  Training over sparse multipath channels is explored. The energy allocation
and the optimal shape of training signals that enable error free communications
over unknown channels are characterized as a function of the channels'
statistics. The performance of training is evaluated by the reduction of the
mean square error of the channel estimate and by the decrease in the
uncertainty of the channel. A connection between the entropy of the wideband
channel and the required energy for training is shown. In addition, there is a
linkage between the sparsity and the entropy of the channel to the number of
required channel measurements when the training is based on compressed sensing.
The ability to learn the channel from few measurements is connected to the low
entropy of sparse channels that enables training in the low SNR regime.
