8,990 research outputs found
Towards Dual-functional Radar-Communication Systems: Optimal Waveform Design
We focus on a dual-functional multi-input-multi-output (MIMO)
radar-communication (RadCom) system, where a single transmitter communicates
with downlink cellular users and detects radar targets simultaneously. Several
design criteria are considered for minimizing the downlink multi-user
interference. First, we consider both the omnidirectional and directional
beampattern design problems, where the closed-form globally optimal solutions
are obtained. Based on these waveforms, we further consider a weighted
optimization to enable a flexible trade-off between radar and communications
performance and introduce a low-complexity algorithm. The computational costs
of the above three designs are shown to be similar to the conventional
zero-forcing (ZF) precoding. Moreover, to address the more practical constant
modulus waveform design problem, we propose a branch-and-bound algorithm that
obtains a globally optimal solution and derive its worst-case complexity as a
function of the maximum iteration number. Finally, we assess the effectiveness
of the proposed waveform design approaches by numerical results.Comment: 13 pages, 10 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
Geometric Properties of Isostables and Basins of Attraction of Monotone Systems
In this paper, we study geometric properties of basins of attraction of
monotone systems. Our results are based on a combination of monotone systems
theory and spectral operator theory. We exploit the framework of the Koopman
operator, which provides a linear infinite-dimensional description of nonlinear
dynamical systems and spectral operator-theoretic notions such as eigenvalues
and eigenfunctions. The sublevel sets of the dominant eigenfunction form a
family of nested forward-invariant sets and the basin of attraction is the
largest of these sets. The boundaries of these sets, called isostables, allow
studying temporal properties of the system. Our first observation is that the
dominant eigenfunction is increasing in every variable in the case of monotone
systems. This is a strong geometric property which simplifies the computation
of isostables. We also show how variations in basins of attraction can be
bounded under parametric uncertainty in the vector field of monotone systems.
Finally, we study the properties of the parameter set for which a monotone
system is multistable. Our results are illustrated on several systems of two to
four dimensions.Comment: 12 pages, to appear in IEEE Transaction on Automatic Contro
Multireference Alignment using Semidefinite Programming
The multireference alignment problem consists of estimating a signal from
multiple noisy shifted observations. Inspired by existing Unique-Games
approximation algorithms, we provide a semidefinite program (SDP) based
relaxation which approximates the maximum likelihood estimator (MLE) for the
multireference alignment problem. Although we show that the MLE problem is
Unique-Games hard to approximate within any constant, we observe that our
poly-time approximation algorithm for the MLE appears to perform quite well in
typical instances, outperforming existing methods. In an attempt to explain
this behavior we provide stability guarantees for our SDP under a random noise
model on the observations. This case is more challenging to analyze than
traditional semi-random instances of Unique-Games: the noise model is on
vertices of a graph and translates into dependent noise on the edges.
Interestingly, we show that if certain positivity constraints in the SDP are
dropped, its solution becomes equivalent to performing phase correlation, a
popular method used for pairwise alignment in imaging applications. Finally, we
show how symmetry reduction techniques from matrix representation theory can
simplify the analysis and computation of the SDP, greatly decreasing its
computational cost
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