  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.
