2,325 research outputs found
Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels
Mobile communication channels are often modeled as linear time-varying
filters or, equivalently, as time-frequency integral operators with finite
support in time and frequency. Such a characterization inherently assumes the
signals are narrowband and may not be appropriate for wideband signals. In this
paper time-scale characterizations are examined that are useful in wideband
time-varying channels, for which a time-scale integral operator is physically
justifiable. A review of these time-frequency and time-scale characterizations
is presented. Both the time-frequency and time-scale integral operators have a
two-dimensional discrete characterization which motivates the design of
time-frequency or time-scale rake receivers. These receivers have taps for both
time and frequency (or time and scale) shifts of the transmitted signal. A
general theory of these characterizations which generates, as specific cases,
the discrete time-frequency and time-scale models is presented here. The
interpretation of these models, namely, that they can be seen to arise from
processing assumptions on the transmit and receive waveforms is discussed. Out
of this discussion a third model arises: a frequency-scale continuous channel
model with an associated discrete frequency-scale characterization.Comment: To appear in Communications in Information and Systems - special
issue in honor of Thomas Kailath's seventieth birthda
Sampling from a system-theoretic viewpoint: Part II - Noncausal solutions
This paper puts to use concepts and tools introduced in Part I to address a wide spectrum of noncausal sampling and reconstruction problems. Particularly, we follow the system-theoretic paradigm by using systems as signal generators to account for available information and system norms (L2 and L∞) as performance measures. The proposed optimization-based approach recovers many known solutions, derived hitherto by different methods, as special cases under different assumptions about acquisition or reconstructing devices (e.g., polynomial and exponential cardinal splines for fixed samplers and the Sampling Theorem and its modifications in the case when both sampler and interpolator are design parameters). We also derive new results, such as versions of the Sampling Theorem for downsampling and reconstruction from noisy measurements, the continuous-time invariance of a wide class of optimal sampling-and-reconstruction circuits, etcetera
On the Performance Limits of Pilot-Based Estimation of Bandlimited Frequency-Selective Communication Channels
In this paper the problem of assessing bounds on the accuracy of pilot-based
estimation of a bandlimited frequency selective communication channel is
tackled. Mean square error is taken as a figure of merit in channel estimation
and a tapped-delay line model is adopted to represent a continuous time channel
via a finite number of unknown parameters. This allows to derive some
properties of optimal waveforms for channel sounding and closed form Cramer-Rao
bounds
Cornerstones of Sampling of Operator Theory
This paper reviews some results on the identifiability of classes of
operators whose Kohn-Nirenberg symbols are band-limited (called band-limited
operators), which we refer to as sampling of operators. We trace the motivation
and history of the subject back to the original work of the third-named author
in the late 1950s and early 1960s, and to the innovations in spread-spectrum
communications that preceded that work. We give a brief overview of the NOMAC
(Noise Modulation and Correlation) and Rake receivers, which were early
implementations of spread-spectrum multi-path wireless communication systems.
We examine in detail the original proof of the third-named author
characterizing identifiability of channels in terms of the maximum time and
Doppler spread of the channel, and do the same for the subsequent
generalization of that work by Bello.
The mathematical limitations inherent in the proofs of Bello and the third
author are removed by using mathematical tools unavailable at the time. We
survey more recent advances in sampling of operators and discuss the
implications of the use of periodically-weighted delta-trains as identifiers
for operator classes that satisfy Bello's criterion for identifiability,
leading to new insights into the theory of finite-dimensional Gabor systems. We
present novel results on operator sampling in higher dimensions, and review
implications and generalizations of the results to stochastic operators, MIMO
systems, and operators with unknown spreading domains
Investigation of zero-crossings as information carriers
Analysis of bandlimited signal transmission by zero crossings of optimum signa
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
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