Training Over Sparse Multipath Channels in the Low SNR Regime

TL;DR

This paper investigates optimal training strategies for sparse multipath channels in low SNR conditions, linking energy, entropy, and compressed sensing to improve channel estimation accuracy.

Contribution

It characterizes optimal training signal shapes and energy allocation based on channel statistics, and connects entropy and sparsity to training efficiency in low SNR regimes.

Findings

Optimal training signals depend on channel statistics.

Sparsity and low entropy enable effective training with few measurements.

Training performance improves with understanding of channel entropy and sparsity.

Abstract

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.