Minimum feedback rates for multicarrier transmission with correlated frequency-selective fading

In this paper, we consider multicarrier transmission through a frequency-selective fading channel with limited feedback. An on-off power allocation activates the set of subchannels with gains above a threshold. We model the sequence of subchannel gains as a Markov process, and give a lower bound on the feedback rate in bits per subchannel needed to specify the sequence of activated subchannels as a function of the activation threshold. Optimizing the threshold gives the same asymptotic growth in capacity as optimal water-filling as the number of subchannels N goes to infinity. If the ratio of coherence bandwidth to the total available bandwidth is fixed, then the ratio between minimum feedback rates with correlated and i.i.d. subchannels, respectively, converges to zero with N. For a sequence of Rayleigh fading subchannels, which are modeled as a first-order autoregressive process, the ratio goes to zero as O (√logN/N) with the optimized threshold. We also consider finite-precision rate control on each subchannel, and show that the feedback rate required to specify the sequence of assigned rate levels across subchannels gives the same asymptotic increase in achievable rate with N as the (infinite-precision) on-off power allocation.