9 research outputs found
On the high-SNR conditional maximum-likelihood estimator full statistical characterization
International audienceIn the field of asymptotic performance characterization of the conditional maximum-likelihood (CML) estimator, asymptotic generally refers to either the number of samples or the signal-to-noise ratio (SNR) value. The first case has been already fully characterized, although the second case has been only partially investigated. Therefore, this correspondence aims to provide a sound proof of a result, i.e., asymptotic (in SNR) Gaussianity and efficiency of the CML estimator in the multiple parameters case, generally regarded as trivial but not so far demonstrated
Bounds for maximum likelihood regular and non-regular DoA estimation in K-distributed noise
We consider the problem of estimating the direction of arrival of a signal embedded in -distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information matrix (FIM) for complex elliptically distributed data, we provide a simple expression of the FIM with the two data sets framework. In the specific case of -distributed noise, we show that, under certain conditions, the FIM for the deterministic part of the model can be unbounded, while the FIM for the covariance part of the model is always bounded. In the general case of elliptical distributions, we provide a sufficient condition for unboundedness of the FIM. Accurate approximations of the FIM for -distributed noise are also derived when it is bounded. Additionally, the maximum likelihood estimator of the signal DoA and an approximated version are derived, assuming known covariance matrix: the latter is then estimated from secondary data using a conventional regularization technique. When the FIM is unbounded, an analysis of the estimators reveals a rate of convergence much faster than the usual . Simulations illustrate the different behaviors of the estimators, depending on the FIM being bounded or not
Statistics of the MLE and Approximate Upper and Lower Bounds - Part 2: Threshold Computation and Optimal Signal Design
Threshold and ambiguity phenomena are studied in Part 1 of this work where
approximations for the mean-squared-error (MSE) of the maximum likelihood
estimator are proposed using the method of interval estimation (MIE), and where
approximate upper and lower bounds are derived. In this part we consider
time-of-arrival estimation and we employ the MIE to derive closed-form
expressions of the begin-ambiguity, end-ambiguity and asymptotic
signal-to-noise ratio (SNR) thresholds with respect to some features of the
transmitted signal. Both baseband and passband pulses are considered. We prove
that the begin-ambiguity threshold depends only on the shape of the envelope of
the ACR, whereas the end-ambiguity and asymptotic thresholds only on the shape
of the ACR. We exploit the results on the begin-ambiguity and asymptotic
thresholds to optimize, with respect to the available SNR, the pulse that
achieves the minimum attainable MSE. The results of this paper are valid for
various estimation problems
On the high-SNR conditional maximum-likelihood estimator full statistical characterization
International audienceIn the field of asymptotic performance characterization of the conditional maximum-likelihood (CML) estimator, asymptotic generally refers to either the number of samples or the signal-to-noise ratio (SNR) value. The first case has been already fully characterized, although the second case has been only partially investigated. Therefore, this correspondence aims to provide a sound proof of a result, i.e., asymptotic (in SNR) Gaussianity and efficiency of the CML estimator in the multiple parameters case, generally regarded as trivial but not so far demonstrated
On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation
After decades of research in Direction of Arrival (DoA) estimation, today
Maximum Likelihood (ML) algorithms still provide the best performance in terms
of resolution capabilities. At the cost of a multidimensional search, ML
algorithms achieve a significant reduction of the outlier production mechanism
in the threshold region, where the number of snapshots per antenna and/or the
signal to noise ratio (SNR) are low. The objective of this paper is to
characterize the resolution capabilities of ML algorithms in the threshold
region. Both conditional and unconditional versions of the ML algorithms are
investigated in the asymptotic regime where both the number of antennas and the
number of snapshots are large but comparable in magnitude. By using random
matrix theory techniques, the finite dimensional distributions of both cost
functions are shown to be Gaussian distributed in this asymptotic regime, and a
closed form expression of the corresponding asymptotic covariance matrices is
provided. These results allow to characterize the asymptotic behavior of the
resolution probability, which is defined as the probability that the cost
function evaluated at the true DoAs is smaller than the values that it takes at
the positions of the other asymptotic local minima