It is known that distributed beamforming techniques can improve the performance of relay networks by using\nchannel state information (CSI). In practical applications, there exist unavoidably estimation errors of the CSI, which\nresults in outage of quality of service (QoS) or overconsumption of transmit power. In this paper, we propose two\nworst-case-based distributed beamforming techniques that are robust to the channel estimation errors. In the\nworst-case-based approaches, the worst case in a set that includes the actual case is optimized. Therefore, the\nperformance of the actual case can be guaranteed. In our first approach, the maximal total relay transmit power in the\nset is minimized subject to the QoS constraint. This distributed beamforming problem can be approximately solved\nusing second-order cone programming (SOCP). In our second method, the worst QoS in the set is maximized subject\nto the constraints of individual relay transmit powers. It is shown that the resultant problem can be approximately\nformulated as a quasi-convex problem and can be solved by using a bisection search method. Simulation results\nshow that the proposed beamforming techniques are robust to the CSI errors and there is no outage of QoS or power\nin the proposed methods.
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