Multi-scale multi-lag channel estimation via linearization of training signal spectrum and sparse approximation

Multi-scale, multi-lag (MSML) models are adopted for time-varying (ultra)-wideband channels that are relevant for underwater acoustic, radar and ultrawideband radio applications. MSML channels are characterized by a limited number of paths, each parameterized by a delay, Doppler scale, and attenuation factor. Herein, a novel MSML channel estimator is proposed. First, in the Fourier domain, it is shown that there is an approximately linear relationship between the received signal and the Doppler scales that enables the recasting of channel estimation into a convex optimization problem. Second, the inherent sparsity of many MSML channels is exploited resulting in a further improvement in estimation performance of about 5 dB in low SNR relative to an unstructured estimation method. Finally, the resultant estimation strategy has very low implementation complexity.