  This paper considers opportunistic scheduler (OS) design using statistical
channel state information~(CSI). We apply max-weight schedulers (MWSs) to
maximize a utility function of users' average data rates. MWSs schedule the
user with the highest weighted instantaneous data rate every time slot.
Existing methods require hundreds of time slots to adjust the MWS's weights
according to the instantaneous CSI before finding the optimal weights that
maximize the utility function. In contrast, our MWS design requires few slots
for estimating the statistical CSI. Specifically, we formulate a weight
optimization problem using the mean and variance of users' signal-to-noise
ratios (SNRs) to construct constraints bounding users' feasible average rates.
Here, the utility function is the formulated objective, and the MWS's weights
are optimization variables. We develop an iterative solver for the problem and
prove that it finds the optimal weights. We also design an online architecture
where the solver adaptively generates optimal weights for networks with varying
mean and variance of the SNRs. Simulations show that our methods effectively
require $4\sim10$ times fewer slots to find the optimal weights and achieve
$5\sim15\%$ better average rates than the existing methods.
