Compressive Estimation of Doubly Selective Channels in Multicarrier Systems: Leakage Effects and Sparsity-Enhancing Processing

We consider the application of
compressed sensing
(CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include orthogonal frequency-division multiplexing (OFDM) systems as a special case). By exploiting sparsity in the delay-Doppler domain, CS-based channel estimation allows for an increase in spectral efficiency through a reduction of the number of pilot symbols. For combating leakage effects that limit the delay-Doppler sparsity, we propose a sparsity-enhancing basis expansion and a method for optimizing the basis with or without prior statistical information about the channel. We also present an alternative CS-based channel estimator for (potentially) strongly time-frequency dispersive channels, which is capable of estimating the ¿off-diagonal¿ channel coefficients characterizing intersymbol and intercarrier interference (ISI/ICI). For this estimator, we propose a basis construction combining Fourier (exponential) and prolate spheroidal sequences. Simulation results assess the performance gains achieved by the proposed sparsity-enhancing processing techniques and by explicit estimation of ISI/ICI channel coefficients.