arXiv subjects

Weichao Zheng

Publications and source records attributed to Weichao Zheng.

5 recordsLinked to original sources

arXiv2026

Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimation

This paper addresses the problem of estimating the Hermitian Toeplitz covariance matrix under practical hardware constraints of sparse observations and coarse quantization. Within the triangular-dithered quantization framework, we propose an estimator called Toeplitz-projected sample covariance matrix (Q-TSCM) to compensate for the quantization-induced bias, together with its finite-bit counterpart termed the $2k$-bit Toeplitz-projected sample covariance matrix ($2k$-TSCM), obtained by truncating the pre-quantization observations. Under the complex Gaussian assumption, we derive non-asymptotic error bounds of the estimators that reveal a quadratic dependence on the quantization level and capture the effect of sparse sampling patterns through the so-called coverage coefficient. To further improve performance, we propose the quantized sparse and parametric approach (Q-SPA) based on a covariance-fitting criterion, which enforces additionally positive semidefiniteness at the cost of solving a semidefinite program. Numerical experiments are presented that corroborate our theoretical findings and demonstrate the effectiveness of the proposed estimators in the application to direction-of-arrival estimation.

eess.SP↗

arXiv2026

Deterministic Cramer-Rao Bounds for Coherent Direction-of-Arrival Estimation: Rank Information Versus Coherence Structure

Direction-of-arrival (DOA) estimation is a fundamental problem in array signal processing, for which the Cramer-Rao bound (CRB) serves as a standard performance benchmark under both stochastic and deterministic source models. In multipath environments, the source matrix is of low-rank and, more specifically, exhibits a within-group proportionality structure. Although stochastic CRBs for coherent DOA estimation have been studied, theoretical results for their deterministic counterparts remain limited. This paper aims to bridge this gap. We first derive a tangent-space condition characterizing when structural constraints on the source matrix can strictly reduce the frequency CRB. We then prove that, for uniform linear arrays, imposing only the low-rankness of the source matrix leaves the frequency CRB unchanged, although it reduces the source-matrix CRB whenever the rank constraint is nontrivial, whereas fully exploiting the coherence structure yields a strictly smaller frequency CRB for almost all parameter values under mild conditions. These conclusions are further extended to analytic array manifolds and multidimensional DOA models, with componentwise results established for uniform planar arrays. The results demonstrate that performance gains in DOA estimation arise from the detailed coherence structure rather than low-rankness alone. Numerical experiments are finally provided to validate the theoretical findings.

eess.SP↗

arXiv2024

Experimental testing of the Prandtl-Tomlinson model: Molecular origin of rotational friction

Structural superlubricity, one of the most important concepts in modern tribology, has attracted lots of interest in both fundamental research and practical applications. However, the underlying model, known as the Prandtl-Tomlinson (PT) model, is oversimplified and not for real processes, despite its prevalence in frictional and structural lubricant studies. Here, with a realistic system, cholesteric liquid crystals, confined between two atomically smooth surfaces, we measure both the surface torque during rotational friction and the molecular rotation from the commensurate to incommensurate configuration at the onset of structural lubricity. Furthermore, by changing the surface potential or the strain, the Aubry transition is confirmed. The results agree well with the description by a quasi-one-dimensional version of the PT model and provide molecular evidence for rupture nucleation during static friction. Our study bridges the gap between theories and experiments and reinforces the connection between friction and fracture.

cond-mat.soft↗

arXiv2023

On the origin of permeative flows in cholesteric liquid crystals

Permeative flows, known for the explanation of the anomalous viscosity (10^5 Poise) in cholesterics at low shear rates, are still under debate due to the difficulty of experiments. Here we use the Surface Force Balance, in which uniform domains with regular circular defects are formed, to probe the forces generated by compression in the direction of the helical axis. At the quasi-static speed of the surface approach, the measured forces are shown to be elastic (not dissipative), arising from the twist elastic deformation when the planar anchoring at the walls is strong. A mechanism involving frictional surface torque under strong planar surface anchoring will be proposed. The results indicate that the strong resistance to flow observed, previously interpreted as an enormous apparent viscosity, may in fact originate from the intrinsic non-linear increase of elasticity when the molecules are rotated away from equilibrium. The system is found to store energy (the force is reversible), without dissipation, as long as the applied stress is below the threshold for nucleating new defects. Our study underpins the importance of boundary conditions that may dramatically change the rheology of other viscoelastic materials and sheds light on the rational design of strain-stiffening materials, nanomotors, and artificial muscles involving helical architectures.

cond-mat.soft↗

arXiv2023

Anchoring-mediated stick-slip winding of cholesteric liquid crystals

The stick-slip phenomenon widely exists in contact mechanics, from the macroscale to the nanoscale. During cholesteric-nematic unwinding by external fields, there is controversy regarding the role of planar surface anchoring, which may induce discontinuous stick-slip behaviors despite the well-known continuous transitions observed in past experiments. Here, we observe three regimes, namely constrained, stick-slip, and sliding-slip, under mechanical winding with different anchoring conditions, and measure the responded forces by the Surface Force Balance. These behaviors result from a balance of cholesteric elastic torque and surface torque, reminiscent of the slip morphology on frictional substrates [T. G. Sano et al., Phys. Rev. Lett. 118, 178001 (2017)], and provide evidence of dynamics in static rotational friction.

cond-mat.soft↗