Secrecy Rate Optimizations for a MISO Secrecy Channel with Multiple Multiantenna Eavesdroppers

Zheng Chu, Hong Xing, Martin Johnston, Stéphane Le Goff

Research output: Journal PublicationArticlepeer-review

100 Citations (Scopus)


This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.

Original languageEnglish
Article number7219473
Pages (from-to)283-297
Number of pages15
JournalIEEE Transactions on Wireless Communications
Issue number1
Publication statusPublished - Jan 2016
Externally publishedYes


  • convex optimization
  • MISO system
  • physical-layer secrecy
  • robust optimization
  • secrecy capacity

ASJC Scopus subject areas

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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