Georg Tauböck

A compressed sensing technique for OFDM channel estimation in mobile environments: Exploiting channel sparsity for reducing pilots

We consider the estimation of doubly selective wireless channels within pulse-shaping multicarrier systems (which include OFDM systems as a special case). A new channel estimation technique using the recent methodology of compressed sensing (CS) is proposed. CS-based channel estimation exploits a channels delay-Doppler sparsity to reduce the number of pilots and, hence, increase spectral efficiency. Simulation results demonstrate a significant reduction of the number of pilots relative to least-squares channel estimation.

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.

Complex-Valued Random Vectors and Channels: Entropy, Divergence, and Capacity

Recent research has demonstrated significant achievable performance gains by exploiting circularity/noncircularity or properness/improperness of complex-valued signals. In this paper, we investigate the influence of these properties on important information theoretic quantities such as entropy, divergence, and capacity. We prove two maximum entropy theorems that strengthen previously known results. The proof of the first maximum entropy theorem is based on the so-called circular analog of a given complex-valued random vector. The introduction of the circular analog is additionally supported by a characterization theorem that employs a minimum Kullback-Leibler divergence criterion. In the proof of the second maximum entropy theorem, results about the second-order structure of complex-valued random vectors are exploited. Furthermore, we address the capacity of multiple-input multiple-output (MIMO) channels. Regardless of the specific distribution of the channel parameters (noise vector and channel matrix, if modeled as random), we show that the capacity-achieving input vector is circular for a broad range of MIMO channels (including coherent and noncoherent scenarios). Finally, we investigate the situation of an improper and Gaussian distributed noise vector. We compute both capacity and capacity-achieving input vector and show that improperness increases capacity, provided that the complementary covariance matrix is exploited. Otherwise, a capacity loss occurs, for which we derive an explicit expression.Recent research has demonstrated significant achievable performance gains by exploiting circularity/noncircularity or properness/improperness of complex-valued signals. In this paper, we investigate the influence of these properties on important information theoretic quantities such as entropy, divergence, and capacity. We prove two maximum entropy theorems that strengthen previously known results. The proof of the first maximum entropy theorem is based on the so-called circular analog of a given complex-valued random vector. The introduction of the circular analog is additionally supported by a characterization theorem that employs a minimum Kullback-Leibler divergence criterion. In the proof of the second maximum entropy theorem, results about the second-order structure of complex-valued random vectors are exploited. Furthermore, we address the capacity of multiple-input multiple-output (MIMO) channels. Regardless of the specific distribution of the channel parameters (noise vector and channel matrix, if modeled as random), we show that the capacity-achieving input vector is circular for a broad range of MIMO channels (including coherent and noncoherent scenarios). Finally, we investigate the situation of an improper and Gaussian distributed noise vector. We compute both capacity and capacity-achieving input vector and show that improperness increases capacity, provided that the complementary covariance matrix is exploited. Otherwise, a capacity loss occurs, for which we derive an explicit expression.

Low-Complexity ICI/ISI Equalization in Doubly Dispersive Multicarrier Systems Using a Decision-Feedback LSQR Algorithm

We propose a low-complexity intercarrier interference/intersymbol interference (ICI/ISI) equalizer for multicarrier transmissions over doubly dispersive channels. Decision-feedback (or interference cancellation) is used with respect to both time and frequency. The ICI stage employs an extension of the iterative LSQR algorithm using groupwise interference cancellation with reliability-based sorting of sets of subcarriers and a band approximation of the frequency-domain channel matrix. The LSQR algorithm is attractive because of its excellent numerical properties and low complexity. Optimal pulse design is optionally considered for shaping the ICI/ISI. Simulation results demonstrate the excellent performance of the proposed ICI/ISI equalizer.

Multichannel-compressive estimation of doubly selective channels in MIMO-OFDM systems: Exploiting and enhancing joint sparsity

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.

Compressive Spectral Estimation for Nonstationary Random Processes

Estimating the spectral characteristics of a nonstationary random process is an important but challenging task, which can be facilitated by exploiting structural properties of the process. In certain applications, the observed processes are underspread, i.e., their time and frequency correlations exhibit a reasonably fast decay, and approximately time-frequency sparse, i.e., a reasonably large percentage of the spectral values are small. For this class of processes, we propose a compressive estimator of the discrete Rihaczek spectrum (RS). This estimator combines a minimum variance unbiased estimator of the RS (which is a smoothed Rihaczek distribution using an appropriately designed smoothing kernel) with a compressed sensing technique that exploits the approximate time-frequency sparsity. As a result of the compression stage, the number of measurements required for good estimation performance can be significantly reduced. The measurements are values of the ambiguity function of the observed signal at randomly chosen time and frequency lag positions. We provide bounds on the mean-square estimation error of both the minimum variance unbiased RS estimator and the compressive RS estimator, and we demonstrate the performance of the compressive estimator by means of simulation results. The proposed compressive RS estimator can also be used for estimating other time-dependent spectra (e.g., the Wigner-Ville spectrum), since for an underspread process most spectra are almost equal.

Group sparsity methods for compressive channel estimation in doubly dispersive multicarrier systems

We propose advanced compressive estimators of doubly dispersive channels within multicarrier communication systems (including classical OFDM systems). The performance of compressive channel estimation has been shown to be limited by leakage components impairing the channels effective delay-Doppler sparsity. We demonstrate a group sparse structure of these leakage components and apply recently proposed recovery techniques for group sparse signals. We also present a basis optimization method for enhancing group sparsity. Statistical knowledge about the channel can be incorporated in the basis optimization if available. The proposed estimators outperform existing compressive estimators with respect to estimation accuracy and, in one instance, also computational complexity.

Compressive tracking of doubly selective channels in multicarrier systems based on sequential delay-Doppler sparsity

We propose a compressive method for tracking doubly selective channels within multicarrier systems, including OFDM systems. Using the recently introduced concept of modified compressed sensing (MOD-CS), the sequential delay-Doppler sparsity of the channel is exploited to improve estimation performance through a recursive estimation mode. The proposed compressive channel tracking algorithm uses a MOD-CS version of OMP with reduced complexity. Simulation results demonstrate substantial performance gains over conventional compressive channel estimation.

Sequential LSQR-based ICI equalization and decision-feedback ISI cancellation in pulse-shaped multicarrier systems

We propose a frequency-domain method for equalizing intercarrier interference (ICI) and intersymbol interference (ISI) in multicarrier transmissions over rapidly time-varying and strongly delay-spread channels. Postcursor ISI is cancelled by a decision-feedback structure, and ICI is equalized by a sequential version of the recently proposed LSQR equalizer, based on a band approximation for the frequency-domain channel matrix. The sequential LSQR equalizer uses an interference cancellation scheme with reliability-based sorting of sets of subcarriers. This approach is shown to yield excellent performance at moderate complexity. A pulse-shaped multicarrier system is considered because of its generality and advantages. This framework includes cyclic-prefix OFDM as a special case.

Compressive spectral estimation for nonstationary random processes

Estimating the spectral characteristics of a nonstationary random process is an important but challenging task, which can be facilitated by exploiting structural properties of the process. In certain applications, the observed processes are underspread, i.e., their time and frequency correlations exhibit a reasonably fast decay, and approximately time-frequency sparse, i.e., a reasonably large percentage of the spectral values are small. For this class of processes, we propose a compressive estimator of the discrete Rihaczek spectrum (RS). This estimator combines a minimum variance unbiased estimator of the RS (which is a smoothed Rihaczek distribution using an appropriately designed smoothing kernel) with a compressed sensing technique that exploits the approximate time-frequency sparsity. As a result of the compression stage, the number of measurements required for good estimation performance can be significantly reduced. The measurements are values of the ambiguity function of the observed signal at randomly chosen time and frequency lag positions. We provide bounds on the mean-square estimation error of both the minimum variance unbiased RS estimator and the compressive RS estimator, and we demonstrate the performance of the compressive estimator by means of simulation results. The proposed compressive RS estimator can also be used for estimating other time-dependent spectra (e.g., the Wigner-Ville spectrum), since for an underspread process most spectra are almost equal.