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 $O(\log ^{3} N)$. 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 $O\left (\sqrt {{ \log N}\over { N}}\right)$ 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.