159 research outputs found
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
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.
On Max-SINR Receiver for Hexagonal Multicarrier Transmission Over Doubly Dispersive Channel
In this paper, a novel receiver for Hexagonal Multicarrier Transmission (HMT)
system based on the maximizing Signal-to-Interference-plus-Noise Ratio
(Max-SINR) criterion is proposed. Theoretical analysis shows that the prototype
pulse of the proposed Max-SINR receiver should adapt to the root mean square
(RMS) delay spread of the doubly dispersive (DD) channel with exponential power
delay profile and U-shape Doppler spectrum. Simulation results show that the
proposed Max-SINR receiver outperforms traditional projection scheme and
obtains an approximation to the theoretical upper bound SINR performance within
the full range of channel spread factor. Meanwhile, the SINR performance of the
proposed prototype pulse is robust to the estimation error between the
estimated value and the real value of time delay spread.Comment: 6 pages. The paper has been published in Proc. IEEE GLOBECOM 2012.
Copyright transferred to IEEE. arXiv admin note: text overlap with
arXiv:1212.579
Max-SINR Receiver for HMCT Systems over Non-Stationary Doubly Dispersive Channel
In this paper, a maximizing Signal-to-Interference plus-Noise Ratio
(Max-SINR) receiver for Hexagonal Multicarrier Transmission (HMCT) system over
non-stationary doubly dispersive (NSDD) channel is proposed. The closed-form
timing offset expression of the prototype pulse for the proposed Max-SINR HMCT
receiver over NSDD channel is derived. Simulation results show that the
proposed Max-SINR receiver outperforms traditional projection scheme and
obtains an approximation to the theoretical upper bound SINR performance within
all the local stationarity regions (LSRs). Meanwhile, the SINR performance of
the proposed Max-SINR HMCT receiver is robust to the estimation error between
the estimated value and the real value of root mean square (RMS) delay spread.Comment: This paper has been accepted by URSI GASS 2014 and will be presented
in the proceeding of URSI GASS 201
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
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