Spreading in block-fading channels

We consider wideband fading channels which are block-fading in time and in frequency (doubly block-fading). We show that, as the bandwidth increases to infinity, the capacity goes to zero when signaling is constrained in its second moment and peak signal amplitude. This result is consistent with similar results which do not consider doubly block-fading channels. None of these results, however, offer a range for the optimal spreading bandwidth, because they consider only upper bounds to capacity. While we know that spreading over very large bandwidths is detrimental in terms of capacity, we wish to determine over what range of bandwidths spreading is beneficial. We are able to give a range for the optimal spreading bandwidth by combining our upper bound with a suitable lower bound.