arXiv subjects

Shafayat Abrar

Publications and source records attributed to Shafayat Abrar.

6 recordsLinked to original sources

arXiv2026

Blind Adaptive Equalization in Additive Impulsive Noise Using the Logarithmic Product Fractional-Moment (LP-FM) Criterion

The blind mitigation of inter-symbol interference in additive white impulsive noise modeled by a symmetric $\alpha$-stable (S$\alpha$S) distribution is investigated. A novel logarithmic product fractional-moment statistics (LP-FMS) criterion is proposed by combining complementary fractional-moment statistics with logarithmic normalization in a constrained optimization framework. Based on this criterion, a normalized blind equalization algorithm for symmetric alpha-stable noise (NBEA-SAS) is derived using stochastic gradient ascent with recursive fractional-moment estimation and Bussgang-consistent constrained adaptation. Simulation results for $64$-APSK signaling over fractionally spaced multipath microwave channels show that the proposed algorithm converges faster than FLOS-CMA, RAW-CMA, and NBEA-GG while achieving a comparable steady-state residual intersymbol interference floor under both moderately and highly impulsive S$\alpha$S noise conditions. The results demonstrate that the proposed LP-FMS criterion provides a robust framework for blind adaptive equalization in impulsive noise environments.

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arXiv2026

Design and Analysis of a Higher-Order Enhanced Phase-Locked Loop via the Ahmadi-Chaudhry-Zhang Newton Framework

The enhanced phase-locked loop (EPLL) is widely used in power systems to estimate the amplitude, phase, and frequency of sinusoidal voltages. Existing EPLL formulations are primarily derived from first- or second-order optimization methods, which may exhibit slow convergence, saddle-point attraction, or undesired oscillatory behavior. This paper presents a new higher-order EPLL based on the recently proposed Ahmadi-Chaudhry-Zhang (ACZ) higher-order Newton framework. Since the ACZ method was originally developed for scalar discrete-time optimization, a continuous-time higher-order Newton flow is formulated for adaptive systems. The resulting framework is then applied to the EPLL through a coordinate optimization strategy, whereby the higher-order Newton flow is applied only to the phase update, while the amplitude update retains its classical form because its cost function is exactly quadratic. The proposed autonomous system is analyzed through phase portraits and compared with the standard, Newton, and modified EPLL formulations. Phase-portrait analysis of the autonomous model shows that the proposed flow eliminates the spurious equilibria and saddle points present in the autonomous Newton EPLL, substantially enlarges the basin of attraction associated with the desired equilibrium, and shares several desirable convergence characteristics with the modified EPLL.

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arXiv2026

Analyzing Uncertainty in the Spatial Representation of the Kinematic Bicycle Model

Locating a vehicle and determining its orientation in an uncertain environment is a critical challenge in autonomous vehicle navigation and path planning. To address these challenges, a vehicle estimates its pose while depending on sensor data that offer noisy measurements. These uncertainties in pose quantities are expressed mathematically as a covariance matrix. The real-time computation of the covariance matrix is critical because of the non-linearity involved in the kinematic model. The challenge is thus to evaluate the evolution of the covariance matrix of a vehicle's discretized stochastic kinematics. The purpose of this study is to obtain a near-accurate evolution of the covariance matrix of the rear-wheel bicycle kinematic model under uncertainties in wheel displacement and steering angle. We used Taylor's series to linearize the nonlinear trigonometric functions and provided closed-form expectations of random variables with the required accuracy. Our analytical findings are in good agreement with those obtained from Monte-Carlo simulations. Our contribution is probably the first detailed closed-form presentation of the covariance matrix constituents of the vehicle under evaluation, which were previously reported either incorrectly or incompletely. These findings aid in identifying the potential and constraints of the discretized kinematic model as well as its stochastic analysis. The techniques presented here are useful for the simultaneous localization and odometry self-calibration of certain mobile robots and autonomous vehicles.

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arXiv2017

Adaptive Blind Sparse-Channel Equalization

In this article, a fractional-norm constrained blind adaptive algorithm is presented for sparse channel equalization. In essence, the algorithm improves on the minimization of the constant modulus (CM) criteria by adding a sparsity inducing $\ell_p$-norm penalty. Simulation results demonstrate that the proposed regularized equalizer exploits the inherent channel sparsity effectively and exhibits faster convergence compared to its counterparts.

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arXiv2017

Steepest Descent Multimodulus Algorithm for Blind Signal Retrieval in QAM Systems

We present steepest descent (SD) implementation of multimodulus algorithm (MMA2-2) for blind signal retrieval in digital communication systems. In comparison to stochastic approximate (gradient descent) realization, the proposed SD implementation of MMA2-2 equalizer mitigates inter-symbol interference with relatively smooth convergence and superior steady-state performance.

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arXiv2016

Higher-Degree Stochastic Integration Filtering

We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted multivariate integrals found in nonlinear Bayesian filtering. The superiority of the proposed scheme is demonstrated by comparing the performance of the proposed fifth-degree SIF against a number of existing stochastic, quasi-stochastic and cubature (Kalman) filters. The proposed filter is demonstrated to outperform existing filters in all cases.

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