How costly is it to learn fading channels?

Recent results in communication theory suggest that substantial throughput gains in wireless fading networks can be achieved by exploiting network coordination (e.g., CoMP, network MIMO, interference alignment). However, these results are often based on the simplifying assumption that each node in the network has perfect channel knowledge and ignore the channel-estimation overhead. In this tutorial paper, we take a fresh look at the problem of learning fading channels. By focusing on simple channel models, we will illustrate how to quantify rigorously the throughput loss due to channel-estimation overhead. Specifically, by exploiting that in the absence of a priori channel knowledge at the receiver, the noiseless received signal is a nonlinear function of the transmitted signals and the propagation channel, we will show how to unveil the geometric structure underlying the channel input output relation, and how to use this geometry to characterize capacity at high SNR. We will also demonstrate that this approach is useful to determine the largest rate achievable at finite SNR and finite blocklength.