arXiv subjects
Publications and source records attributed to Hans Georg Feichtinger.
It is the purpose of this paper to give a characterization of the pre-dual of the spaces introduced by I.~Fofana on the basis of Wiener amalgam spaces. Those spaces have a specific dilation behaviour similar to the spaces $L^α(\mathbb R^d)$. The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators).
We consider channel estimation within pulse-shaping 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.
This article describes how the ideas promoted by the fundamental papers published by M. Frazier and B. Jawerth in the eighties have influenced subsequent developments related to the theory of atomic decompositions and Banach frames for function spaces such as the modulation spaces and Besov-Triebel-Lizorkin spaces. Both of these classes of spaces arise as special cases of two different, general constructions of function spaces: coorbit spaces and decomposition spaces. Coorbit spaces are defined by imposing certain decay conditions on the so-called voice transform of the function/distribution under consideration. As a concrete example, one might think of the wavelet transform, leading to the theory of Besov-Triebel-Lizorkin spaces. Decomposition spaces, on the other hand, are defined using certain decompositions in the Fourier domain. For Besov-Triebel-Lizorkin spaces, one uses a dyadic decomposition, while a uniform decomposition yields modulation spaces. Only recently, the second author has established a fruitful connection between modern variants of wavelet theory with respect to general dilation groups (which can be treated in the context of coorbit theory) and a particular family of decomposition spaces. In this way, optimal inclusion results and invariance properties for a variety of smoothness spaces can be established. We will present an outline of these connections and comment on the basic results arising in this context.