Minimum Feedback Rates for Multi-Carrier Transmission with Correlated Frequency-Selective Fading

We consider multi-carrier transmission through a frequency-selective fading channel with limited feedback. An on-off power allocation activates the set of sub-channels with gains above a threshold. We model the sequence of sub-channel gains as a Markov process, and give a lower bound on the feedback rate in bits per sub-channel needed to specify the sequence of activated sub-channels 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 sub-channels 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, sub-channels, respectively, converges to zero with N. For a sequence of Rayleigh fading sub-channels, which are modeled as a first-order autoregressive process, the ratio goes to zero as O (√log N/N) with the optimized threshold. We also consider finite-precision rate control on each sub-channel, and show that the feedback rate required to specify the sequence of assigned rate levels across sub-channels gives the same asymptotic increase in achievable rate with N as the (infinite-precision) on-off power allocation.