  In this paper, we consider multiuser multiple-input single-output (MISO)
interference channel where the received signal is divided into two parts for
information decoding and energy harvesting (EH), respectively. The transmit
beamforming vectors and receive power splitting (PS) ratios are jointly
designed in order to minimize the total transmission power subject to both
signal-to-interference-plus-noise ratio (SINR) and EH constraints. Most joint
beamforming and power splitting (JBPS) designs assume that perfect channel
state information (CSI) is available; however CSI errors are inevitable in
practice. To overcome this limitation, we study the robust JBPS design problem
assuming a norm-bounded error (NBE) model for the CSI. Three different solution
approaches are proposed for the robust JBPS problem, each one leading to a
different computational algorithm. Firstly, an efficient semidefinite
relaxation (SDR)-based approach is presented to solve the highly non-convex
JBPS problem, where the latter can be formulated as a semidefinite programming
(SDP) problem. A rank-one recovery method is provided to recover a robust
feasible solution to the original problem. Secondly, based on second order cone
programming (SOCP) relaxation, we propose a low complexity approach with the
aid of a closed-form robust solution recovery method. Thirdly, a new iterative
method is also provided which can achieve near-optimal performance when the
SDR-based algorithm results in a higher-rank solution. We prove that this
iterative algorithm monotonically converges to a Karush-Kuhn-Tucker (KKT)
solution of the robust JBPS problem. Finally, simulation results are presented
to validate the robustness and efficiency of the proposed algorithms.
