On the use of sounding in wideband channels

In wideband channels, the energy per degree of freedom does not suffice to provide an accurate measurement of the channel over the entire spectrum. However, in the presence of feedback, we may garner information at the sender about some aspects of the channel quality over certain portion of the spectrum. In this paper, we investigate a scheme to capture the effect of such information. We consider channel sounding with a finite amount of energy over a block-fading channel in both time and frequency. The quality of each subchannel is assessed as being the cross-over probability in a BSC. In order to characterize a judicious policy for allocating energy to different subchannels in view of establishing their usefulness for transmission, we use a multi-armed bandit approach. This approach provides us with a cohesive framework to consider the relative costs and benefits of allotting energy for sounding versus transmission, and for repeated sounding of a single channel versus sounding of different channels. In particular, we are able to give a characterization of the number of subchannels that should be probed for capacity maximization in terms of the available transmission energy, the available bandwidth and the fading characteristics of the channel