249 research outputs found
On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix
Polarity coincidence correlator (PCC), when used to estimate the covariance
matrix on an element-by-element basis, may not yield a positive semi-definite
(PSD) estimate. Devlin et al. [1], claimed that element-wise PCC is not
guaranteed to be PSD in dimensions p>3 for real signals. However, no
justification or proof was available on this issue. In this letter, it is
proved that for real signals with p<=3 and for complex signals with p<=2, a PSD
estimate is guaranteed. Counterexamples are presented for higher dimensions
which yield invalid covariance estimates.Comment: IEEE Signal Processing Letters, Volume 15, pp. 73-76, 200
Cramer-Rao bounds for source localization in shallow ocean with generalized Gaussian noise
Localization of underwater acoustic sources is a problem of great interest in the area of ocean acoustics. There exist several algorithms for source localization based on array signal processing.It is of interest to know the theoretical performance limits of these estimators. In this paper we develop expressions for the Cramer-Rao-Bound (CRB) on the variance of direction-of-arrival(DOA) and range-depth estimators of underwater acoustic sources in a shallow range-independent ocean for the case of generalized Gaussian noise. We then study the performance of some of the popular source localization techniques,through simulations, for DOA/range-depth estimation of underwater acoustic sources in shallow ocean by comparing the variance of the estimators with the corresponding CRBs
Near-far resistant CML propagation delay estimation and multi-user detection for asynchronous DS-CDMA systems
Multi-user receivers in asynchronous direct sequence code division multiple access (DS-CDMA) systems require the knowledge of several parameters such as timing delay between users. The goal of this work is to present a near-far resistant joint multi-user synchronization and detection algorithm for DS-CDMA systems. The solution is based on the conditional maximum likelihood (CML) estimation method (classically used in the context of sensor array processing) that leads to a fast convergence algorithm to estimate the time delays among users. At the same time the estimator implements the decorrelating detector, identifying the transmitted symbols for the different users.Peer ReviewedPostprint (published version
Cramer-Rao Bound for Sparse Signals Fitting the Low-Rank Model with Small Number of Parameters
In this paper, we consider signals with a low-rank covariance matrix which
reside in a low-dimensional subspace and can be written in terms of a finite
(small) number of parameters. Although such signals do not necessarily have a
sparse representation in a finite basis, they possess a sparse structure which
makes it possible to recover the signal from compressed measurements. We study
the statistical performance bound for parameter estimation in the low-rank
signal model from compressed measurements. Specifically, we derive the
Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number
of compressed samples needs to be larger than the number of sources for the
existence of an unbiased estimator with finite estimation variance. We further
consider the applications to direction-of-arrival (DOA) and spectral estimation
which fit into the low-rank signal model. We also investigate the effect of
compression on the CRB by considering numerical examples of the DOA estimation
scenario, and show how the CRB increases by increasing the compression or
equivalently reducing the number of compressed samples.Comment: 14 pages, 1 figure, Submitted to IEEE Signal Processing Letters on
December 201
Finite sample performance of linear least squares estimators under sub-Gaussian martingale difference noise
Linear Least Squares is a very well known technique for parameter estimation,
which is used even when sub-optimal, because of its very low computational
requirements and the fact that exact knowledge of the noise statistics is not
required. Surprisingly, bounding the probability of large errors with finitely
many samples has been left open, especially when dealing with correlated noise
with unknown covariance. In this paper we analyze the finite sample performance
of the linear least squares estimator under sub-Gaussian martingale difference
noise. In order to analyze this important question we used concentration of
measure bounds. When applying these bounds we obtained tight bounds on the tail
of the estimator's distribution. We show the fast exponential convergence of
the number of samples required to ensure a given accuracy with high
probability. We provide probability tail bounds on the estimation error's norm.
Our analysis method is simple and uses simple type bounds on the
estimation error. The tightness of the bounds is tested through simulation. The
proposed bounds make it possible to predict the number of samples required for
least squares estimation even when least squares is sub-optimal and used for
computational simplicity. The finite sample analysis of least squares models
with this general noise model is novel
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