semidefinite relaxation
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This paper considers the multicast transmit beamforming and receive power splitting problem for sum transmit power minimization for a simultaneous wireless information and power transfer (SWIPT) system subject to signal-to-interference-plus-noise ratio (SINR), and energy harvesting constraints at the receiver. In particular, we consider the case of perfect and imperfect channel state information (CSI) at the base station. Using semidefinite relaxation (SDR) technique, we obtain solution to the problem with imperfect channel state information of the self-interfering channels. Keywords: Simultaneous wireless information and power transfer, channel state information, Energy harvesting, semidefinite relaxation.

AbstractWe develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (Ann Oper Res 265:155–182, 2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded SD bases contains the set of all diagonally dominant matrices and is contained in the set of all scaled diagonally dominant matrices. We also prove that the set of all scaled diagonally dominant matrices can be expressed using an infinite number of expanded SD bases. We use our approximations as the initial approximation in cutting plane methods for solving a semidefinite relaxation of the maximum stable set problem. It is found that the proposed methods with expanded SD bases are significantly more efficient than methods using other existing approximations or solving semidefinite relaxation problems directly.