9,351 research outputs found
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.Comment: 5 twocolumn pages,2 figures, accepted for 2006 IEEE International
Symposium on Information Theory, typos corrected, some additional cites,
legend in Fig.2 correcte
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.Comment: 6 pages, 2 figures, invited pape
On the Szeg\"o-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 Szeg\"o 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).Comment: 5 pages, to be presented at ISIT 2011, minor typos corrected,
references update
A Group-Theoretic Approach to the WSSUS Pulse Design Problem
We consider the pulse design problem in multicarrier transmission where the
pulse shapes are adapted to the second order statistics of the WSSUS channel.
Even though the problem has been addressed by many authors analytical insights
are rather limited. First we show that the problem is equivalent to the pure
state channel fidelity in quantum information theory. Next we present a new
approach where the original optimization functional is related to an eigenvalue
problem for a pseudo differential operator by utilizing unitary representations
of the Weyl--Heisenberg group.A local approximation of the operator for
underspread channels is derived which implicitly covers the concepts of pulse
scaling and optimal phase space displacement. The problem is reformulated as a
differential equation and the optimal pulses occur as eigenstates of the
harmonic oscillator Hamiltonian. Furthermore this operator--algebraic approach
is extended to provide exact solutions for different classes of scattering
environments.Comment: 5 pages, final version for 2005 IEEE International Symposium on
Information Theory; added references for section 2; corrected some typos;
added more detailed discussion on the relations to quantum information
theory; added some more references; added additional calculations as an
appendix; corrected typo in III.
Stable Recovery from the Magnitude of Symmetrized Fourier Measurements
In this note we show that stable recovery of complex-valued signals
up to global sign can be achieved from the magnitudes of
Fourier measurements when a certain "symmetrization and zero-padding" is
performed before measurement ( 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,
.Comment: 4 pages, will be submitted to ICASSP1
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