  We study the problem of allocating limited feedback resources across multiple
users in an orthogonal-frequency-division-multiple-access downlink system with
slow frequency-domain scheduling. Many flavors of slow frequency-domain
scheduling (e.g., persistent scheduling, semi-persistent scheduling), that
adapt user-sub-band assignments on a slower time-scale, are being considered in
standards such as 3GPP Long-Term Evolution. In this paper, we develop a
feedback allocation algorithm that operates in conjunction with any arbitrary
slow frequency-domain scheduler with the goal of improving the throughput of
the system. Given a user-sub-band assignment chosen by the scheduler, the
feedback allocation algorithm involves solving a weighted sum-rate maximization
at each (slow) scheduling instant. We first develop an optimal
dynamic-programming-based algorithm to solve the feedback allocation problem
with pseudo-polynomial complexity in the number of users and in the total
feedback bit budget. We then propose two approximation algorithms with
complexity further reduced, for scenarios where the problem exhibits additional
structure.
