### Abstract

The article considers the joint optimization of artificial noise (AN) and information signal precoders in a MIMO wiretap interference network where the transmission of each user may be overheard by several MIMO-capable eavesdroppers. We use the theory of non-cooperative games to propose a distributed framework to optimize the covariance matrices of the information signal and AN at each link. To tackle the non-convexity of each link/player's optimization problem, we recruit a relaxed equilibrium concept in game theory, called quasi-Nash equilibrium (QNE). Under the assumption of no coordination between links, we derive sufficient conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness of QNE is not always guaranteed, especially in the case of high interference. Hence, multiple QNEs might exist, and an ordinary updating process (e.g., Gauss-Seidel, Jacobi, or asynchronous update) does not guarantee the convergence to a QNE. Instead, by using the Tikhonov regularization method for variational inequality problems, we modify our algorithm to guarantee the game's convergence to a QNE even in the case of having multiple QNEs. The modified algorithm also allows the links to select between multiple QNEs so as to reduce the received interference at the legitimate receivers. Simulations are then used to confirm the above theoretical findings and the efficacy (in terms of secrecy sum-rate, convergence guarantee, and energy efficiency) of the latter algorithm.

Language | English (US) |
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Title of host publication | 2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781509013289 |

DOIs | |

State | Published - Feb 2 2017 |

Event | 59th IEEE Global Communications Conference, GLOBECOM 2016 - Washington, United States Duration: Dec 4 2016 → Dec 8 2016 |

### Other

Other | 59th IEEE Global Communications Conference, GLOBECOM 2016 |
---|---|

Country | United States |

City | Washington |

Period | 12/4/16 → 12/8/16 |

### Fingerprint

### Keywords

- Equilibrium selection
- Friendly jamming
- MIMO precoders
- Wiretap interference network

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Networks and Communications
- Hardware and Architecture
- Safety, Risk, Reliability and Quality

### Cite this

*2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings*[7841504] Institute of Electrical and Electronics Engineers Inc.. DOI: 10.1109/GLOCOM.2016.7841504

**A game theoretic design of artificial-noise aided transmissions in MIMO wiretap interference network.** / Siyari, Peyman; Krunz, Marwan; Nguyen, Diep N.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings.*, 7841504, Institute of Electrical and Electronics Engineers Inc., 59th IEEE Global Communications Conference, GLOBECOM 2016, Washington, United States, 12/4/16. DOI: 10.1109/GLOCOM.2016.7841504

}

TY - GEN

T1 - A game theoretic design of artificial-noise aided transmissions in MIMO wiretap interference network

AU - Siyari,Peyman

AU - Krunz,Marwan

AU - Nguyen,Diep N.

PY - 2017/2/2

Y1 - 2017/2/2

N2 - The article considers the joint optimization of artificial noise (AN) and information signal precoders in a MIMO wiretap interference network where the transmission of each user may be overheard by several MIMO-capable eavesdroppers. We use the theory of non-cooperative games to propose a distributed framework to optimize the covariance matrices of the information signal and AN at each link. To tackle the non-convexity of each link/player's optimization problem, we recruit a relaxed equilibrium concept in game theory, called quasi-Nash equilibrium (QNE). Under the assumption of no coordination between links, we derive sufficient conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness of QNE is not always guaranteed, especially in the case of high interference. Hence, multiple QNEs might exist, and an ordinary updating process (e.g., Gauss-Seidel, Jacobi, or asynchronous update) does not guarantee the convergence to a QNE. Instead, by using the Tikhonov regularization method for variational inequality problems, we modify our algorithm to guarantee the game's convergence to a QNE even in the case of having multiple QNEs. The modified algorithm also allows the links to select between multiple QNEs so as to reduce the received interference at the legitimate receivers. Simulations are then used to confirm the above theoretical findings and the efficacy (in terms of secrecy sum-rate, convergence guarantee, and energy efficiency) of the latter algorithm.

AB - The article considers the joint optimization of artificial noise (AN) and information signal precoders in a MIMO wiretap interference network where the transmission of each user may be overheard by several MIMO-capable eavesdroppers. We use the theory of non-cooperative games to propose a distributed framework to optimize the covariance matrices of the information signal and AN at each link. To tackle the non-convexity of each link/player's optimization problem, we recruit a relaxed equilibrium concept in game theory, called quasi-Nash equilibrium (QNE). Under the assumption of no coordination between links, we derive sufficient conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness of QNE is not always guaranteed, especially in the case of high interference. Hence, multiple QNEs might exist, and an ordinary updating process (e.g., Gauss-Seidel, Jacobi, or asynchronous update) does not guarantee the convergence to a QNE. Instead, by using the Tikhonov regularization method for variational inequality problems, we modify our algorithm to guarantee the game's convergence to a QNE even in the case of having multiple QNEs. The modified algorithm also allows the links to select between multiple QNEs so as to reduce the received interference at the legitimate receivers. Simulations are then used to confirm the above theoretical findings and the efficacy (in terms of secrecy sum-rate, convergence guarantee, and energy efficiency) of the latter algorithm.

KW - Equilibrium selection

KW - Friendly jamming

KW - MIMO precoders

KW - Wiretap interference network

UR - http://www.scopus.com/inward/record.url?scp=85015434141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015434141&partnerID=8YFLogxK

U2 - 10.1109/GLOCOM.2016.7841504

DO - 10.1109/GLOCOM.2016.7841504

M3 - Conference contribution

BT - 2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -