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As a parametric polynomial curve family, B\'ezier curves are widely used in safe and smooth motion design of intelligent robotic systems from flying drones to autonomous vehicles to robotic manipulators. In such motion planning settings, the critical features of high-order B\'ezier curves such as curve length, distance-to-collision, maximum curvature/velocity/acceleration are either numerically computed at a high computational cost or inexactly approximated by discrete samples. To address these issues, in this paper we present a novel computationally efficient approach for adaptive approximation of high-order B\'ezier curves by multiple low-order B\'ezier segments at any desired level of accuracy that is specified in terms of a B\'ezier metric. Accordingly, we introduce a new B\'ezier degree reduction method, called parameterwise matching reduction, that approximates B\'ezier curves more accurately compared to the standard least squares and Taylor reduction methods. We also propose a new B\'ezier metric, called the maximum control-point distance, that can be computed analytically, has a strong equivalence relation with other existing B\'ezier metrics, and defines a geometric relative bound between B\'ezier curves. We provide extensive numerical evidence to demonstrate the effectiveness of our proposed B\'ezier approximation approach. As a rule of thumb, based on the degree-one matching reduction error, we conclude that an $n^\text{th}$-order B\'ezier curve can be accurately approximated by $3(n-1)$ quadratic and $6(n-1)$ linear B\'ezier segments, which is fundamental for B\'ezier discretization.

This paper considers device-free sensing in an orthogonal frequency division multiplexing (OFDM) cellular network to enable integrated sensing and communication (ISAC). A novel two-phase sensing framework is proposed to localize the passive targets that cannot transmit/receive reference signals to/from the base stations (BSs), where the ranges of the targets are estimated based on their reflected OFDM signals to the BSs in Phase I, and the location of each target is estimated based on its ranges to different BSs in Phase II. Specifically, in Phase I, we design a model-free range estimation approach by leveraging the OFDM channel estimation technique for determining the delay values of all the two-way BS-target-BS paths, which does not rely on any BS-target channel model. In Phase II, we reveal that ghost targets may be falsely detected in some cases as all the targets reflect the same signals to the BSs, which thus do not know how to match each estimated range with the right target. Interestingly, we show that the above data association issue is not a fundamental limitation for device-free sensing: under the ideal case of perfect range estimation in Phase I, the probability for ghost targets to exist is proved to be negligible when the targets are randomly located. Moreover, under the practical case of imperfect range estimation in Phase I, we propose an efficient algorithm for joint data association and target localization in Phase II. Numerical results show that our proposed two-phase framework can achieve very high accuracy in the localization of passive targets, which increases with the system bandwidth.

Integrated sensing and communication (ISAC) has been regarded as one of the most promising technologies for future wireless communications. However, the mutual interference in the communication radar coexistence system cannot be ignored. Inspired by the studies of reconfigurable intelligent surface (RIS), we propose a double-RIS-assisted coexistence system where two RISs are deployed for enhancing communication signals and suppressing mutual interference. We aim to jointly optimize the beamforming of RISs and radar to maximize communication performance while maintaining radar detection performance. The investigated problem is challenging, and thus we transform it into an equivalent but more tractable form by introducing auxiliary variables. Then, we propose a penalty dual decomposition (PDD)-based algorithm to solve the resultant problem. Moreover, we consider two special cases: the large radar transmit power scenario and the low radar transmit power scenario. For the former, we prove that the beamforming design is only determined by the communication channel and the corresponding optimal joint beamforming strategy can be obtained in closed-form. For the latter, we minimize the mutual interference via the block coordinate descent (BCD) method. By combining the solutions of these two cases, a low-complexity algorithm is also developed. Finally, simulation results show that both the PDD-based and low-complexity algorithms outperform benchmark algorithms.

In vehicular communications, reliable channel estimation is critical for the system performance due to the doubly-dispersive nature of vehicular channels. IEEE 802.11p standard allocates insufficient pilots for accurate channel tracking. Consequently, conventional IEEE 802.11p estimators suffer from a considerable performance degradation, especially in high mobility scenarios. Recently, deep learning (DL) techniques have been employed for IEEE 802.11p channel estimation. Nevertheless, these methods suffer either from performance degradation in very high mobility scenarios or from large computational complexity. In this paper, these limitations are solved using a long short term memory (LSTM)-based estimation. The proposed estimator employs an LSTM unit to estimate the channel, followed by temporal averaging (TA) processing as a noise alleviation technique. Moreover, the noise mitigation ratio is determined analytically, thus validating the TA processing ability in improving the overall performance. Simulation results reveal the performance superiority of the proposed schemes compared to recently proposed DL-based estimators, while recording a significant reduction in the computational complexity.

We propose a joint channel estimation and signal detection approach for the uplink non-orthogonal multiple access using unsupervised machine learning. We apply the Gaussian mixture model to cluster the received signals, and accordingly optimize the decision regions to enhance the symbol error rate (SER). We show that, when the received powers of the users are sufficiently different, the proposed clustering-based approach achieves an SER performance on a par with that of the conventional maximum-likelihood detector with full channel state information. However, unlike the proposed approach, the maximum-likelihood detector requires the transmission of a large number of pilot symbols to accurately estimate the channel. The accuracy of the utilized clustering algorithm depends on the number of the data points available at the receiver. Therefore, there exists a tradeoff between accuracy and block length. We provide a comprehensive performance analysis of the proposed approach as well as deriving a theoretical bound on its SER performance as a function of the block length. Our simulation results corroborate the effectiveness of the proposed approach and verify that the calculated theoretical bound can predict the SER performance of the proposed approach well.

Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for realizing future wireless systems. In this paper, we propose an ISAC processing framework relying on millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Specifically, we provide a compressed sampling (CS) perspective to facilitate ISAC processing, which can not only recover the large-scale channel state information or/and radar imaging information, but also significantly reduce pilot overhead. First, an energy-efficient widely spaced array (WSA) architecture is tailored for the radar receiver, which enhances the angular resolution of radar sensing at the cost of angular ambiguity. Then, we propose an ISAC frame structure for time-variant ISAC systems considering different timescales. The pilot waveforms are judiciously designed by taking into account both CS theories and hardware constraints. Next, we design the dedicated dictionary for WSA that serves as a building block for formulating the ISAC processing as sparse signal recovery problems. The orthogonal matching pursuit with support refinement (OMP-SR) algorithm is proposed to effectively solve the problems in the existence of the angular ambiguity. We also provide a framework for estimating and compensating the Doppler frequencies during payload data transmission to guarantee communication performances. Simulation results demonstrate the good performances of both communications and radar sensing under the proposed ISAC framework.

Communication in Millimeter wave (mmWave) band relies on narrow beams due to directionality, high path loss, and shadowing. One can use beam alignment (BA) techniques to find and adjust the direction of these narrow beams. In this paper, BA at the base station (BS) is considered, where the BS sends a set of BA packets to scan different angular regions while the user listens to the channel and sends feedback to the BS for each received packet. It is assumed that the packets and feedback received at the user and BS, respectively, can be correctly decoded. Motivated by practical constraints such as propagation delay, a feedback delay for each BA packet is considered. At the end of the BA, the BS allocates a narrow beam to the user including its angle of departure for data transmission and the objective is to maximize the resulting expected beamforming gain. A general framework for studying this problem is proposed based on which a lower bound on the optimal performance as well as an optimality achieving scheme are obtained. Simulation results reveal significant performance improvements over the state-of-the-art BA methods in the presence of feedback delay.

A finite element solution of an ion channel dielectric continuum model such as Poisson-Boltzmann equation (PBE) and a system of Poisson-Nernst-Planck equations (PNP) requires tetrahedral meshes for an ion channel protein region, a membrane region, and an ionic solvent region as well as an interface fitted irregular tetrahedral mesh of a simulation box domain. However, generating these meshes is very difficult and highly technical due to the related three regions having very complex geometrical shapes. Currently, an ion channel mesh generation software package developed in Lu's research group is one available in the public domain. To significantly improve its mesh quality and computer performance, in this paper, new numerical schemes for generating membrane and solvent meshes are presented and implemented in Python, resulting in a new ion channel mesh generation software package. Numerical results are then reported to demonstrate the efficiency of the new numerical schemes and the quality of meshes generated by the new package for ion channel proteins with ion channel pores having different geometric complexities.

We present MultiBodySync, a novel, end-to-end trainable multi-body motion segmentation and rigid registration framework for multiple input 3D point clouds. The two non-trivial challenges posed by this multi-scan multibody setting that we investigate are: (i) guaranteeing correspondence and segmentation consistency across multiple input point clouds capturing different spatial arrangements of bodies or body parts; and (ii) obtaining robust motion-based rigid body segmentation applicable to novel object categories. We propose an approach to address these issues that incorporates spectral synchronization into an iterative deep declarative network, so as to simultaneously recover consistent correspondences as well as motion segmentation. At the same time, by explicitly disentangling the correspondence and motion segmentation estimation modules, we achieve strong generalizability across different object categories. Our extensive evaluations demonstrate that our method is effective on various datasets ranging from rigid parts in articulated objects to individually moving objects in a 3D scene, be it single-view or full point clouds.