On training with feedback in wideband channels

Transmitter knowledge of channel state has a great impact on wideband fading channel capacity. However, in the low SNR regime, power per dimension does not suffice to provide an accurate measurement of the channel over the entire spectrum. In the presence of feedback, we may collect information at the transmitter about some aspects of the channel quality over a certain portion of the spectrum. In this work, we investigate the effect of such information. We consider channel testing with a finite amount of energy over a block-fading channel in both time and frequency. We consider a transmission scheme in which the wideband channel is decomposed into many parallel narrowband subchannels, each used with a binary modulation scheme. The quality of each subchannel corresponds to the crossover probability of a binary symmetric channel. We use a multi-armed bandit approach to consider the relative costs and benefits of allotting energy for testing versus transmission, and for repeated testing a single subchannel versus testing different subchannels. We give both upper and lower bounds on the number of subchannels that should be probed for throughput maximization under the scheme we have chosen. Our bounds are in terms of available transmission energy, available bandwidth and fading characteristics of the channel. Moreover, in our numerical results, the two bounds are close.