38 research outputs found
Identification of Parametric Underspread Linear Systems and Super-Resolution Radar
Identification of time-varying linear systems, which introduce both
time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task
in many engineering applications. This paper studies the problem of
identification of underspread linear systems (ULSs), whose responses lie within
a unit-area region in the delay Doppler space, by probing them with a known
input signal. It is shown that sufficiently-underspread parametric linear
systems, described by a finite set of delays and Doppler-shifts, are
identifiable from a single observation as long as the time bandwidth product of
the input signal is proportional to the square of the total number of delay
Doppler pairs in the system. In addition, an algorithm is developed that
enables identification of parametric ULSs from an input train of pulses in
polynomial time by exploiting recent results on sub-Nyquist sampling for time
delay estimation and classical results on recovery of frequencies from a sum of
complex exponentials. Finally, application of these results to super-resolution
target detection using radar is discussed. Specifically, it is shown that the
proposed procedure allows to distinguish between multiple targets with very
close proximity in the delay Doppler space, resulting in a resolution that
substantially exceeds that of standard matched-filtering based techniques
without introducing leakage effects inherent in recently proposed compressed
sensing-based radar methods.Comment: Revised version of a journal paper submitted to IEEE Trans. Signal
Processing: 30 pages, 17 figure
Density Criteria for the Identification of Linear Time-Varying Systems
This paper addresses the problem of identifying a linear time-varying (LTV)
system characterized by a (possibly infinite) discrete set of delays and
Doppler shifts. We prove that stable identifiability is possible if the upper
uniform Beurling density of the delay-Doppler support set is strictly smaller
than 1/2 and stable identifiability is impossible for densities strictly larger
than 1/2. The proof of this density theorem reveals an interesting relation
between LTV system identification and interpolation in the Bargmann-Fock space.
Finally, we introduce a subspace method for solving the system identification
problem at hand.Comment: IEEE International Symposium on Information Theory (ISIT), Hong Kong,
China, June 201
Super-Resolution Radar
In this paper we study the identification of a time-varying linear system
from its response to a known input signal. More specifically, we consider
systems whose response to the input signal is given by a weighted superposition
of delayed and Doppler shifted versions of the input. This problem arises in a
multitude of applications such as wireless communications and radar imaging.
Due to practical constraints, the input signal has finite bandwidth B, and the
received signal is observed over a finite time interval of length T only. This
gives rise to a delay and Doppler resolution of 1/B and 1/T. We show that this
resolution limit can be overcome, i.e., we can exactly recover the continuous
delay-Doppler pairs and the corresponding attenuation factors, by solving a
convex optimization problem. This result holds provided that the distance
between the delay-Doppler pairs is at least 2.37/B in time or 2.37/T in
frequency. Furthermore, this result allows the total number of delay-Doppler
pairs to be linear up to a log-factor in BT, the dimensionality of the response
of the system, and thereby the limit for identifiability. Stated differently,
we show that we can estimate the time-frequency components of a signal that is
S-sparse in the continuous dictionary of time-frequency shifts of a random
window function, from a number of measurements, that is linear up to a
log-factor in S.Comment: Revised versio
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
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Development and Demonstration of a TDOA-Based GNSS Interference Signal Localization System
Background theory, a reference design, and demonstration
results are given for a Global Navigation Satellite
System (GNSS) interference localization system comprising a
distributed radio-frequency sensor network that simultaneously
locates multiple interference sources by measuring their signals’
time difference of arrival (TDOA) between pairs of nodes in
the network. The end-to-end solution offered here draws from
previous work in single-emitter group delay estimation, very long
baseline interferometry, subspace-based estimation, radar, and
passive geolocation. Synchronization and automatic localization
of sensor nodes is achieved through a tightly-coupled receiver
architecture that enables phase-coherent and synchronous sampling
of the interference signals and so-called reference signals
which carry timing and positioning information. Signal and crosscorrelation
models are developed and implemented in a simulator.
Multiple-emitter subspace-based TDOA estimation techniques
are developed as well as emitter identification and localization
algorithms. Simulator performance is compared to the CramérRao
lower bound for single-emitter TDOA precision. Results are
given for a test exercise in which the system accurately locates
emitters broadcasting in the amateur radio band in Austin, TX.Aerospace Engineering and Engineering Mechanic
Spatial Compressive Sensing for MIMO Radar
We study compressive sensing in the spatial domain to achieve target
localization, specifically direction of arrival (DOA), using multiple-input
multiple-output (MIMO) radar. A sparse localization framework is proposed for a
MIMO array in which transmit and receive elements are placed at random. This
allows for a dramatic reduction in the number of elements needed, while still
attaining performance comparable to that of a filled (Nyquist) array. By
leveraging properties of structured random matrices, we develop a bound on the
coherence of the resulting measurement matrix, and obtain conditions under
which the measurement matrix satisfies the so-called isotropy property. The
coherence and isotropy concepts are used to establish uniform and non-uniform
recovery guarantees within the proposed spatial compressive sensing framework.
In particular, we show that non-uniform recovery is guaranteed if the product
of the number of transmit and receive elements, MN (which is also the number of
degrees of freedom), scales with K(log(G))^2, where K is the number of targets
and G is proportional to the array aperture and determines the angle
resolution. In contrast with a filled virtual MIMO array where the product MN
scales linearly with G, the logarithmic dependence on G in the proposed
framework supports the high-resolution provided by the virtual array aperture
while using a small number of MIMO radar elements. In the numerical results we
show that, in the proposed framework, compressive sensing recovery algorithms
are capable of better performance than classical methods, such as beamforming
and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin