A NEW LOW-RANK SOLUTION RESULT FOR A SEMIDEFINITE PROGRAM PROBLEM SUBCLASS WITH APPLICATIONS TO TRANSMIT BEAMFORMING OPTIMIZATION

作者：Li Qiang^*; Ma Wing Kin

来源：IEEE International Conference on Acoustics, Speech, and Signal Processing, 2016-03-20 to 2016-03-25.

• Quadratically constrained quadratic program
• semidefinite relaxation
• SWIPT
• Physical-layer security

This paper considers a special subclass of separable semidefinite programs (SDPs), with the goal of identifying certain conditions under which the SDP has a low-rank solution. We prove that when the data matrices of the SDP satisfy certain matrix inequalities, the SDP has a low-rank solution. Moreover, the rank of this solution is related to parts of the data matrices only, irrespective of any other factors such as the number of constraints. This is quite different from the well-known Shapiro-Barvinok-Pataki rank reduction result, where the rank of the SDP solution relies on the number of constraints. The usefulness of our result is demonstrated through advanced beamforming applications in simultaneous wireless information and power transfer (SWIPT) and physical-layer security, for which rank-one optimal solutions can be easily identified by checking our derived matrix inequality conditions.

• 出版日期2016
• 单位香港中文大学; 电子科技大学