Camera calibration enables the automatic estimation of intrinsic and extrinsic camera parameters, uncovering correspondences between 2D images and 3D real-world coordinates. For highway surveillance cameras, existing methods often rely on cumbersome procedures to extract limited priors (e.g., vanishing points or reference points) and provide incomplete estimations (e.g., roll angle). Therefore, we leverage the multilayered lane lines on highways, which offer rich priors such as segment lengths, intervals, and lane widths, to develop a novel camera calibration and vehicle speed estimation method. For camera calibration, our approach performs road instance segmentation and extractsmultilayered lane-line keypoints (MLK)while mitigating environmental interference and dynamic vehicle occlusions. An MLK-based calibration model is constructed and anangle-polling Levenberg-Marquardt algorithmis designed to estimate key parameters, including focal length, three rotation angles, and lane-line distance. For vehicle speed estimation, multi-object tracking (MOT) algorithms are integrated with the calibration model to infer the average speeds of all identified vehicles. We collected real highway video footage from four different camera setups in Chinese highways. Experimental results demonstrate that our method outperforms existing methods across all setups. The impact of key parameters is evaluated to determine the optimal configuration. Lastly, its effectiveness in vehicle speed estimation is assessed based on advanced MOT algorithms.

A substantial body of work has focused on two-dimensional (2-D) self-localization of linear arrays using wireless sensor networks (WSN). However, tackling the higher-dimensional three-dimensional (3-D) case remains an open research question. This paper explores the use of one-dimensional (1-D) angle-of-arrival (AOA) measurements, also referred to as space angles (SA), to achieve 3-D self-localization of a linear array in the presence of anchor position errors. Unlike traditional 3-D source localization using SAs, 3-D self-localization requires simultaneous estimation of the array’s position and orientation (direction vector). First, we acquire a coarse solution to the weighted least-squares (WLS) problem via semidefinite relaxation (SDR), and then we enhance it through perturbation analysis. We then address the maximum likelihood (ML) estimation problem using block majorization-minimization (block-MM), which guarantees convergence to the Karush-Kuhn-Tucker (KKT) point. In addition, we propose an improved and tighter quadratic upper bound for a Rayleigh-quotient-like function introduced in our previous work. Simulations confirm that the proposed algorithm reaches the Cramér-Rao lower bound (CRLB) performance in low-noise regimes, with the block-MM-based ML method exhibiting minimal bias.

Direct localization (DL) of high-order quadrature amplitude modulation (QAM) sources is a pivotal challenge in wireless communications, particularly in environments characterized by complex multipath propagation and the presence of multiple sensor array-based anchors. This paper introduces a novel solution based on dual atomic norm minimization (DANM) framework that capitalizes on the fourth-order cumulant property of QAM signals to suppress Gaussian noise and expand the effective array aperture. Unlike traditional DL frameworks based on discrete Fourier transform (DFT) and spatial smoothing pre-processing (SSP) techniques, the proposed framework enhances localization accuracy and improves robustness against multipath effects. By framing the localization problem as a semidefinite program that utilizes dual atomic norm properties, our solution eliminates the need for prior knowledge of the number of sources and achieves a favorable balance between computational complexity and localization performance. Simulation results reveal that the DANM-based DL algorithm outperforms existing DFT- and SSP-based DL methods in terms of localization accuracy, with its root mean square error (RMSE) closely approaching the Cramér-Rao bound (CRB) even under challenging conditions. These findings underscore the potential of DANM in advancing high-precision DL for high-order QAM sources, thereby paving the way for more reliable and precise wireless communication systems.

This letter investigates the multi-target direction of arrival (DOA) tracking problem under wireless sensor networks (WSNs), where each node is equipped with a uniform linear array (ULA). A WSN probability hypothesis density (WSN-PHD) tracking algorithm is proposed with two key innovations: 1) an exponential accumulation (EA) fusion strategy that aggregates multi-node measurements to resolve occlusions in WSNs, thereby improving tracking continuity under time-varying targets, and 2) a non-circular phase-assisted likelihood function to enhance target tracking accuracy. Numerical results show that the proposed algorithm achieves average optimal sub-pattern assignment (OSPA) distance and location errors reduction of 78.18% and 76.82% compared to the algorithm without EA fusion.

Time-delay estimation (TDE) holds great significance in pavement surveys, especially in the modern transportation system. Established on the ideal Dirac pulse and white Gaussian noise, the performance of the existing TDE methods may degrade in practical ground penetrating radar (GPR) detection, where radar pulse and noise distribution are diverse. In this letter, we develop a gridless TDE method considering the radar pulse and noise pattern in GPR detection. Co-prime sampling strategy is applied to reduce the number of frequency samples compared with conventional uniform sampling. With the prior knowledge of radar pulse and noise distribution, an enhanced measurement vector is generated from the data covariance matrix, thus improving the signal quality compared with the conventional methods which are based on ideal Dirac pulse and white Gaussian noise. Subsequently, the time-delays are estimated by the proposed atomic norm minimization (ANM) method, where the complexity is further reduced compared with the previous works using multiple measurements. Simulation results show the advantages of the proposed method in terms of running time, weak echo detection, and estimation accuracy.

Array self-position determination methods based on multiple emitter data can avoid significant deviations of vehicle satellite navigation in harsh environments. However, existing array self-position determination methods show decrease in performance under multipath environments. To deal with this problem, we propose an array self-position determination method based on orthogonal grid matching with the spatial differencing method. Specifically, the direction of arrival (DOA) of direct path and multipath signals are respectively estimated by array spatial differencing method. The matching accuracy is enhanced by utilizing the prior information of direct path signal. After calculating correlation coefficients of different sources, estimated angles with high correlation are then classified into the same set. Then, the noise subspace of each angle set is reconstructed and the position is estimated by grid matching with the orthogonal property between the noise subspaces and the characteristic steering vectors. The matching results of redundant angle sets are removed as non-matching items, thus averting positioning deviations. The simulation results demonstrate that the computational complexity of the proposed method is comparable to that of the signal subspace fitting (SSF). Moreover, in terms of positioning precision, the proposed method outperforms multiple signal classification with enhanced spatial smoothing (ESSMUSIC), initial signal fitting (ISF), and SSF.

The global navigation satellite systems (GNSS) are crucial for applications such as traffic monitoring, intelligent transportation systems and advanced driver assistance systems; however, they are prone to large deviations or even failures in hidden scenarios such as urban canyons and tunnels. In this paper, we investigate a system based on distributed arrays for positioning and tracking of multiple vehicles as a supplement to the GNSS. Conventional tracking methods often assume a constant signal-to-noise ratio (SNR) across arrays; however, this assumption does not hold in dynamic, dense traffic or signal-obstructed areas where variable SNR conditions frequently arise. To address this, this paper proposes two adaptive passive position tracking methods utilizing distributed sparse arrays, which are robust to variations in SNR and capable of maintaining reliable tracking performance. The first method relies on the extended Kalman filter (EKF) algorithm, while the second employs the unscented Kalman filter (UKF) algorithm. A novel tracking system model is developed, including a multi-target state transfer equation and a fused signal equation. The unknown noise covariance and signal covariance of the fused signal are estimated using vectorization and least squares methods, respectively. Prior state information and minimum mean square error estimation are incorporated to address unknown signal challenges within the EKF and UKF frameworks. Additionally, the posterior Cramér-Rao bound provides a performance benchmark, underscoring the robustness of the proposed methods. Computer simulation studies and practical tests show that the proposed methods significantly improve computational efficiency and tracking performance in vehicle tracking, demonstrating high adaptability to noise variations compared to traditional methods.

Recently, direction-of-arrival (DOA) estimation in impulsive noise scenarios has been extensively investigated in the field of co-prime array signal processing. This paper proposes a combined enhanced bounded nonlinear covariance and phased fractional low-order moment (EBNC-PFLOM) method, which incorporates the advantages of both EBNC and PFLOM and mitigates the impulsive noise by constructing the equivalent data covariance matrix of the received signals. Furthermore, when dealing with a limited number of input signals, the proposed method is capable of directly estimating the signals’ DOA without spatial smoothing. Simulation results show that the proposed method outperforms the recently reported methods.

In this paper, we propose a nested sampling based off-grid block sparse representation method (Nested-OGBSR) for time-delay estimation (TDE) of coherent ground penetrating radar (GPR) backscattered echoes. Nested sampling strategy is taken to reduce the sampling rate and computational burden. The off-grid data model is adopted to eliminate the effect of basis mismatch caused by the predefined grids in sparse representation (SR) and thus improve the estimation accuracy. The non-circularity of GPR signals is also utilized to enhance the temporal resolution of sparse block representation (BSR). Numerical and experimental results are provided to show the superiority of the proposed method in terms of estimation accuracy, temporal resolution and computational complexity.

Direct position determination (DPD) (a.k.a. direct localization) offers enhanced precision over traditional two-step approaches. This technique, however, involves considerable communication overhead for transmitting raw data. Low-bit direct localization methods have recently been introduced to address this issue. In this letter, we present a gridless, one-bit maximum likelihood (ML) approach for the direct localization of an orthogonal frequency division multiplexing (OFDM) signal source. A recent majorization-minimization (MM) algorithm introduced a surrogate function for the log-likelihood function, which lacks a closed-form optimal solution and requires exhaustive searches at each iteration. Our method improves upon this algorithm by developing a refined surrogate function that yields a closed-form optimal solution, thereby eliminating the need for exhaustive searches. Accordingly, the proposed MM approach can eliminate grid quantization errors (GQE) by eliminating the search process. Simulation results validate the proposed method's efficacy in mitigating GQE and its efficiency in scenarios with densely populated search grids.

Direct position determination (DPD) approaches of non-circular (NC) signals for distributed antenna arrays are outstanding in location accuracy and available degrees of freedom. Nevertheless, the existing grid-based DPD approaches involve unnecessary computational costs because of NC phases. Besides, the cost function utilized in DPD could cause performance deterioration as ignoring the non-homogeneity error of the received data. To this end, we propose a DPD approach implemented by polynomial rooting and optimal weighting. Aiming to reduce computational costs, we first construct a computationally efficient cost function. Meanwhile, to mitigate the adverse impact induced by non-homogeneity errors in an effective manner, we assign an optimal weight to each antenna array. Simulation results demonstrate that the proposed approach achieves a good compromise between performance and computational complexity.

Coprime array possesses a larger array aperture and element spacing compared with the conventional uniform linear array (ULA) for the equivalent number of sensors, attracting considerable scholarly attention. However, the direction of arrival (DOA) estimation of coherent signals has been a major challenge for the practical application of the coprime array. In this paper, based upon the perspective of signal subspace reconstruction, we propose two effective approaches to resolve the DOA of completely correlated signals with a coprime array. For the first method, we exploit two selection matrices to separate the signal subspace into two parts and rearrange the elements within them to construct two Hankel matrices. By applying the MUSIC method to these Hankel matrices and finding common solutions, we can determine the DOA of coherent signals. In the second method, we first convert the signal subspace of the coprime array into the signal subspace of ULA using a mapping matrix and the total least squares method. We then construct a Hankel matrix and restore its rank by solving a rank minimization problem. Finally, by applying the MUSIC method to the rank-restored Hankel matrix, we can obtain the angles of the coherent signals. Finally, simulation results are presented to demonstrate the efficiency and superiority of our proposed methods.

The global positioning system (GPS), which provides ubiquitous location-awareness with a constellation of satellites, has become an instrumental function of multiple mass-market applications. Satellite signals, however, may not be capable of penetrating obstacles in harsh environments (e.g., urban canyons, tree canopies, and flyovers). Hence, GPS may not provide adequate localization accuracy for applications like autonomous vehicles. Resorting to data fusion of heterogeneous signals emanating from multiple anchors, we advocate a self-localization method that provides accurate estimates of the vehicle position. To be more specific, several heterogenous emitters whose positions are known are used as anchors to determine the vehicle’s position based on the weighted direct position determination (DPD) method that eliminates nonhomogeneity among different emitters. However, the weighted DPD method requires an exhaustive search of the parameter search space and is thus time-consuming. To reduce the computational burden, we propose a weighted cascade compensation estimator (WCCE) that is tailored for real-time tracking and self-localization. The proposed WCCE outperforms traditional DPD methods in terms of computational complexity while achieving nearly comparable localization accuracy. The effectiveness of the proposed method is corroborated by extensive simulated examples.

Existing path planning schemes designed for wireless sensor networks generally account for abstract payload sensors, rendering them inapplicable to concrete sensor-array-based localization systems due to differences in measurement models. In this paper, we establish a general framework for path planning of a practical sensor array and factor in an oft-neglected degree of freedom regarding optimality, i.e., the array’s orientation/attitude. The optimization problem is formulated based on the A-optimality criterion under constraints arising from the maximum distance between consecutive waypoints, maximal heading change, and forbidden regions. To facilitate semidefinite relaxation (SDR), we recast the optimization function into a fractional nonhomogeneous quadratic structure and transform the constraints into a bilinear form. By applying SDR and replacing the bilinear terms with a matrix variable, the problem is relaxed into a single-ratio fractional program. By leveraging the Charnes-Cooper variable transformation, we transform the single-ratio fractional program into a mixed semidefinite/second-order cone program (SD/SOCP) that can be solved in polynomial time. Finally, we apply the results to angle-of-arrival (AOA) and direct localization. Simulation results demonstrate that the proposed path planning scheme attains near-optimal performance.

In this article, source localization exploiting time difference of arrival (TDOA) information is discussed, and a parallel factor (PARAFAC) analysis-based method for multi-TDOA estimation and direct position determination (DPD) is proposed. First, signals from the radiation source are received by multiple antennas through synchronous sensing. Then, the data from multiple antennas is fused by extracting the time-delay matrix to construct a PARAFAC model. Thereafter, the time-delay matrix is obtained by fast iterative decomposition using the trilinear alternating least square (TALS) algorithm. In the case of no multipath or weak multipath, where the typical scenario is the antennas being deployed on the airborne platform, the multi-TDOA estimation can be obtained simultaneously according to the time-delay matrix to improve the processing speed. In the case of multipath, such as the antennas being located on the ground, the DPD cost function directly related to the source position can be established based on the time-delay matrix, and the source position estimation can be achieved through grid search. Compared with the other DPD methods, the proposed DPD method has better positioning performance and lower complexity. The effectiveness and superiority of the proposed methods are verified by both simulations and actual scenario tests.

Unmanned aerial vehicle (UAV)-to-ground (U2G) channel models play a pivotal role in reliable communications between UAV and ground terminal. This paper proposes a three-dimensional (3D) non-stationary hybrid model including large-scale and small-scale fading for U2G multiple-input-multiple-output (MIMO) channels. Distinctive channel characteristics under U2G scenarios, i.e., 3D trajectory and posture of UAV, fuselage scattering effect (FSE), and posture variation fading (PVF) are incorporated into the proposed model. The channel parameters, i.e., path loss (PL), shadow fading (SF), path delay, and path angle, are generated incorporating machine learning (ML) and ray tracing (RT) techniques to capture the structure-related characteristics. In order to guarantee the physical continuity of channel parameters such as Doppler phase and path power, the time evolution methods of inter- and intra- stationary intervals are proposed. Key statistical properties, including temporal auto-correction function (ACF), power delay profile (PDP), level crossing rate (LCR), average fading duration (AFD), and stationary interval (SI), are analyzed with the impact of the change of fuselage and posture variation. It is demonstrated that both posture variation and fuselage scattering have crucial effects on channel characteristics. The validity and practicability of the proposed model are verified by comparing the simulation results with the measured ones.

For the target tracking problem where the number of targets fluctuates with time and the measurement is a point measurement, the random finite set (RFS) class filtering is an available solution. However, in direction of arrival (DOA) tracking, the array observation is a super-positional value, and the tracking performance can be severely impaired if the RFS-based filter approach is applied. As a result, a novel measurement association mapping (NMAP) approach has been presented to cope with the mapping problem between the array observations and sources. Nevertheless, the tracking performance is poor when the number of particles is small. In this paper, a modified delta-Generalized Labeled Multi-Bernoulli ($\delta $-GLMB) DOA tracking particle filter is proposed in combination with the NMAP strategy, which can achieve the same tracking performance with a smaller number of particles by modifying the particles in the$\delta $-GLMB prediction step. Furthermore, the approach is extended to a coprime array and can achieve better DOA tracking performance than a uniform linear array. Simulation experiments validate the effectiveness of the proposed algorithm.

Abstract Large‐scale multiple‐input multiple‐output (LS‐MIMO) is one of the promising technologies beyond the 5G cellular system in which large antenna arrays at the base station (BS) improve the system capacity and energy‐efficiency. However, the large number of antennas at the BS makes it challenging to design low‐complexity high‐performance data detectors. Thus, a number of iterative detection methods, such as Gauss–Seidel and conjugate gradient, are introduced to achieve complexity‐performance tradeoff. However, their performance deteriorates for the systems with small BS‐to‐user antenna ratio or for the channels that exhibit correlation. This paper proposes a new efficient iterative detection algorithm based on the improved Gauss–Seidel iteration to address this problem. The proposed method performs one conjugate gradient iteration that enables better performance with less number of iterations. A new hybrid iteration is introduced and a low‐complexity initial estimation is utilised to enhance detection accuracy while reducing the complexity further. In addition, a novel preconditioning technique is proposed to maintain the benefits of the proposed detector in correlated MIMO channels. It is mathematically demonstrate that the proposed detector achieves low approximated error. Theoretical analysis and numerical results show that the proposed algorithm provides a faster convergence rate compared to conventional methods.

An unmanned aerial vehicle (UAV) array is composed of multiple UAVs carrying array elements, which can sense signals synchronously through a global positioning system (GPS) trigger. However, gain-phase errors caused by synchronization errors and the inconsistent complex gains of receiving array channels result in array manifold perturbation, which makes the performance of traditional localization methods degrade or even fail. In this article, two efficient algorithms for source direction finding and direct localization using a UAV array are, respectively, presented. First, the array manifold changes with the movement of UAVs, which contributes to multiposition fusion, thus avoiding the infinite solutions of underdetermined equations. Then, the quadratic optimization problem can be constructed by using the orthogonal relation between noise subspaces and contaminated steering vectors obtained from multiple observations. Thereafter, we can construct the cost function and obtain the spectral function, from which the source directions and positions can be all estimated by grid search. Meanwhile, the gain-phase error values can be solved successively. Moreover, in order to avoid the influence of heteroscedasticity of different observation positions in direct localization, we carry out a blind weighting operation. Simulation results demonstrate the effectiveness and superiority of the proposed algorithms.

The three-dimensional localization problem for noncircular sources in near-field with a centro-symmetric cross array is rarely studied. In this paper, we propose an algorithm with improved estimation performance. We decompose the multiple parameters of the steering vector in a specific order so that it can be converted into the products of several matrices, and each of the matrices includes only one parameter. On this basis, each parameter to be resolved can be estimated by performing a one-dimensional spatial spectral search. Although the computational complexity of the proposed algorithm is several times that of our previous algorithm, the estimation performance, including its error and resolution, with respect to the direction of arrival, is improved, and the range estimation performance can be maintained. The superiority of the proposed algorithm is verified by simulation results.

Arrays deployed in antenna-array-based direct position determination (DPD) systems are conventionally placed parallel to each other with invariant orientations, which may be inappropriate. This paper proposes a novel array orientation adjustment method to achieve optimal DPD performance, in which we seek optimal array orientations that maximize the trace of the Fisher information matrix (FIM) and then minimize localization uncertainty. The optimization problem is unconstrained, multivariable, and can be converted into multiple tractable single-variable optimization problems. An exact solution can be obtained by a straightforward but computationally tedious one-dimensional exhaustive search. To reduce the computational load, we then derive an asymptotic solution in cases where the arrays consist of massive antennas. Numerical examples demonstrate the effectiveness and feasibility of the proposed method in resolution and precision enhancement, especially in a low signal-to-noise ratio (SNR).

Millimeter-wave (mmWave) fifth-generation (5G) and beyond 5G localization enables the provisioning of extremely accurate positioning information, a feature that has attracted substantial research efforts. In this paper, we contribute to this effort by exploring optimal array geometric structures of direct position determination (DPD) systems, inspired by sensor placement problems that predominantly focus on two-step localization and have not yet been extended to DPD. Specifically, we research an optimal array placement and orientation strategy for two-dimensional (2-D) DPD systems that use sensors equipped with uniform linear arrays (ULA) to localize an agent. The A-optimality criterion in Bayesian optimal (experimental) design theory is invoked to formulate this problem. We use an optimization subproblem that optimizes array orientations when array locations are arbitrary but fixed to tackle this high-dimensional optimization problem. Then the optimization problem is converted into a typical optimal angular separation problem in two-step localization. Experimental results show that judiciously designed array geometric structures can lead to significant performance improvements.

Time-delay estimation (TDE) for thin top layers of asphalt pavement is a challenging task due to the limited resolution of ground penetrating radar (GPR) as well as small permittivity difference between top layers. Echoes backscattered from the interfaces of top layers with similar permittivity have usually much smaller amplitudes compared with other echoes, which can be called weak signals. The weak backscattered echoes are usually too sensitive to the noise and other strong echoes that current signal processing approaches (subspace-based methods and compressed sensing based methods) might have false estimation results even failures without proper processing of them. Therefore, in this paper, an enhanced orthogonal matching pursuit (OMP) method is proposed to deal with weak signals resulting from similar permittivity of adjacent asphalt layers. Based on the orthogonality between signal and noise subspaces, we firstly apply the truncated singular value decomposition (SVD) on the received signals, in order to reduce the noise impact. Secondly, we build an orthogonal matrix to the mode matrix of the pre-estimated strong backscattered echoes, and map it to the overcomplete dictionary matrix, such that the influence of the residual of the strong backscattered echoes can be reduced. Finally, the time-delays of backscattered echoes and layer thicknesses are estimated. Compared with conventional approaches, the proposed method is more suitable for TDE in thin asphalt pavement detection. The accuracy of the proposed method is validated by both numerical and experimental data.

The coprime array owns a sparse array structure, which can effectively alleviate mutual coupling, while the holes existing in the difference co-array(DCA) greatly reduce the number of uniform degrees of freedom(uDOFs). In this letter, we propose a new coprime array structure called hole-free coprime array (HFCA) by carefully assembling the subarrays, and the resulting HFCA can generate a hole-free DCA. Furthermore, we derive the optimal HFCA that can produce the largest hole-free DCA with a given number of sensors, which contributes to an increase of uDOFs compared with existing coprime array structures. In addition, the simulations are provided to demonstrate the superiority of HFCA in terms of uDOFs, direction of arrival estimation performance, and spatial resolution.

The increasing of illegal radiations, which are either artificial or unintentional, has seriously influenced the reliable communication and operation of industrial facilities. In this article, we discuss the simultaneous localization of multiple emitters based on big data monitored by a moving unmanned aerial vehicle. Conventional direct position determination (DPD) method suffers from the non-homogeneity of the observation error and is sensitive to the environment, so we develop the weight DPD methods. First, we consider to strengthen the spectrums obtained at slots with higher signal-to-noise ratio, which is blindly calculated. Thereafter, an improved weight is designed to further enhance the localization accuracy, and it can obtain the asymptotically optimal performance under the general Gaussian noise model, which is proved theoretically. Numerical simulations demonstrate that the proposed weight DPD methods outperform the conventional two-step methods and subspace data fusion DPD method in terms of localization accuracy and resolution.

Direction of arrival (DOA) estimation using the improved unfolded coprime array (IUFCA) subject to array motion isdiscussed in this study. Unfolded coprime array (UFCA) consists of two uniform linear subarrays, and the two subarrays are arranged at different sides of theaxis, which leads to a large number of holes in the difference co‐array (DCA). With array motion and DCA synthesis,part of the holes can be filled, but there are still holes in the center which lead to the virtual arrays separated.By analyzing the hole positions in the synthetic DCA generated by UFCA motion, the authors improve the originalUFCA by relocating some physical elements, then the two dominantconsecutive DCA segments in the positive and negative sides can be connected. The expression of synthetic DCA is analyzed, and the closed‐form expression of theuniform degree of freedom (uDOF) subject to IUFCA motion is studied. Simulation results show that IUFCA motion can obtain a largenumber of uDOFs, which leads to better DOA estimation performance and more identifiable signals compared with existingcoprime array configurations.

The authors investigate the issue of direction of arrival (DOA) estimation in the presence of phase noise for multiple sources with a synthetic linear array, which is synthesised by a short moving array. The extended towed array measurements (ETAM) method can extend the array aperture greatly, but can only be applied to multiple coherent sources and requires the array to move with constant velocity. To tackle the problems, the authors generalise the ETAM method to multiple incoherent sources and array non‐uniform motion case. The authors first formulate the manifold of the extended synthetic array (SA) moving with known velocity in a straight line. Then the initial DOA estimates and phase correction factors are estimated successively by two‐dimensional multiple signal classification (2D‐MUSIC) spectrum search using adjacent measurements sampled by the moving array. Moreover, to reduce the complexity, the authors also propose a reduced dimensional MUSIC (RD‐MUSIC) method to turn the two‐dimensional peak search to one‐dimensional. As the array aperture is extended by proper compensation, the DOA estimation performance of the proposed SA method improves. Besides, the proposed method can resolve more number of sources than sensors since every two measurements are used for estimation in each process. Simulation results validate the effectiveness of the proposed method.

In this study, the authors propose a fast quadrilinear decomposition algorithm for estimation of the directions‐of‐arrival and polarisations of the incident sources via a uniform rectangular array of electromagnetic vector sensors (EMVSs). Conventional quadrilinear alternating least squares (QALS), involves computationally intensive Khatri‐Rao products in each iteration, to update the parameter matrices (factors). Moreover, QALS is more likely to fall in a local minimum and tends to take more steps before an acceptable solution, which further slows down the convergence and often mis‐converges, thereby yielding meaningless results. To preserve the quadrilinearity, they arrange the measurements as a four‐dimensional (4D) data (fourth‐order tensor), from which a third‐order sub‐tensor (3D slice) can be obtained by fixing one index along any dimension. These slices are used to create new cost functions that are alternately minimised while updating the factors until convergence. They show that the rows of parameter matrices form the diagonal elements of a tensor, which capture the internal quadrilinearity of data and significantly reduce the cost function in few iterations only. Simulation results verify that the authors’ algorithm holds faster convergence, does not mis‐converge, provides parameter estimation accuracy similarly to the QALS and superior of the Estimation of Signal Parameters via Rotational Invariance Technique and propagator method.

In this paper, the topic of coherent two-dimensional direction of arrival (2D-DOA) estimation is investigated. Our study jointly utilizes the compressed sensing (CS) technique and the parallel profiles with linear dependencies (PARALIND) model and presents a 2D-DOA estimation algorithm for coherent sources with the uniform rectangular array. Compared to the traditional PARALIND decomposition, the proposed algorithm owns lower computational complexity and smaller data storage capacity due to the process of compression. Besides, the proposed algorithm can obtain autopaired azimuth angles and elevation angles and can achieve the same estimation performance as the traditional PARALIND, which outperforms some familiar algorithms presented for coherent sources such as the forward backward spatial smoothing-estimating signal parameters via rotational invariance techniques (FBSS-ESPRIT) and forward backward spatial smoothing-propagator method (FBSS-PM). Extensive simulations are provided to validate the effectiveness of the proposed CS-PARALIND algorithm.

Due to the limitations of large-scale APD arrays, the traditional airborne LiDAR systems can hardly achieve significant improvement of 3D imaging resolution. To overcome this difficulty, a novel airborne array-encoding LiDAR is proposed in this paper. The system structure and work principle are first presented. Then the key modules involving encoding, multiplexing and data decoding are introduced. In particular, the data decoding method is designed and verified for data processing of the encoded full waveforms. The experimental results indicate that the proposed LiDAR can complete 128×128 -pixel 3D imaging with only 64-element APD array under scannerless condition by employing 16×16 array-encoding.

The distributed Luby transform (LT) coding is investigated for the multisource networks, especially with three sources. Based on the three‐source single‐relay network model, the authors propose a threefold deconvolution method of the robust soliton distribution (RSD). The deconvolved distribution is used at each source, and a simple and feasible combining algorithm is developed for re‐encoding at the relay. Such a modified LT code with three sources (MLT‐3) is constructed. Simulation results verify that the overall degree distribution of the proposed MLT‐3 codes agrees well with the RSD. The performance of MLT‐3 codes is evaluated and compared with other coding schemes. Simulations reveal that MLT‐3 codes have similar behaviour with the two‐source or four‐source distributed LT codes and the benefits are observed in comparison with the separate LT codes. Simulations also show that MLT‐3 codes exhibit good performance on various erasure channels.

This work addresses the resource allocation problem with the proportional fair constraint condition based on quantised feedback for multiuser orthogonal frequency division multiplexing access system. The resource allocation problem is converted as an optimisation problem with maximising the lower bound of the total average throughput and this formulation provides the low complexity of solving the above resource allocation problem. Tailored for the above optimisation problem, the authors design the codebook of equivalent channel quantisation threshold and the codebook of power and rate according to the equal probability quantiser and the Lagrange multiplier method, respectively. Further, they develop a suboptimal algorithm based on the stochastic approximate method. The proposed algorithm not only satisfies the constraint condition of the proportional fair very well, but also reduces the feedback overhead of the resource allocation result greatly. Moreover, the average throughput of the proposed algorithm is very close to that of the optimal resource allocation algorithm with full feedback when the equivalent channel gain in every subcarrier is quantised by 4 bit.

The issue of joint angle and array gain‐phase error estimation for a bistatic multiple‐input multiple‐output array is discussed in this study, and an algorithm for the joint estimation with non‐linear arrays is proposed. First, the estimations of the transmit and receive direction matrices can be obtained via trilinear decomposition, then the relationship between the columns of the direction matrices is utilised to eliminate the influence of the gain‐phase errors, and the angles can be estimated two by two via least squares. Finally, the array gain‐phase error vectors can be estimated for calibration according to the estimated angles and direction matrices. The proposed algorithm requires no eigenvalue decomposition of the received data, and can achieve automatically paired estimations of the angles. Furthermore, no information of the gain‐phase error is needed. The simulation results verify the algorithmic effectiveness of the proposed algorithm.

In this letter, we investigate the subject of joint angle and array gain-phase error estimation for bistatic multiple-input multiple-output radar, and propose a joint scheme for angle and array gain-phase error estimation based on trilinear decomposition. The estimations of transmit and receive direction matrices are primarily obtained via trilinear decomposition, after which the optimization problem for estimating array gain-phase errors and angles can be constructed. Array gain-phase error vectors are obtained by Lagrange multipliers, and the angles are estimated according to the estimated gain-phase errors. In contrast to the ESPRIT-like algorithm, the proposed method not only obtains automatically paired estimations of the angles but also has much better performance for angle and array gain-phase error estimation. Simulations verify the effectiveness of our approach.

The authors consider the link of parallel profiles with linear dependencies (PARALIND) model with multiple-input multiple-output orthogonal frequency division multiplexing receiver. The authors derive a PARALIND-based blind receiver algorithm that has much close performance to non-blind minimum mean-squared error and it has better performance than constant modulus method. Neither the channel state information nor statistical characteristic is a necessity for the presented PARALIND algorithm, whereas the proposed algorithm distinctively supports small sample sizes. Numerical results verify its useful behaviour.

This letter discusses the problem of direction of departure (DOD) and direction of arrival (DOA) estimation for multi-input multi-output (MIMO) array system, which is configured with multiple transmit sensors and multiple velocity receive sensors. Reference presented a successive multiple signal classification MUSIC algorithm for joint estimation of DOD and DOA for the bistatic MIMO array system with velocity receive sensors. In this letter, we propose an improved joint DOD and DOA estimation algorithm, which has much better angle estimation performance and lower complexity than the successive MUSIC algorithm in . Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired 2-D angle estimation, and avoid 2-D searching. Simulation results verify the usefulness of the proposed algorithm.

In this paper, we address the problem of carrier frequency offset (CFO) estimation for Orthogonal Frequency Division Multiplexing (OFDM) systems with multiple antennas. The received signal can be denoted as a trilinear model, then the trilinear decomposition-based CFO estimation algorithm is proposed. Comparing to both ESPRIT method and the cyclostationarity (CS) approach, the algorithm that we presented has improved CFO estimation performance. Furthermore, our proposed algorithm can even work in condition of no virtual carrier. Simulation results illustrate performance of this algorithm.