We propose a new one-bit feedback scheme with scheduling decision based on the maximum expected weighted rate. We show the concavity of the $2$-user case and provide the optimal solution which achieves the maximum weighted rate of the users. For the general asymmetric M-user case, we provide a heuristic method to achieve the maximum expected weighted rate. We show that the sum rate of our proposed scheme is very close to the sum rate of the full channel state information case, which is the upper bound performance.
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