Asymptotic capacity of multicarrier transmission with frequency-selective fading and limited feedback

We study the capacity of multicarrier transmission through a slow frequency-selective fading channel with limited feedback, which specifies channel state information. Our results are asymptotic in the number of subchannels N. We first assume independent and identically distributed (i.i.d.) subchannel gains, and show that, for a large class of fading distributions, a uniform power distribution over an optimized subset of subchannels, or on-off power allocation, gives the same asymptotic growth in capacity as optimal water filling, e.g., O(\log N) with Rayleigh fading. Furthermore, the O(log N)growth in data rate can be achieved with a feedback rate as O(log³ N). If the number of active subchannels is bounded, the capacity grows only as O(log log N) with the feedback rate of O(log N). We then consider correlated subchannels modeled as a Markov process, and study the savings in feedback. Assuming a fixed ratio of coherence bandwidth to the total bandwidth, the ratio between minimum feedback rates with correlated and i.i.d. subchannels converges to zero with N, e.g., as O (√log N/N) for Rayleigh-fading subchannels satisfying a first-order autoregressive process. We also show that adaptive modulation, or rate control schemes, in which the rate on each subchannel is selected from a quantized set, achieves the same asymptotic growth rates in capacity and required feedback. Finally, our results are extended to cellular uplink and downlink channel models.