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Scheduling in a Broadcast (BC) channel based on partial Channel State Information at the Transmitter (CSIT) is carried out in an opportunistic way, where several orthogonal beams are randomly generated at the Base Station transmitter to simultaneously deliver several users with their intended data. The paper presents a power allocation over the transmitting beams, where a minimum rate per user restriction is required for each scheduled user, standing as a potential Quality of Service (QoS) indicator for the system behaviour. However, in practical wireless scenarios the CSIT is imperfect due to non-accurate estimation, so that robust schemes are required to meet the system demands. Based on the allowed system outage in the QoS achievement, different robust power allocation schemes are proposed, which are efficiently solved through convex optimization tools. The presented strategies are later compared via simulations for the different scenarios and the system specifications.