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