy precoding for SWIPT in cognitive MIMO broadcast channels,”IEEE Commun. Lett.,vol. 19, no. 9, pp. 1632–1635, Sep. 2015) are identified. Their corrections as well as new results are reported. After these corrections in the analysis, the successive convex approximation algorithm for secrecy rate maximization with artificial noise is shown to generate an increasing, converging sequence of secrecy rates. For a degraded channel, (i) this sequence converges to the maximum secrecy rate of the channel, and (ii) it is optimal to use no artificial noise. For a reversely-degraded channel, the maximum achievable secrecy rate is zero.
In this letter, we study the secrecy precoding problem for simultaneous wireless information and power transfer (SWIPT) in a cognitive multiple-input multiple-output (MIMO) broadcast channel. We adopt an artificial noise (AN)-aided precoding scheme and formulate the problem as a secrecy rate maximization (SRM) problem, which is subject to both an interference power constraint imposed to protect the primary user (PU) and an energy harvesting constraint required by the secondary energy receiver (SER). Since the formulated SRM problem constitutes a difference convex (DC)-type programming problem, we solve it by employing a successive convex approximation (SCA) method. With the SCA method, the nonconvex part of the SRM problem can be locally linearized to its first-order Taylor expansion. Then, relying on solving a series of convexified optimization problems, an iterative precoding algorithm is developed. Numerical simulations are also provided to demonstrate the proposed algorithm. Results show that our algorithm can achieve a near-optimal performance with guaranteed convergence.
Several gaps and errors in “Precoding and Artificial Noise Design for Cognitive MIMOME Wiretap Channels” by Fang et al. are identified and corrected. While accommodating these corrections, a rigours proof is given that the successive convex approximation algorithm of Fang et al. for secrecy rate maximization (SRM) does generate an increasing and bounded sequence of true secrecy rates and hence converges. It is further shown that its convergence point is a KKT point of the original SRM problem and, if the original problem is convex, this convergence point is globally-optimal, which is not necessarily the case in general. An interlacing property of the sequences of the true and approximate secrecy rates is established.
The popular technique of secure signaling over Gaussian MIMO wiretap channels, which makes use of artificial noise (AN) to increase secrecy rates, is considered. First, we briefly review the current state of affairs in this area and then provide new analytical results and insights on the usefulness of AN (jamming) to boost secrecy rates. The settings considered here go beyond the total transmit power constraint and include a number of additional constraints, such as interference (cognitive radio) and energy-harvesting constraints, for which the feasible set is not isotropic anymore so that the standard tools of the analysis cannot be used. By closely examining optimal precoding for the information-bearing and AN signals, we identify a number of cases where it is optimal to transmit no artificial noise at all (so that all the transmit power goes to the information-bearing signal). These cases include a fixed (no fading) MIMO WTC with single eavesdropper (for which we give a direct matrix-theoretic proof using novel matrix inequalities), multi-eavesdropper (com-pound) degraded and reversely-degraded channels, and multi-eavesdropper channels where there exists a dominant eavesdropper (for which we give a precise definition) or when the eavesdroppers collude. To improve secrecy rates by using AN, one has to look elsewhere.
In this paper, we study the energy-efficient secrecy precoding problem for a general multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel. The system model considered here consists of a common transmitter, a legitimate receiver, and multiple eavesdroppers, all mounted with multiple antennas. In order to improve the energy efficiency (EE) performance of the proposed system, an artificial noise (AN)-aided precoding scheme is adopted. Because the formulated EE maximization problem is of huge nonconvex complexity, we solve it by employing a two-tier optimization structure. Although the outer-tier optimization problem is quite simple and can be efficiently solved by the famous golden section searching method, the inner-tier optimization problem turns out to be nonconvex and cannot be easily solved. To solve it, we relax it to a secrecy rate maximization (SRM) problem, which naturally constitutes a difference convex (DC)-type programming problem and can be iteratively solved by employing a successive convex approximation (SCA) method. Numerical simulations are further provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a near-optimal solution.