In a downlink orthogonal frequency division multiple access (OFDMA) system, optimally allocating sub-channels across mobile users can require excessive feedback of channel state information (CSI). We consider an OFDMA model in which the feedback overhead is explicitly taken into account, given a fixed feedback rate and finite coherence time. The tradeoff between feedback rate and sum capacity is studied for two limited feedback schemes: a sequential scheme in which the users send compressed feedback bits over consecutive time slots, and a contention scheme in which users send their feedback via a random access protocol. For both schemes each feedback bit indicates a request for a group containing multiple subchannels. We show that the sum capacity for both schemes with optimized sub-channel groups grows linearly with the number of sub-channels N, and that the associated constant increases as the log of the normalized feedback rate measured in bits per coherence time per sub-channel. We also compare the asymptotic (large N) performance of the two limited feedback schemes as a function of the feedback rate and load (users per sub-channel). The sequential scheme performs best with moderate to large feedback rates, or small loads, whereas the contention scheme performs best with small feedback rates or large loads.

We consider the capacity of a downlink orthogonal frequency division multiple access (OFDMA) system with limited feedback rate RFper sub-channel and finite coherence time T. The feedback is used to relay channel state information (CSI) from K users to the base station. The order-optimal capacity growth with Rayleigh fading sub-channels is ominus(N log log K) as N and K increase with fixed ratio, where N is the number of sub-channels. However, to achieve this, previous work requires a feedback rate per subchannel that scales linearly with the system size. Here we explicitly include the feedback overhead when calculating the sum capacity, and study the tradeoff between feedback rate and sum capacity. We propose two limited feedback schemes, one based on sequential transmissions across users and the other based on random access, in which the each feedback bit requests the use of a sub-channel group containing multiple subchannels. With fixed RFT, the sum capacity for both schemes with optimized sub-channel groups increases as ominus(N). If RFT grows faster than log K, then both schemes can achieve the order- optimal capacity growth. We also show that when RFT is small, the random access scheme performs better than the sequential transmission scheme, whereas the reverse is true for large RFT.

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