26 research outputs found
Crystallization in large wireless networks
We analyze fading interference relay networks where M single-antenna
source-destination terminal pairs communicate concurrently and in the same
frequency band through a set of K single-antenna relays using half-duplex
two-hop relaying. Assuming that the relays have channel state information
(CSI), it is shown that in the large-M limit, provided K grows fast enough as a
function of M, the network "decouples" in the sense that the individual
source-destination terminal pair capacities are strictly positive. The
corresponding required rate of growth of K as a function of M is found to be
sufficient to also make the individual source-destination fading links converge
to nonfading links. We say that the network "crystallizes" as it breaks up into
a set of effectively isolated "wires in the air". A large-deviations analysis
is performed to characterize the "crystallization" rate, i.e., the rate (as a
function of M,K) at which the decoupled links converge to nonfading links. In
the course of this analysis, we develop a new technique for characterizing the
large-deviations behavior of certain sums of dependent random variables. For
the case of no CSI at the relay level, assuming amplify-and-forward relaying,
we compute the per source-destination terminal pair capacity for M,K converging
to infinity, with K/M staying fixed, using tools from large random matrix
theory.Comment: 30 pages, 6 figures, submitted to journal IEEE Transactions on
Information Theor
Super-Resolution of Positive Sources: the Discrete Setup
In single-molecule microscopy it is necessary to locate with high precision
point sources from noisy observations of the spectrum of the signal at
frequencies capped by , which is just about the frequency of natural
light. This paper rigorously establishes that this super-resolution problem can
be solved via linear programming in a stable manner. We prove that the quality
of the reconstruction crucially depends on the Rayleigh regularity of the
support of the signal; that is, on the maximum number of sources that can occur
within a square of side length about . The theoretical performance
guarantee is complemented with a converse result showing that our simple convex
program convex is nearly optimal. Finally, numerical experiments illustrate our
methods.Comment: 31 page, 7 figure
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
On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity
The noncoherent capacity of stationary discrete-time fading channels is known
to be very sensitive to the fine details of the channel model. More
specifically, the measure of the support of the fading-process power spectral
density (PSD) determines if noncoherent capacity grows logarithmically in SNR
or slower than logarithmically. Such a result is unsatisfactory from an
engineering point of view, as the support of the PSD cannot be determined
through measurements. The aim of this paper is to assess whether, for general
continuous-time Rayleigh-fading channels, this sensitivity has a noticeable
impact on capacity at SNR values of practical interest.
To this end, we consider the general class of band-limited continuous-time
Rayleigh-fading channels that satisfy the wide-sense stationary
uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread.
We show that, for all SNR values of practical interest, the noncoherent
capacity of every channel in this class is close to the capacity of an AWGN
channel with the same SNR and bandwidth, independently of the measure of the
support of the scattering function (the two-dimensional channel PSD). Our
result is based on a lower bound on noncoherent capacity, which is built on a
discretization of the channel input-output relation induced by projecting onto
Weyl-Heisenberg (WH) sets. This approach is interesting in its own right as it
yields a mathematically tractable way of dealing with the mutual information
between certain continuous-time random signals.Comment: final versio
On the Sensitivity of Noncoherent Capacity to the Channel Model
The noncoherent capacity of stationary discrete-time fading channels is known
to be very sensitive to the fine details of the channel model. More
specifically, the measure of the set of harmonics where the power spectral
density of the fading process is nonzero determines if capacity grows
logarithmically in SNR or slower than logarithmically. An engineering-relevant
problem is to characterize the SNR value at which this sensitivity starts to
matter.
In this paper, we consider the general class of continuous-time
Rayleigh-fading channels that satisfy the wide-sense stationary
uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread.
For this class of channels, we show that the noncoherent capacity is close to
the AWGN capacity for all SNR values of practical interest, independently of
whether the scattering function is compactly supported or not. As a byproduct
of our analysis, we obtain an information-theoretic pulse-design criterion for
orthogonal frequency-division multiplexing systems.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2009, Seoul, Kore
Region-of-Interest Prioritised Sampling for Constrained Autonomous Exploration Systems
Goal oriented autonomous operation of space rovers has been known to increase
scientific output of a mission. In this work we present an algorithm, called
the RoI Prioritised Sampling (RPS), that prioritises Region-of-Interests (RoIs)
in an exploration scenario in order to utilise the limited resources of the
imaging instrument on the rover effectively. This prioritisation is based on an
estimator that evaluates the change in information content at consecutive
spatial scales of the RoIs without calculating the finer scale reconstruction.
The estimator, called the Refinement Indicator (RI), is motivated and derived.
Multi-scale acquisition approaches, based on classical and multilevel
compressed sensing, with respect to the single pixel camera architecture are
discussed. The performance of the algorithm is verified on remote sensing
images and compared with the state-of-the-art multi-resolution reconstruction
algorithms. At the considered sub-sampling rates the RPS is shown to better
utilise the system resources for reconstructing the RoIs