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This paper studies the structure of downlink sum-rate maximizing selectivedecentralized feedback policies for opportunistic beamforming under finitefeedback constraints on the average number of mobile users feeding back.Firstly, it is shown that any sum-rate maximizing selective decentralizedfeedback policy must be a threshold feedback policy. This result holds for allfading channel models with continuous distribution functions. Secondly, theresulting optimum threshold selection problem is analyzed in detail. This is anon-convex optimization problem over finite dimensional Euclidean spaces. Byutilizing the theory of majorization, an underlying Schur-concave structure inthe sum-rate function is identified, and the sufficient conditions for theoptimality of homogenous threshold feedback policies are obtained. Applicationsof these results are illustrated for well known fading channel models such asRayleigh, Nakagami and Rician fading channels, along with various engineeringand design insights. Rather surprisingly, it is shown that using the samethreshold value at all mobile users is not always a rate-wise optimal feedbackstrategy, even for a network with identical mobile users experiencingstatistically the same channel conditions. For the Rayleigh fading channelmodel, on the other hand, homogenous threshold feedback policies are proven tobe rate-wise optimal if multiple orthonormal data carrying beams are used tocommunicate with multiple mobile users simultaneously.

Optimal Selective Feedback Policies for Opportunistic Beamforming