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

We propose a compressive estimator of doubly selective channels within pulse-shaping multicarrier MIMO systems (including MIMO-OFDM as a special case). The use of multichannel compressed sensing exploits the joint sparsity of the MIMO channel for improved performance. We also propose a multichannel basis optimization for enhancing joint sparsity. Simulation results demonstrate significant advantages over channel-by-channel compressive estimation.

We consider channel estimation within pulseshaping multicarrier multiple-input multiple-output (MIMO) systems transmitting over doubly selective MIMO channels. This setup includes MIMO orthogonal frequency-division multiplexing (MIMO-OFDM) systems as a special case. We show that the component channels tend to exhibit an approximate joint group sparsity structure in the delay-Doppler domain. We then develop a compressive channel estimator that exploits this structure for improved performance. The proposed channel estimator uses the methodology of multichannel group sparse compressed sensing, which combines the methodologies of group sparse compressed sensing and multichannel compressed sensing. We derive an upper bound on the channel estimation error and analyze the estimator's computational complexity. The performance of the estimator is further improved by introducing a basis expansion yielding enhanced joint group sparsity, along with a basis optimization algorithm that is able to utilize prior statistical information if available. Simulations using a geometry-based channel simulator demonstrate the performance gains due to leveraging the joint group sparsity and optimizing the basis.Index Terms-Channel estimation, doubly selective channel, group sparse compressed sensing, MIMO-OFDM, multicarrier modulation, multichannel compressed sensing, multiple-input multiple-output (MIMO) communications, orthogonal frequencydivision multiplexing (OFDM), sparse reconstruction.

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