  Threshold feedback policies are well known and provably rate-wise optimal
selective feedback techniques for communication systems requiring partial
channel state information (CSI). However, optimal selection of thresholds at
mobile users to maximize information theoretic data rates subject to feedback
constraints is an open problem. In this paper, we focus on the optimal
threshold selection problem, and provide a solution for this problem for finite
feedback systems. Rather surprisingly, we show that using the same threshold
values at all mobile users is not always a rate-wise optimal feedback strategy,
even for a system with identical users experiencing statistically the same
channel conditions. By utilizing the theory of majorization, we identify an
underlying Schur-concave structure in the rate function and obtain sufficient
conditions for a homogenous threshold feedback policy to be optimal. Our
results hold for most fading channel models, and we illustrate an application
of our results to familiar Rayleigh fading channels.
