arXiv subjects

Peter Jung

Publications and source records attributed to Peter Jung.

At least 91 records · Page 5Linked to original sources

arXiv2015

Sparse Signal Processing Concepts for Efficient 5G System Design

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.

cs.IT↗

arXiv2014

On the Stability of Sparse Convolutions

We give a stability result for sparse convolutions on $\ell^2(G)\times \ell^1(G)$ for torsion-free discrete Abelian groups $G$ such as $\mathbb{Z}$. It turns out, that the torsion-free property prevents full cancellation in the convolution of sparse sequences and hence allows to establish stability in each entry, that is, for any fixed entry of the convolution the resulting linear map is injective with an universal lower norm bound, which only depends on the support cardinalities of the sequences. This can be seen as a reverse statement of the famous Young inequality for sparse convolutions. Our result hinges on a compression argument in additive set theory.

cs.IT↗

arXiv2014

Sparse Model Uncertainties in Compressed Sensing with Application to Convolutions and Sporadic Communication

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for noncoherent information retrieval in, for example, sporadic blind and semi-blind communication and sampling problems. But, the conventional model is not practical here since the compressible signals have to be estimated from samples taken solely on the output of an un-calibrated system which is unknown during measurement but often compressible. Conventionally, one has either to operate at suboptimal sampling rates or the recovery performance substantially suffers from the dominance of model mismatch. In this work we discuss such type of estimation problems and we focus on bilinear inverse problems. We link this problem to the recovery of low-rank and sparse matrices and establish stable low-dimensional embeddings of the uncalibrated receive signals whereby addressing also efficient communication-oriented methods like universal random demodulation. Exemplary, we investigate in more detail sparse convolutions serving as a basic communication channel model. In using some recent results from additive combinatorics we show that such type of signals can be efficiently low-rate sampled by semi-blind methods. Finally, we present a further application of these results in the field of phase retrieval from intensity Fourier measurements.

cs.IT↗

arXiv2014

Robust Iterative Interference Alignment for Cellular Networks with Limited Feedback

In theory coordinated multi-point transmission (CoMP) promises vast gains in spectral efficiency. But industrial field trials show rather disappointing throughput gains, whereby the major limiting factor is proper sharing of channel state information. Many recent papers consider this so-called limited feedback problem in the context of CoMP. Usually taking the assumptions: 1) infinite SNR regime, 2) no user selection and 3) ideal link adaptation; rendering the analysis too optimistic. In this paper we make a step forward towards a more realistic assessment of the limited feedback problem by introducing an improved metric for the performance evaluation which better captures the throughput degradation. We find the relevant scaling laws (lower and upper bounds) and how that they are different from existing ones. Moreover, we provide a robust iterative interference alignment algorithm and corresponding feedback strategies achieving the obtained scaling laws. The main idea is that instead of sending the complete channel matrix each user fixes a receive filter and feeds back a quantized version of the effective channel. Finally we underline our findings with simulations for the proposed system.

cs.IT↗

arXiv2014

A Stability Result for Sparse Convolutions

We will establish in this note a stability result for sparse convolutions on torsion-free additive (discrete) abelian groups. Sparse convolutions on torsion-free groups are free of cancellations and hence admit stability, i.e. injectivity with a universal lower bound $α=α(s,f)$, only depending on the cardinality $s$ and $f$ of the supports of both input sequences. More precisely, we show that $α$ depends only on $s$ and $f$ and not on the ambient dimension. This statement follows from a reduction argument which involves a compression into a small set preserving the additive structure of the supports.

cs.DM↗

arXiv2013

Stable Recovery from the Magnitude of Symmetrized Fourier Measurements

In this note we show that stable recovery of complex-valued signals $x\in\mathbb{C}^n$ up to global sign can be achieved from the magnitudes of $4n-1$ Fourier measurements when a certain "symmetrization and zero-padding" is performed before measurement ($4n-3$ is possible in certain cases). For real signals, symmetrization itself is linear and therefore our result is in this case a statement on uniform phase retrieval. Since complex conjugation is involved, such measurement procedure is not complex-linear but recovery is still possible from magnitudes of linear measurements on, for example, $(\Re(x),\Im(x))$.

cs.IT↗

arXiv2013

Nearly Doubling the Throughput of Multiuser MIMO Systems Using Codebook Tailored Limited Feedback Protocol

We present and analyze a new robust feedback and transmit strategy for multiuser MIMO downlink communication systems, termed Rate Approximation (RA). RA combines the flexibility and robustness needed for reliable communications with the user terminal under a limited feedback constraint. It responds to two important observations. First, it is not so significant to approximate the channel but rather the rate, such that the optimal scheduling decision can be mimicked at the base station. Second, a fixed transmit codebook at the transmitter is often better when therefore the channel state information is more accurate. In the RA scheme the transmit and feedback codebook are separated and user rates are delivered to the base station subject to a controlled uniform error. The scheme is analyzed and proved to have better performance below a certain interference plus noise margin and better behavior than the classical Jindal formula. LTE system simulations sustain the analytic results showing performance gains of up to 50% or 70% compared to zeroforcing when using multiple antennas at the base station and multiple antennas or a single antenna at the terminals, respectively. A new feedback protocol is developed which inherently considers the transmit codebook and which is able to deal with the complexity issue at the terminal.

cs.IT↗

arXiv2012

Compressed Sensing on the Image of Bilinear Maps

For several communication models, the dispersive part of a communication channel is described by a bilinear operation $T$ between the possible sets of input signals and channel parameters. The received channel output has then to be identified from the image $T(X,Y)$ of the input signal difference sets $X$ and the channel state sets $Y$. The main goal in this contribution is to characterize the compressibility of $T(X,Y)$ with respect to an ambient dimension $N$. In this paper we show that a restricted norm multiplicativity of $T$ on all canonical subspaces $X$ and $Y$ with dimension $S$ resp. $F$ is sufficient for the reconstruction of output signals with an overwhelming probability from $\mathcal{O}((S+F)\log N)$ random sub-Gaussian measurements.

cs.IT↗

arXiv2011

Approximation of Löwdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultrawideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Per-Olov Löwdin. Our objective is to obtain a set of N orthogonal (Löwdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate Löwdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation. We show that the centered ALO and Löwdin pulses converge pointwise to the same Nyquist pulse as N tends to infinity. The set of translates of the Nyquist pulse forms an orthonormal basis or the shift-invariant space generated by the initial spectral optimal pulse. The ALO transform provides a closed-form approximation of the Löwdin transform, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant spaces. Finally we develop a connection between our results and wavelet and frame theory.

cs.IT↗

arXiv2011

On the Szegö-Asymptotics for Doubly-Dispersive Gaussian Channels

We consider the time-continuous doubly-dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this result is a new Szegö formula for certain pseudo-differential operators. The formula justifies the water-filling principle along time and frequency in terms of the time--continuous time-varying transfer function (the symbol).

cs.IT↗

arXiv2009

Pulse Shaping, Localization and the Approximate Eigenstructure of LTV Channels

In this article we show the relation between the theory of pulse shaping for WSSUS channels and the notion of approximate eigenstructure for time-varying channels. We consider pulse shaping for a general signaling scheme, called Weyl-Heisenberg signaling, which includes OFDM with cyclic prefix and OFDM/OQAM. The pulse design problem in the view of optimal WSSUS--averaged SINR is an interplay between localization and "orthogonality". The localization problem itself can be expressed in terms of eigenvalues of localization operators and is intimately connected to the concept of approximate eigenstructure of LTV channel operators. In fact, on the L_2-level both are equivalent as we will show. The concept of "orthogonality" in turn can be related to notion of tight frames. The right balance between these two sides is still an open problem. However, several statements on achievable values of certain localization measures and fundamental limits on SINR can already be made as will be shown in the paper.

cs.IT↗

arXiv2008

On the Approximate Eigenstructure of Time-Varying Channels

In this article we consider the approximate description of doubly--dispersive channels by its symbol. We focus on channel operators with compactly supported spreading, which are widely used to represent fast fading multipath communication channels. The concept of approximate eigenstructure is introduced, which measures the accuracy E_p of the approximation of the channel operation as a pure multiplication in a given L_p-norm. Two variants of such an approximate Weyl symbol calculus are studied, which have important applications in several models for time--varying mobile channels. Typically, such channels have random spreading functions (inverse Weyl transform) defined on a common support U of finite non--zero size such that approximate eigenstructure has to be measured with respect to certain norms of the spreading process. We derive several explicit relations to the size |U| of the support. We show that the characterization of the ratio of E_p to some L_q-norm of the spreading function is related to weighted norms of ambiguity and Wigner functions. We present the connection to localization operators and give new bounds on the ability of localization of ambiguity functions and Wigner functions in U. Our analysis generalizes and improves recent results for the case p=2 and q=1.

cs.IT↗

arXiv2007

Spin conductivity in almost integrable spin chains

The spin conductivity in the integrable spin-1/2 XXZ-chain is known to be infinite at finite temperatures T for anisotropies -1 < Delta < 1. Perturbations which break integrability, e.g. a next-nearest neighbor coupling J', render the conductivity finite. We construct numerically a non-local conserved operator J_parallel which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small J'. This allows us to obtain a lower bound for the spin conductivity sigma_s >= c(T) / J'^2, where c(T) is finite for J' to 0. We discuss the implication of our result for the general question how non-local conservation laws affect transport properties.

cond-mat.str-el↗

arXiv2007

Lower bounds for the conductivities of correlated quantum systems

We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.

cond-mat.str-el↗

arXiv2007

Approximate Eigenstructure of LTV Channels with Compactly Supported Spreading

In this article we obtain estimates on the approximate eigenstructure of channels with a spreading function supported only on a set of finite measure $|U|$.Because in typical application like wireless communication the spreading function is a random process corresponding to a random Hilbert--Schmidt channel operator $\BH$ we measure this approximation in terms of the ratio of the $p$--norm of the deviation from variants of the Weyl symbol calculus to the $a$--norm of the spreading function itself. This generalizes recent results obtained for the case $p=2$ and $a=1$. We provide a general approach to this topic and consider then operators with $|U|<\infty$ in more detail. We show the relation to pulse shaping and weighted norms of ambiguity functions. Finally we derive several necessary conditions on $|U|$, such that the approximation error is below certain levels.

cs.IT↗

arXiv2007

The WSSUS Pulse Design Problem in Multicarrier Transmission

Optimal link adaption to the scattering function of wide sense stationary uncorrelated mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission such link adaption is performed by pulse shaping, i.e. by properly adjusting the transmit and receive filters. For example pulse shaped Offset--QAM systems have been recently shown to have superior performance over standard cyclic prefix OFDM (while operating at higher spectral efficiency).In this paper we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so-called Weyl--Heisenberg or Gabor signaling with respect to the scattering function of the WSSUS channel. In our framework the pulse shape optimization problem is translated to an optimization problem over trace class operators which in turn is related to fidelity optimization in quantum information processing. By convexity relaxation the problem is shown to be equivalent to a \emph{convex constraint quasi-convex maximization problem} thereby revealing the non-convex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization providing applicable results even for large--scale problem constellations. We show that with transmitter-side knowledge of the channel statistics a gain of $3 - 6$dB in $\SINR$ can be expected.

cs.IT↗

arXiv2006

Weighted Norms of Ambiguity Functions and Wigner Distributions

In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in wide-sense stationary uncorrelated scattering channels for example it is a key step to find the optimal waveforms for a given scattering statistics which is a problem also well known in radar and sonar waveform optimizations. The same situation arises in quantum information processing and optical communication when optimizing pure quantum states for communicating in bosonic quantum channels, i.e. find optimal channel input states maximizing the pure state channel fidelity. Due to the non-convex nature of this problem the optimum and the maximizers itself are in general difficult find, numerically and analytically. Therefore upper bounds on the achievable performance are important which will be provided by this contribution. Based on a result due to E. Lieb, the main theorem states a new upper bound which is independent of the waveforms and becomes tight only for Gaussian weights and waveforms. A discussion of this particular important case, which tighten recent results on Gaussian quantum fidelity and coherent states, will be given. Another bound is presented for the case where scattering is determined only by some arbitrary region in phase space.

cs.IT↗

arXiv2006

Precoding for 2x2 Doubly-Dispersive WSSUS Channels

Optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission such link adaption is performed by pulse shaping which in turn is equivalent to precoding with respect to the second order channel statistics. In the present framework a translation of the precoder optimization problem into an optimization problem over trace class operators is used. This problem which is also well-known in the context of quantum information theory is unsolved in general due to its non-convex nature. However in very low dimension the problem formulation reveals an additional analytic structure which again admits the solution to the optimal precoder and multiplexing scheme. Hence, in this contribution the analytic solution of the problem for the 2x2 doubly--dispersive WSSUS channel is presented.

cs.IT↗