18 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
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.
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
Multipath Parameter Estimation from OFDM Signals in Mobile Channels
We study multipath parameter estimation from orthogonal frequency division
multiplex signals transmitted over doubly dispersive mobile radio channels. We
are interested in cases where the transmission is long enough to suffer time
selectivity, but short enough such that the time variation can be accurately
modeled as depending only on per-tap linear phase variations due to Doppler
effects. We therefore concentrate on the estimation of the complex gain, delay
and Doppler offset of each tap of the multipath channel impulse response. We
show that the frequency domain channel coefficients for an entire packet can be
expressed as the superimposition of two-dimensional complex sinusoids. The
maximum likelihood estimate requires solution of a multidimensional non-linear
least squares problem, which is computationally infeasible in practice. We
therefore propose a low complexity suboptimal solution based on iterative
successive and parallel cancellation. First, initial delay/Doppler estimates
are obtained via successive cancellation. These estimates are then refined
using an iterative parallel cancellation procedure. We demonstrate via Monte
Carlo simulations that the root mean squared error statistics of our estimator
are very close to the Cramer-Rao lower bound of a single two-dimensional
sinusoid in Gaussian noise.Comment: Submitted to IEEE Transactions on Wireless Communications (26 pages,
9 figures and 3 tables
Nouvelles formes d'ondes par paquets d'ondelettes pour les modulations multiporteuses
La qualité d'une transmission multiporteuses dépend directement des formes d'onde modulantes utilisées. Dans cet article, la Wavelet Packet Modulation (WPM) est appliquée aux communications sans fil et une nouvelle modulation est proposée qui utilise les ondelettes complexes. Nous montrons que, pour une transmission à travers un canal multi-trajets, l'utilisation des ondelettes complexes permet d'améliorer l'utilisation des ondelettes réelles. Nous montrons également que l'utilisation des ondelettes permet de réduire considérablement les fluctuations d'enveloppe du signal transmis. Les performances de la WPM sont comparées à celle de la modulation OFDM
Frequency Diversity in Mode-Division Multiplexing Systems
In the regime of strong mode coupling, the modal gains and losses and the
modal group delays of a multimode fiber are known to have well-defined
statistical properties. In mode-division multiplexing, mode-dependent gains and
losses are known to cause fluctuations in the channel capacity, so that the
capacity at finite outage probability can be substantially lower than the
average capacity. Mode-dependent gains and losses, when frequency-dependent,
have a coherence bandwidth that is inversely proportional to the modal group
delay spread. When mode-division-multiplexed signals occupy a bandwidth far
larger than the coherence bandwidth, the mode-dependent gains and losses are
averaged over frequency, causing the outage capacity to approach the average
capacity. The difference between the average and outage capacities is found to
be inversely proportional to the square-root of a diversity order that is given
approximately by the ratio of the signal bandwidth to the coherence bandwidth.Comment: 8 pages, 6 figure