Large system performance of downlink OFDMA with limited feedback

We consider allocation of sub-channels to users in a downlink OFDMA system. Each user feeds back one bit per sub-channel, which indicates whether or not the gain exceeds a threshold. Users are assigned priority weights, and the thresholds are selected to maximize the weighted sum capacity. We analyze the behavior of the optimal thresholds and growth in capacity, assuming i.i.d. Rayleigh fading sub-channels, in the large system limit in which users K and sub-channels tend to infinity with fixed ratio. If all users have the same priority weight, then the optimized threshold increases as log K minus a second-order term, which is asymptotically bounded between log log K and log log log K. Furthermore, the sum capacity per sub-channel increases as log log K plus a second-order term, which decreases to a constant as log log K/ log K. We then consider two classes of users, each assigned a different weight, and show that the capacity of the low priority group tends to zero. Finally, we solve for the optimal thresholds given a fairness constraint on the ratio between the rates of different classes.