The feedback-capacity tradeoff for opportunistic beamforming under optimal user selection

Opportunistic beamforming   is a reduced feedback communication strategy for vector broadcast channels which requires partial channel state information (CSI) at the base station for its operation. Although reducing feedback, this strategy in its plain implementations displays a linear growth in the feedback load with the total number of users in the system nn, which is an onerous requirement for large systems. This paper focuses on a more stringent but realistic O(1)O(1) feedback constraint on the feedback load. Starting with a set of statistically identical users, we obtain the tradeoff curve tracing the Pareto optimal boundary between feasible and infeasible feedback-capacity pairs for opportunistic beamforming. Any point on this tradeoff curve can be obtained by means of homogeneous decentralized threshold feedback policies, which are rate-wise optimal, in which a user feeds back only if the received signal quality is good enough. The paper includes the derivation of these optimum policies, and further shows to what extent the O(1)O(1) feedback constraint must be relaxed to achieve the same sum-rate scaling as with perfect CSI. Extensions of these results to heterogeneous communication environments in which different users experience non-identical path-loss gains are also provided. We also show how threshold feedback policies can be used to provide fairness in a heterogeneous system, while simultaneously achieving optimal capacity scaling. Although most of our results are asymptotic in the sense that they are derived by letting nn grow large, they provide promising performance figures with a close match to the asymptotically optimal results when used in finite size systems.