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

Abstract

We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulseshaping multicarrier systems (which include 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 CSbased channel estimator for (potentially) strongly time-frequency dispersive channels, which is capable of estimating the "offdiagonal" 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.Index Terms-channel estimation, compressed sensing, CoSaMP, dictionary learning, doubly selective channel, intercarrier interference, intersymbol interference, Lasso, multicarrier modulation, orthogonal frequency-division multiplexing (OFDM), orthogonal matching pursuit (OMP), sparse reconstruction.CP-OFDM is a simple special case of the pulse-shaping MC framework; it is obtained for a rectangular transmit pulse g[n] that is 1 for n = 0, . . . , N−1 and 0 otherwise, and a rectangular receive pulse γ[n] that is 1 for n = N −K, . . . , N −1 and 0 otherwise (N −K ≥ 0 is the CP length). Georg Tauböck (S'01-M'07) received the Dipl.-Ing. degree and the Dr.techn. degree (with highest honors) in electrical engineering and the Dipl.-Ing. degree in mathematics (with highest honors) from His research interests include wireline and wireless communications, compressed sensing, signal processing, and information theory.Franz Hlawatsch (S'85-M'88-SM'00) received the Diplom-Ingenieur, Dr. techn., and Univ.-Dozent (habilitation) degrees in electrical engineering/signal processing

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