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In this paper, beamforming and consumed power minimization in base station is studied for an underlay device-to-device communication within a cellular network. It is assumed that the channel state information are not available at the base station, and only estimations of their covariance are available. The estimation errors are considered in two models. In the first model, the errors are upper bounded in their Frobenius norms and the goal is to find the beamforming in the base station in order to minimize the consumed power in BS under the constraint that the signal to interference plus noise ratio for users are guaranteed to be above a certain predefined threshold. In the second model, a probabilistic model is considered for the uncertainty of channel covariance matrices and the BS consumed power is minimized while the non- outage probability of users are guaranteed to be above a certain predefined threshold. Although our approaches initially lead to non-convex optimization problems, they can be reformulated in convex forms by using the semidefinite relaxation technique to find  lower bounds for them. Simulation results show that our proposed methods outperform Hybrid MRT-ZF, ZFBF and MRT beamforming schemes.
 

Keywords: Device to divice communication, beamforming, estimation error, non-outage probability

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