Secrecy rate optimizations for a MIMO secrecy channel with a cooperative jammer

Zheng Chu, Kanapathippillai Cumanan, Zhiguo Ding, Martin Johnston, Stephane Y. Le Goff

Research output: Contribution to journalArticlepeer-review

179 Scopus citations


In this paper, we study different secrecy rate optimization techniques for a multiple-input-multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into a Stackelberg game where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game, Stackelberg equilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, the Stackelberg equilibrium solution has been validated through numerical results.

Original languageBritish English
Article number6848758
Pages (from-to)1833-1847
Number of pages15
JournalIEEE Transactions on Vehicular Technology
Issue number5
StatePublished - 1 May 2015


  • Convex optimization
  • multiple-input multipleoutput (MIMO) system
  • physical-layer secrecy
  • robust optimization
  • secrecy capacity
  • Stackelberg game


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