15,171 research outputs found
Near-optimal bounds for phase synchronization
The problem of phase synchronization is to estimate the phases (angles) of a
complex unit-modulus vector from their noisy pairwise relative measurements
, where is a complex-valued Gaussian random matrix.
The maximum likelihood estimator (MLE) is a solution to a unit-modulus
constrained quadratic programming problem, which is nonconvex. Existing works
have proposed polynomial-time algorithms such as a semidefinite relaxation
(SDP) approach or the generalized power method (GPM) to solve it. Numerical
experiments suggest both of these methods succeed with high probability for
up to , yet, existing analyses only
confirm this observation for up to . In this
paper, we bridge the gap, by proving SDP is tight for , and GPM converges to the global optimum under
the same regime. Moreover, we establish a linear convergence rate for GPM, and
derive a tighter bound for the MLE. A novel technique we develop
in this paper is to track (theoretically) closely related sequences of
iterates, in addition to the sequence of iterates GPM actually produces. As a
by-product, we obtain an perturbation bound for leading
eigenvectors. Our result also confirms intuitions that use techniques from
statistical mechanics.Comment: 34 pages, 1 figur
The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies
Capacity gains from transmitter and receiver cooperation are compared in a
relay network where the cooperating nodes are close together. Under
quasi-static phase fading, when all nodes have equal average transmit power
along with full channel state information (CSI), it is shown that transmitter
cooperation outperforms receiver cooperation, whereas the opposite is true when
power is optimally allocated among the cooperating nodes but only CSI at the
receiver (CSIR) is available. When the nodes have equal power with CSIR only,
cooperative schemes are shown to offer no capacity improvement over
non-cooperation under the same network power constraint. When the system is
under optimal power allocation with full CSI, the decode-and-forward
transmitter cooperation rate is close to its cut-set capacity upper bound, and
outperforms compress-and-forward receiver cooperation. Under fast Rayleigh
fading in the high SNR regime, similar conclusions follow. Cooperative systems
provide resilience to fading in channel magnitudes; however, capacity becomes
more sensitive to power allocation, and the cooperating nodes need to be closer
together for the decode-and-forward scheme to be capacity-achieving. Moreover,
to realize capacity improvement, full CSI is necessary in transmitter
cooperation, while in receiver cooperation optimal power allocation is
essential.Comment: Accepted for publication in IEEE Transactions on Wireless
Communication
On bounds and algorithms for frequency synchronization for collaborative communication systems
Cooperative diversity systems are wireless communication systems designed to
exploit cooperation among users to mitigate the effects of multipath fading. In
fairly general conditions, it has been shown that these systems can achieve the
diversity order of an equivalent MISO channel and, if the node geometry
permits, virtually the same outage probability can be achieved as that of the
equivalent MISO channel for a wide range of applicable SNR. However, much of
the prior analysis has been performed under the assumption of perfect timing
and frequency offset synchronization. In this paper, we derive the estimation
bounds and associated maximum likelihood estimators for frequency offset
estimation in a cooperative communication system. We show the benefit of
adaptively tuning the frequency of the relay node in order to reduce estimation
error at the destination. We also derive an efficient estimation algorithm,
based on the correlation sequence of the data, which has mean squared error
close to the Cramer-Rao Bound.Comment: Submitted to IEEE Transaction on Signal Processin
On recovery guarantees for angular synchronization
The angular synchronization problem of estimating a set of unknown angles
from their known noisy pairwise differences arises in various applications. It
can be reformulated as a optimization problem on graphs involving the graph
Laplacian matrix. We consider a general, weighted version of this problem,
where the impact of the noise differs between different pairs of entries and
some of the differences are erased completely; this version arises for example
in ptychography. We study two common approaches for solving this problem,
namely eigenvector relaxation and semidefinite convex relaxation. Although some
recovery guarantees are available for both methods, their performance is either
unsatisfying or restricted to the unweighted graphs. We close this gap,
deriving recovery guarantees for the weighted problem that are completely
analogous to the unweighted version.Comment: 20 pages, 5 figure
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Synchronization learning of coupled chaotic maps
We study the dynamics of an ensemble of globally coupled chaotic logistic
maps under the action of a learning algorithm aimed at driving the system from
incoherent collective evolution to a state of spontaneous full synchronization.
Numerical calculations reveal a sharp transition between regimes of
unsuccessful and successful learning as the algorithm stiffness grows. In the
regime of successful learning, an optimal value of the stiffness is found for
which the learning time is minimal
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