  Consider a channel allocation problem over a frequency-selective
channel.There are K channels (frequency bands) and N users such that K=bN for
some positive integer b. We want to allocate b channels (or resource blocks) to
each user. Due to the nature of the frequency-selective channel, each user
considers some channels to be better than others. The optimal solution to this
resource allocation problem can be computed using the Hungarian algorithm.
However, this requires knowledge of the numerical value of all the channel
gains, which makes this approach impractical for large networks. We suggest a
suboptimal approach, that only requires knowing what the M-best channels of
each user are. We find the minimal value of M such that there exists an
allocation where all the b channels each user gets are among his M-best. This
leads to feedback of significantly less than one bit per user per channel. For
a large class of fading distributions, including Rayleigh, Rician, m-Nakagami
and others, this suboptimal approach leads to both an asymptotically (in K)
optimal sum-rate and an asymptotically optimal minimal rate. Our
non-opportunistic approach achieves (asymptotically) full multiuser diversity
as well as optimal fairness, by contrast to all other limited feedback
algorithms.
