Tensors can efficiently represent high-dimensional data, simplify the modeling and computation of complex systems and enhance the performance and flexibility of algorithms in tasks such as multi-sensor fusion and nonlinear system estimation. Meanwhile, the unscented Kalman filter (UKF) directly handles nonlinear systems through the unscented transformation, avoiding linearization errors. This ensures estimation accuracy and numerical stability, making it suitable for highly nonlinear scenarios. Based on the Bayesian filtering principle, this article derives the UKF for recursively estimate tensors based on the streaming tensor measurements. The proposed algorithm leverages the tensor Kronecker product for deriving the covariance of tensor distribution based on the sigma points, which allow for accurately propagating the first two moments of tensor posterior. Simulation results show that the proposed tensor UKF (TUKF) in this letter outperforms the state-of-art algorithm, thus verifies the effectiveness of TUKF.

This paper discusses the problem of streaming coupled tensor factorization based on sensor networks, where each sensor observes only some features of the targets, and the measurements from sensors are provided in a streaming tensor fashion. Moreover, the observed features of different sensors might overlap (i.e., coupled tensor), and there is no central processing unit to collect all sensor data. Then, in our work, the canonical polyadic (CP) decomposition is exploited to perform local tensor decomposition based on the measurements of each sensor, and average consensus (AC) for diffusing information throughout the network. The proposed method is verified via simulations.

A key feature of extended target (ET) is that it can produce multiple measurements, thus providing detailed information such as size, orientation. However, due to the measurement number decrease, the ET tends to be a point target (PT) when it becomes far from the sensor, leading to disability of estimating the extensions. In this paper we consider the problem of distributed ETs tracking based on multiple sensors. In such a case the measurements decrease of an ET can be compensated by other sensors, so that the tracking performance can be maintained. In the proposed algorithm the targets are modeled by Poisson multi-Bernoulli (PMB) random finite set (RFS) and the state of each target consists of two parts representing the possibility of being ET and PT, respectively. In the local filtering state, interaction between ET and PT states is considered in the prediction step for target identity change between ET and PT, based on which the local PMB filter is achieved for seamlessly tracking ETs and PTs. In the fusion part a generalized covariance intersection (GCI) based criterion is proposed to fuse the posteriors of each sensor. The performance of proposed algorithm is verified via simulations.

This paper focuses on the wideband frequency invariant (FI) deterministic beamformer design problem for mitigating beam squint and presents a spatial response variation (SRV)-constrained array response control (ARC) synthesis approach. By regarding the SRV matrix as the covariance matrix of an extra virtual colored noise, we extend the ARC-based narrowband beampattern synthesis techniques to wide band FI scenarios. Furthermore, we introduce the FI maximum magnitude response (FI-MMR) based design principle, which maximizes the array magnitude response at the main-beam direction on the reference frequency. Based on this principle, we present an iterative FI beampattern synthesis algorithm under arbitrary array configurations. Simulation results show the effectiveness of the proposed algorithm in comparison with several popular FI beampattern synthesis techniques.

With discrete modulation techniques, such as quadrature amplitude modulation and phase-shift keying, maximum likelihood (ML) signal detection in massive multi-input multi-output (MIMO) systems fundamentally relies on convex integer programming, executed efficiently through linear operations. However, for 1-bit massive MIMO systems, the nonlinearity introduced by 1-bit quantization impedes the linear realization of the ML detector. To achieve ML detector performance with manageable computational costs, researchers have proposed a two-stage strategy consisting of relaxed continuous convex programming followed by refinement using discrete search within the candidate solution set surrounding the optimal solution of the relaxed continuous convex programming. This article specifically examines the refinement stage. We demonstrate that it is possible to approximate the ML detection’s log-likelihood function using a 1-degree freedom quadratic function. We subsequently modify the decomposition algorithm for convex integer quadratic programming (CIQP) with a$d$-degree freedom matrix and box constraint. Finally, we employ the modified decomposition algorithm for refinement to obtain an initial candidate solution set, which is then expanded and pruned. This method is referred to as the improved CIQP-based algorithm. Numerical results indicate that the improved CIQP-based algorithm outperforms existing approaches in this domain.

In the wireless communication system, the pilot is essential for channel estimation. This paper study the pilot design of the 1-bit massive multi-input multi-output system with the flat Rayleigh fading channel. This paper aims to design the pilot matrix minimizing the estimation error of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator, of which the estimation error is given by a closed-form formula. An approximate BLMMSE channel estimation error is derived in the low signal-to-noise ratio (SNR) region. The lower bound of the approximate channel estimation error for all possible pilot matrices is derived. The analysis shows that the pilot matrix with pairwise orthogonal and equal-norm row vectors and equal-norm column vectors is optimal in terms of approximate channel estimation error. The hypersphere-based steepest descent (HSD) algorithm is proposed to design the pilot matrix by optimizing the performance of the BLMMSE estimator. The numerical results show that the proposed HSD algorithm has a noticeable improvement in channel estimation compared with the DFT pilot and the random pilot. The HSD algorithm is also valid for the near maximum likelihood estimator and SNR mismatch.

The interest of this paper is to detect an unmanned aerial vehicle (UAV) and then initialize its trajectory, if it exists. The difficulties of detecting a UAV mainly lie in two aspects: a) small radar cross section (RCS), which causes extremely low signal-to-noise ratio (SNR); and b) low velocity, which results in weak Doppler effect. In this case, traditional track-before-detect (TBD) algorithms cannot achieve the satisfying probability of detection. In this paper, we propose to solve the problem of detecting a UAV based on micro-Doppler aided dynamic programming TBD (MA-DP-TBD) algorithm where the effect of micro-Doppler caused by the blades of UAV is taken into consideration to aid the detection process. The performance of proposed algorithm is examined via simulations.

Blind despreading of long-code direct sequence spread spectrum (DS-SS) signal with unknown carrier frequency offset (CFO) is considered. The maximum likelihood estimate (MLE) of spreading waveform is first derived, and to cope with the unknown CFO, we then use the semidefinite relaxation (SDR) technique to approximate our MLE problem as a convex semidefinite programming (SDP) problem, which can be solved efficiently using modern convex optimization methods. Simulation results demonstrate that the proposed approach significantly outperforms the dominant mode despreading estimator whether or not CFO exists at low signal to noise ratio (SNR).

In this study, the problem of estimating the spreading waveform of long-code direct sequence spread spectrum (DSSS) signals is considered. A novel spreading waveform estimation method based on a missing data model is proposed. By showing that the long-code DSSS signal can be equivalently represented as a short-code DSSS signal with missing data, the spreading waveform estimation problem can be viewed as a low-rank matrix approximation problem with missing data that can be approximately solved by the existing optimisation methods. To evaluate the performance of the author's proposed estimator, the authors also derive the Cramer–Rao lower bound (CRB) on the mean square error of spreading waveform estimators. The simulation results demonstrate that the proposed estimator approaches the CRB and provides significant performance improvement compared with the existing estimators in the case of low signal-to-noise ratio situations.