arXiv subjects

Joseph Tabrikian

Publications and source records attributed to Joseph Tabrikian.

14 recordsLinked to original sources

arXiv2026

Revisiting the Misspecified Cram\'er-Rao Bound

Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound (MCRB) is a widely recognized mean-squared-error (MSE) lower bound for this case, which has originally been used to describe the asymptotic behavior of the misspecified maximum likelihood (MML) estimator. Despite its widespread use, the MCRB lacks a rigorous characterization of the class of estimators for which it is valid. In this paper, we revisit the theory of parameter estimation under model misspecification and re-examine the foundations of the MCRB. We first demonstrate these limitations and examine a naive version of the MCRB, which relies only on local misspecified unbiasedness. We show that this bound is generally not tight and may be unattainable. To obtain a meaningful bound, we develop a new derivation based on the concept of pointwise equivalent models. By maximizing the naive bound for these models, we recover the classical MCRB, now supported by a constructive derivation, an explicit characterization of the associated estimator class, and an equality condition. This formulation establishes a formal link between local unbiasedness conditions and achievable bounds, offering new insights into the MCRB structure and its relevance to practical estimators. Finally, we define the notion of an efficient misspecified estimator and show that if it exists, it is achieved by the MML estimator.

math.ST↗

arXiv2025

Tangential Velocity Estimation Using Near-Field Automotive Radar Model

This work investigates the problem of tangential velocity estimation in automotive radar systems, addressing the limitations of conventionally considered models. Conventional automotive radars are usually based on far-field models and estimate the target's range, radial velocity, and direction-of-arrival (DOA) but are not able to estimate the tangential component of the target 2-D velocity, which is a critical parameter for reliable perception of dynamic environments. To address this challenge, we introduce the near-field radar model, which considers various migration elements in range, radial velocity, and Doppler along time and space. Conventionally, these migration effects result in smearing of the likelihood function for estimating the target parameters. However, if the model is correctly specified, these migration effects are informative for tangential velocity estimation. We conduct an identifiability analysis for tangential velocity estimation using the Cramér-Rao bound and ambiguity function. The insights from this study motivate the use of a separated array configuration and the development of a computationally efficient maximum likelihood based algorithm designed to utilize target migrations for tangential velocity estimation, while maintaining practical computational complexity. In addition to tangential velocity estimation, the proposed algorithm mitigates likelihood smearing in range, radial velocity, and Doppler. Simulations validate the theoretical feasibility study, and evaluate the algorithms' performance in both single- and multi-target scenarios. The proposed approach improves the accuracy and reliability of automotive radars, enhancing situational awareness for advanced driver assistance systems and autonomous vehicles.

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arXiv2025

Model Selection via MCRB Optimization

In many estimation theory and statistical analysis problems, the true data model is unknown, or partially unknown. To describe the model generating the data, parameterized models of some degree are used. A question that arises is which model should be used to best approximate the true model, a.k.a. model selection. In the field of machine learning, it is encountered in the form of architecture types of neural networks, number of model parameters, etc. In this paper, we propose a new model selection criterion, based on the misspecified Cramer-Rao bound (MCRB) for mean-squared-error (MSE) performance. The criterion selects the model in which the bound on the estimated parameters MSE is the lowest, compared to other candidate models. Its goal is to minimize the MSE with-respect-to (w.r.t.) the model. The criterion is applied to the problems of direction-of-arrival (DOA) estimation under unknown clutter / interference, and spectrum estimation of auto-regressive (AR) model. It is shown to incorporate the bias-variance trade-off, and outperform the Akaike information criterion (AIC), finite-sample corrected AIC (AICc), and minimum description length (MDL) in terms of MSE performance.

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arXiv2025

MCRB for Parameter Estimation from One-Bit Quantized and Oversampled Measurements

One-bit quantization has garnered significant attention in recent years for various signal processing and communication applications. Estimating model parameters from one bit quantized data can be challenging, particularly when the quantization process is explicitly accounted for in the estimator. In many cases, the estimator disregards quantization effects, leading to model misspecification. Consequently, estimation errors arise from both quantization and misspecification. Traditional performance bounds, such as the Cramer-Rao bound (CRB), fail to capture the impact of misspecification on estimation performance. To address this limitation, we derive the misspecified CRB (MCRB) for parameter estimation in a quantized data model consisting of a signal component in additive Gaussian noise. We apply this bound to direction-of-arrival estimation using quantized measurements from a sensor array and to frequency estimation with oversampled quantized data. The simulations show that the MCRB is asymptotically achieved by the mean-squared-error of the misspecified maximum-likelihood estimator. Our results demonstrate that, unlike in finely quantized scenarios, oversampling can significantly enhance the estimation performance in the presence of misspecified one-bit quantized measurements.

eess.SP↗

arXiv2023

Asymptotically Tight Bayesian Cramér-Rao Bound

Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cramér-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB (BCRB) in the Bayesian framework. However, unlike the CRB, the BCRB is asymptotically unattainable in general, and its equality condition is restrictive. This paper introduces an extension of the Bobrovsky--Mayer-Wolf--Zakai class of bounds, also known as the weighted BCRB (WBCRB). The WBCRB is optimized by tuning the weighting function in the scalar case. Based on this result, we propose an asymptotically tight version of the bound called AT-BCRB. We prove that the AT-BCRB is asymptotically attained by the maximum {\it a-posteriori} probability (MAP) estimator. Furthermore, we extend the WBCRB and the AT-BCRB to the case of vector parameters. The proposed bounds are evaluated in several fundamental signal processing examples, such as variance estimation of white Gaussian process, direction-of-arrival estimation, and mean estimation of Gaussian process with unknown variance and prior statistical information. It is shown that unlike the BCRB, the proposed bounds are asymptotically attainable and coincide with the expected CRB (ECRB). The ECRB, which imposes uniformly unbiasedness, cannot serve as a valid lower bound in the Bayesian framework, while the proposed bounds are valid for any estimator.

cs.IT↗

arXiv2023

Barankin-Type Bound for Constrained Parameter Estimation

In constrained parameter estimation, the classical constrained Cramer-Rao bound (CCRB) and the recent Lehmann-unbiased CCRB (LU-CCRB) are lower bounds on the performance of mean-unbiased and Lehmann-unbiased estimators, respectively. Both the CCRB and the LU-CCRB require differentiability of the likelihood function, which can be a restrictive assumption. Additionally, these bounds are local bounds that are inappropriate for predicting the threshold phenomena of the constrained maximum likelihood (CML) estimator. The constrained Barankin-type bound (CBTB) is a nonlocal mean-squared-error (MSE) lower bound for constrained parameter estimation that does not require differentiability of the likelihood function. However, this bound requires a restrictive mean-unbiasedness condition in the constrained set. In this work, we propose the Lehmann-unbiased CBTB (LU-CBTB) on the weighted MSE (WMSE). This bound does not require differentiability of the likelihood function and assumes uniform Lehmann-unbiasedness, which is less restrictive than the CBTB uniform mean-unbiasedness. We show that the LU-CBTB is tighter than or equal to the LU-CCRB and coincides with the CBTB for linear constraints. For nonlinear constraints the LU-CBTB and the CBTB are different and the LU-CBTB can be a lower bound on the WMSE of constrained estimators in cases, where the CBTB is not. In the simulations, we consider direction-of-arrival estimation of an unknown constant modulus discrete signal. In this case, the likelihood function is not differentiable and constrained Cramer-Rao-type bounds do not exist, while CBTBs exist. It is shown that the LU-CBTB better predicts the CML estimator performance than the CBTB, since the CML estimator is Lehmann-unbiased but not mean-unbiased.

eess.SP↗

arXiv2023

Neural Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with a-priori unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.

eess.SP↗

arXiv2023

MCRB on DOA Estimation for Automotive MIMO Radar in the Presence of Multipath

Autonomous driving and advanced active safety features require accurate high-resolution sensing capabilities. Automotive radars are the key component of the vehicle sensing suit. However, when these radars operate in proximity to flat surfaces, such as roads and guardrails, they experience a multipath phenomenon that can degrade the accuracy of the direction-of-arrival (DOA) estimation. Presence of multipath leads to misspecification in the radar data model, resulting in estimation performance degradation, which cannot be reliably predicted by conventional performance bounds. In this paper, the misspecified Cramér-Rao bound (MCRB), which accounts for model misspecification, is derived for the problem of DOA estimation in the presence of multipath which is ignored by the estimator. Analytical relations between the MCRB and the Cramér-Rao bound are established, and the DOA estimation performance degradation due to multipath is investigated. The results show that the MCRB reliably predicts the asymptotic performance of the misspecified maximum-likelihood estimator and therefore, can serve as an efficient tool for automotive radar performance evaluation and system design.

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arXiv2023

Neural Network-Based Multi-Target Detection within Correlated Heavy-Tailed Clutter

This work addresses the problem of range-Doppler multiple target detection in a radar system in the presence of slow-time correlated and heavy-tailed distributed clutter. Conventional target detection algorithms assume Gaussian-distributed clutter, but their performance is significantly degraded in the presence of correlated heavy-tailed distributed clutter. Derivation of optimal detection algorithms with heavy-tailed distributed clutter is analytically intractable. Furthermore, the clutter distribution is frequently unknown. This work proposes a deep learning-based approach for multiple target detection in the range-Doppler domain. The proposed approach is based on a unified NN model to process the time-domain radar signal for a variety of signal-to-clutter-plus-noise ratios (SCNRs) and clutter distributions, simplifying the detector architecture and the neural network training procedure. The performance of the proposed approach is evaluated in various experiments using recorded radar echoes, and via simulations, it is shown that the proposed method outperforms the conventional cell-averaging constant false-alarm rate (CA-CFAR), the ordered-statistic CFAR (OS-CFAR), and the adaptive normalized matched-filter (ANMF) detectors in terms of probability of detection in the majority of tested SCNRs and clutter scenarios.

eess.SP↗

arXiv2018

Cramer-Rao Bound for Constrained Parameter Estimation Using Lehmann-Unbiasedness

The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained maximum likelihood (CML) estimator, in the non-asymptotic region these conditions are usually too strict and the commonly-used estimators, such as the CML estimator, do not satisfy them. Therefore, the CCRB may not be a lower bound on the MSE matrix of such estimators. In this paper, we propose a new definition for unbiasedness under constraints, denoted by C-unbiasedness, which is based on using Lehmann-unbiasedness with a weighted MSE (WMSE) risk and taking into account the parametric constraints. In addition to C-unbiasedness, a Cramer-Rao-type bound on the WMSE of C-unbiased estimators, denoted as Lehmann-unbiased CCRB (LU-CCRB), is derived. This bound is a scalar bound that depends on the chosen weighted combination of estimation errors. It is shown that C-unbiasedness is less restrictive than the CCRB unbiasedness conditions. Thus, the set of estimators that satisfy the CCRB unbiasedness conditions is a subset of the set of C-unbiased estimators and the proposed LU-CCRB may be an informative lower bound in cases where the corresponding CCRB is not. In the simulations, we examine linear and nonlinear estimation problems under nonlinear constraints in which the CML estimator is shown to be C-unbiased and the LU-CCRB is an informative lower bound on the WMSE, while the corresponding CCRB on the WMSE is not a lower bound and is not informative in the non-asymptotic region.

cs.IT↗

arXiv2018

Performance Analysis for Channel Estimation with 1-bit ADC and Unknown Quantization Threshold

In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with $1$-bit output resolution and an unknown quantization threshold is considered. Single-comparator ADCs are energy-efficient and can be operated at ultra-high sampling rates. For analysis of such systems, a fixed and known quantization threshold is usually assumed. In the symmetric case, i.e., zero hard-limiting offset, it is known that in the low signal-to-noise ratio (SNR) regime the signal processing performance degrades moderately by ${2}/π$ ($-1.96$ dB) when comparing to an ideal $\infty$-bit converter. Due to hardware imperfections, low-complexity $1$-bit ADCs will in practice exhibit an unknown threshold different from zero. Therefore, we study the accuracy which can be obtained with receive data processed by a hard-limiter with unknown quantization level by using asymptotically optimal channel estimation algorithms. To characterize the estimation performance of these nonlinear algorithms, we employ analytic error expressions for different setups while modeling the offset as a nuisance parameter. In the low SNR regime, we establish the necessary condition for a vanishing loss due to missing offset knowledge at the receiver. As an application, we consider the estimation of single-input single-output wireless channels with inter-symbol interference and validate our analysis by comparing the analytic and experimental performance of the studied estimation algorithms. Finally, we comment on the extension to multiple-input multiple-output channel models.

cs.IT↗

arXiv2016

Performance Analysis for Pilot-based 1-bit Channel Estimation with Unknown Quantization Threshold

Parameter estimation using quantized observations is of importance in many practical applications. Under a symmetric $1$-bit setup, consisting of a zero-threshold hard-limiter, it is well known that the large sample performance loss for low signal-to-noise ratios (SNRs) is moderate ($\frac{2}π$ or $-1.96$dB). This makes low-complexity analog-to-digital converters (ADCs) with $1$-bit resolution a promising solution for future wireless communications and signal processing devices. However, hardware imperfections and external effects introduce the quantizer with an unknown hard-limiting level different from zero. In this paper, the performance loss associated with pilot-based channel estimation, subject to an asymmetric hard limiter with unknown offset, is studied under two setups. The analysis is carried out via the Cramér-Rao lower bound (CRLB) and an expected CRLB for a setup with random parameter. Our findings show that the unknown threshold leads to an additional information loss, which vanishes for low SNR values or when the offset is close to zero.

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arXiv2010

General Classes of Lower Bounds on the Probability of Error in Multiple Hypothesis Testing

In this paper, two new classes of lower bounds on the probability of error for $m$-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion is usually not tractable. The new classes are derived using Holder's inequality and reverse Holder's inequality. The bounds in these classes provide good prediction of the minimum probability of error in multiple hypothesis testing. The new classes generalize and extend existing bounds and their relation to some existing upper bounds is presented. It is shown that the tightest bounds in these classes asymptotically coincide with the optimum probability of error provided by the MAP criterion for binary or multiple hypothesis testing problem. These bounds are compared with other existing lower bounds in several typical detection and classification problems in terms of tightness and computational complexity.

cs.IT↗

arXiv2010

Classes of lower bounds on outage error probability and MSE in Bayesian parameter estimation

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 generalized maximum a-posteriori probability and the minimum MSE (MMSE) estimators, respectively. However, computation of these estimators and their corresponding performance is usually not tractable and thus, lower bounds on these terms can be very useful for performance analysis. The proposed class of lower bounds on the outage error probability is derived using Holder's inequality. This class is utilized to derive a new class of Bayesian MSE bounds. It is shown that for unimodal symmetric conditional probability density functions (pdf) the tightest probability of outage error lower bound in the proposed class attains the minimum probability of outage error and the tightest MSE bound coincides with the MMSE performance. In addition, it is shown that the proposed MSE bounds are always tighter than the Ziv-Zakai lower bound (ZZLB). The proposed bounds are compared with other existing performance lower bounds via some examples.

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