18,247 research outputs found
On optimum parameter modulation-estimation from a large deviations perspective
We consider the problem of jointly optimum modulation and estimation of a
real-valued random parameter, conveyed over an additive white Gaussian noise
(AWGN) channel, where the performance metric is the large deviations behavior
of the estimator, namely, the exponential decay rate (as a function of the
observation time) of the probability that the estimation error would exceed a
certain threshold. Our basic result is in providing an exact characterization
of the fastest achievable exponential decay rate, among all possible
modulator-estimator (transmitter-receiver) pairs, where the modulator is
limited only in the signal power, but not in bandwidth. This exponential rate
turns out to be given by the reliability function of the AWGN channel. We also
discuss several ways to achieve this optimum performance, and one of them is
based on quantization of the parameter, followed by optimum channel coding and
modulation, which gives rise to a separation-based transmitter, if one views
this setting from the perspective of joint source-channel coding. This is in
spite of the fact that, in general, when error exponents are considered, the
source-channel separation theorem does not hold true. We also discuss several
observations, modifications and extensions of this result in several
directions, including other channels, and the case of multidimensional
parameter vectors. One of our findings concerning the latter, is that there is
an abrupt threshold effect in the dimensionality of the parameter vector: below
a certain critical dimension, the probability of excess estimation error may
still decay exponentially, but beyond this value, it must converge to unity.Comment: 26 pages; Submitted to the IEEE Transactions on Information Theor
Outage analysis of superposition modulation aided network coded cooperation in the presence of network coding noise
We consider a network, where multiple sourcedestination pairs communicate with the aid of a half-duplex relay node (RN), which adopts decode-forward (DF) relaying and superposition-modulation (SPM) for combining the signals transmitted by the source nodes (SNs) and then forwards the composite signal to all the destination nodes (DNs). Each DN extracts the signals transmitted by its own SN from the composite signal by subtracting the signals overheard from the unwanted SNs. We derive tight lower-bounds for the outage probability for transmission over Rayleigh fading channels and invoke diversity combining at the DNs, which is validated by simulation for both the symmetric and the asymmetric network configurations. For the high signal-to-noise ratio regime, we derive both an upperbound as well as a lower-bound for the outage performance and analyse the achievable diversity gain. It is revealed that a diversity order of 2 is achieved, regardless of the number of SN-DN pairs in the network. We also highlight the fact that the outage performance is dominated by the quality of the worst overheated link, because it contributes most substantially to the network coding noise. Finally, we use the lower bound for designing a relay selection scheme for the proposed SPM based network coded cooperative communication (SPM-NC-CC) system.<br/
Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees
This paper addresses the problem of ad hoc microphone array calibration where
only partial information about the distances between microphones is available.
We construct a matrix consisting of the pairwise distances and propose to
estimate the missing entries based on a novel Euclidean distance matrix
completion algorithm by alternative low-rank matrix completion and projection
onto the Euclidean distance space. This approach confines the recovered matrix
to the EDM cone at each iteration of the matrix completion algorithm. The
theoretical guarantees of the calibration performance are obtained considering
the random and locally structured missing entries as well as the measurement
noise on the known distances. This study elucidates the links between the
calibration error and the number of microphones along with the noise level and
the ratio of missing distances. Thorough experiments on real data recordings
and simulated setups are conducted to demonstrate these theoretical insights. A
significant improvement is achieved by the proposed Euclidean distance matrix
completion algorithm over the state-of-the-art techniques for ad hoc microphone
array calibration.Comment: In Press, available online, August 1, 2014.
http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal
Processing, 201
Interpolated-DFT-Based Fast and Accurate Amplitude and Phase Estimation for the Control of Power
The quality of energy produced in renewable energy systems has to be at the
high level specified by respective standards and directives. The estimation
accuracy of grid signal parameters is one of the most important factors
affecting this quality. This paper presents a method for a very fast and
accurate amplitude and phase grid signal estimation using the Fast Fourier
Transform procedure and maximum decay sidelobes windows. The most important
features of the method are the elimination of the impact associated with the
conjugate's component on the results and the straightforward implementation.
Moreover, the measurement time is very short - even far less than one period of
the grid signal. The influence of harmonics on the results is reduced by using
a bandpass prefilter. Even using a 40 dB FIR prefilter for the grid signal with
THD = 38%, SNR = 53 dB and a 20-30% slow decay exponential drift the maximum
error of the amplitude estimation is approximately 1% and approximately 0.085
rad of the phase estimation in a real-time DSP system for 512 samples. The
errors are smaller by several orders of magnitude for more accurate prefilters.Comment: in Metrology and Measurement Systems, 201
A Selective Review of Group Selection in High-Dimensional Models
Grouping structures arise naturally in many statistical modeling problems.
Several methods have been proposed for variable selection that respect grouping
structure in variables. Examples include the group LASSO and several concave
group selection methods. In this article, we give a selective review of group
selection concerning methodological developments, theoretical properties and
computational algorithms. We pay particular attention to group selection
methods involving concave penalties. We address both group selection and
bi-level selection methods. We describe several applications of these methods
in nonparametric additive models, semiparametric regression, seemingly
unrelated regressions, genomic data analysis and genome wide association
studies. We also highlight some issues that require further study.Comment: Published in at http://dx.doi.org/10.1214/12-STS392 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Atomic norm denoising with applications to line spectral estimation
Motivated by recent work on atomic norms in inverse problems, we propose a
new approach to line spectral estimation that provides theoretical guarantees
for the mean-squared-error (MSE) performance in the presence of noise and
without knowledge of the model order. We propose an abstract theory of
denoising with atomic norms and specialize this theory to provide a convex
optimization problem for estimating the frequencies and phases of a mixture of
complex exponentials. We show that the associated convex optimization problem
can be solved in polynomial time via semidefinite programming (SDP). We also
show that the SDP can be approximated by an l1-regularized least-squares
problem that achieves nearly the same error rate as the SDP but can scale to
much larger problems. We compare both SDP and l1-based approaches with
classical line spectral analysis methods and demonstrate that the SDP
outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix
Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in
the Proceedings of the 49th Annual Allerton Conference in September 2011.
Numerous numerical experiments added to this version in accordance with
suggestions by anonymous reviewer
- …