Learning sparse doubly-selective channels

Coherent data communication over doubly-selective channels requires that the channel response be known at the receiver. Training-based schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel parameters, are commonly employed to learn the channel response in practice. Conventional training-based methods, often comprising of linear least squares channel estimators, are known to be optimal under the assumption of rich multipath channels. Numerous measurement campaigns have shown, however, that physical multipath channels tend to exhibit a sparse structure at high signal space dimension (time-bandwidth product), and can be characterized with significantly fewer parameters compared to the maximum number dictated by the delay-Doppler spread of the channel. In this paper, it is established that traditional training-based channel learning techniques are ill-suited to fully exploiting the inherent low-dimensionality of sparse channels. In contrast, key ideas from the emerging theory of compressed sensing are leveraged to propose sparse channel learning methods for both single-carrier and multicarrier probing waveforms that employ reconstruction algorithms based on convex/linear programming. In particular, it is shown that the performance of the proposed schemes come within a logarithmic factor of that of an ideal channel estimator, leading to significant reductions in the training energy and the loss in spectral efficiency associated with conventional training-based methods.