相关论文: Functional Properties of the Ziv-Zakai bound with …
This paper explores Bayesian lower bounds on the minimum mean squared error (MMSE) that belong to the Ziv-Zakai (ZZ) family. The ZZ technique relies on connecting the bound to an M-ary hypothesis testing problem. Three versions of the ZZ…
This paper derives a Ziv-Zakai Bound (ZZB) on the Mean Squared Error (MSE) for Direction-of-Arrival (DoA) estimation in co-located Multiple-Input Multiple-Output (MIMO) radar systems and provides closed-form expressions that hold for…
In the highly non-Gaussian regime, the quantum Ziv-Zakai bound (QZZB) provides a lower bound on the available precision, demonstrating the better performance compared with the quantum Cram\'er-Rao bound. However, evaluating the impact of a…
Lower bounds on the mean square error (MSE) play an important role in evaluating the direction-of-arrival (DOA) estimation performance. Among numerous bounds for DOA estimation, the local Cramer-Rao bound (CRB) is only tight asymptotically.…
In parameter estimation, assumptions about the model are typically considered which allow us to build optimal estimation methods under many statistical senses. However, it is usually the case where such models are inaccurately known or not…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the…
An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected…
The increasing carrier frequencies and growing physical dimensions of antenna arrays in modern wireless systems are driving renewed interest in localization and sensing under near-field conditions. In this paper, we analyze the Ziv-Zakai…
A fairly general class of Bayesian "large-error" lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized…
In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…
In this paper, new classes of lower bounds on the outage error probability and on the mean-square-error (MSE) in Bayesian parameter estimation are proposed. The minima of the h-outage error probability and the MSE are obtained by the…
I propose Ziv-Zakai-type lower bounds on the Bayesian error for estimating a parameter $\beta:\Theta \to \mathbb R$ when the parameter space $\Theta$ is general and $\beta(\theta)$ need not be a linear function of $\theta$.
This paper studies the minimum mean squared error (MMSE) of estimating $\mathbf{X} \in \mathbb{R}^d$ from the noisy observation $\mathbf{Y} \in \mathbb{R}^k$, under the assumption that the noise (i.e., $\mathbf{Y}|\mathbf{X}$) is a member…
Location-awareness is essential in various wireless applications. The capability of performing precise ranging is substantial in achieving high-accuracy localization. Due to the notorious ambiguity phenomenon, optimal ranging waveforms…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…