The feedback-capacity tradeoff for opportunistic beamforming

Optimum capacity scaling in the downlink of a single-cell multiple-input-multiple-output communication system can be achieved by a communication strategy called opportunistic beamforming in which information carrying beams are randomly formed and users are opportunistically scheduled based on their partial channel state information. Even though opportunistic beamforming reduces the amount of feedback required to achieve optimum capacity scaling laws, the number of users feeding back in its plain implementations still grows linearly with the total number of users in the system, which is an onerous requirement on the feedback channel. In this paper, we focus on a more stringent but realistic O(1) feedback constraint on the feedback channel, and obtain the tradeoff curve tracing the Pareto optimal boundary between feasible and infeasible feedback-rate pairs. We show that any point on this tradeoff curve can be obtained by means of homogeneous decentralized thresholding policies, in which a user feeds back only if the received signal quality at her best link is good enough, and derive the form of these optimum policies. We further show that if the O(1) feedback constraint is relaxed, we can achieve the optimum capacity scaling by a feedback amount growing like O((log n) ^ε for any ε ∈ (0,1), where n is the number of users in the system.