In this paper, we consider the robust beamforming design in a device-to-device (D2D) two-hop one-way relay network. Specifically, we study the amplify-and-forward (AF) scheme in the scenario where both the transmitter-to-relays link and relays-to-receiver link are subject to estimation errors. Assuming that those errors lie in a ball with bounded radius, the resulting design problem can be formulated as a semi-infinite program (SIP) that involves high-degree polynomial inequality constraints, which is difficult to deal with in general. In this paper, we employ the semidefinite relaxation (SDR) technique and tools from polynomial optimization to construct a safe approximation of the aforementioned SIP. Furthermore, we propose an alternating algorithm to tackle the safe approximation. To the best of our knowledge, our work is the first to provide an efficient algorithmic approach to the aforementioned robust beamforming design problem. In addition, our numerical results show that the proposed robust beamforming design is more reliable than the non-robust counterpart, and it can achieve better signal-to-noise ratios (SNRs) than the existing linear approximation approach, which ignores error terms with degree higher than one.
['Sissi Xiaoxiao Wu', 'Xueying Ni', 'Anthony Man-Cho So']
A polynomial optimization approach for robust beamforming design in a device-to-device two-hop one-way relay network