Mutual Coupling Matrix Research Articles

A Novel Weighted Block Sparse DOA Estimation Based on Signal Subspace under Unknown Mutual Coupling

A Novel Weighted Block Sparse DOA Estimation Based on Signal Subspace under Unknown Mutual Coupling

The Mitigation of Mutual Coupling Effects in Multi-Beam Echosounder Calibration under Near-Field Conditions

The advancement of unmanned platforms is driving the miniaturization and cost reduction of the multi-beam echosounder (MBES). In the process of MBES array calibration, the mutual coupling significantly impacts the performance of parameter estimation. We propose a correction method to mitigate the mutual coupling effects in the calibration of MBES acoustic array. Initially, a near-field focused beamforming model is established to assess the influence of mutual coupling. Subsequently, the covariance matrix in the frequency domain is constructed to enhance algorithm efficiency and simplify solution procedures. This construction eliminates the need for a low-pass filtering step after heterodyning through extracting peak values near zero frequency in the signal frequency domain. Meanwhile, the Toeplitz property is leveraged to render the estimation results independent of the mutual coupling matrix. Finally, the mutual coupling coefficients and the direction of arrival (DOA) are joint-estimated and the Cramér–Rao bound is derived. The presented method effectively addresses the engineering challenge of MBES mutual coupling calibration. Additionally, the performance of the proposed method is verified through the measured data in simulation and tank experiments.

Novel Auto-Calibration Method for 7-Elements Hexagonal Array with Mutual Coupling

Mutual coupling between antenna array elements will significantly degrade the performance of the array signal processing methods. Due to the Toeplitz structure of mutual coupling matrix (MCM), there exist some mutual coupling calibration algorithms for the uniform linear array (ULA) or uniform circular array (UCA). But few methods for other arrays. In this letter, we derive a new transformation formula for the MCM of the 7-elements hexagonal array (HA-7). Further, we extend two mutual coupling auto-calibration methods from UCA to HA by the transformation formula. Simulation results demonstrate the validity of the proposed two methods.

Orbital Angular Momentum Radio-Wave-Based 2-D Target Angle Estimation With Mutual Coupling

Vortex electromagnetic waves are conveniently produced by a uniform circular array (UCA). The mutual coupling matrix (MCM) of UCAs presents rotational symmetry, which can be employed to cut down the parameters in the circuit model. The impedance matrix also does not rely on a specific port. This work uses rotational symmetry to expand the MCM into the orbital angular momentum (OAM) mode domain. The OAM-domain phase sequence is derived by the discrete Fourier transform (DFT) of the first row of the MCM. The connection between the number of OAM modes and the excitation of elements is described. Furthermore, an improved propagator method (PM) for OAM-based decoupled 2-D angle estimation is proposed. This method employs the original steering vector of OAM waves to process the receiving signal, which avoids errors caused by the Bessel function approximation. The estimation error is also reduced by redefining the propagator matrix. In terms of computational complexity, the proposed method avoids spectral search-and-element level eigenvalue decomposition (EVD). The results demonstrate that the coupling is compensated effectively by the OAM-mode domain MCM. The error of the proposed method is less than 1° under the condition of SNR = 20 dB and 1000 snapshots. The computational complexity is reduced by 1–2 orders of magnitude compared to the origin PM. The method is also suitable for 1-D estimation scenarios.

Direction of arrival estimation of unknown emitter by deep neural networks with array imperfections

AbstractIn array signal processing, high‐resolution direction‐of‐arrival (DOA) estimation by eigendecomposition method requires knowledge of the array covariance matrix and an exact characterisation of the array. The dependence of most such methods on the array manifold substantially degrades their array performance when the actual sensors deviate from their assumed nominal values. This article aims at formulating a deep neural network framework for DOA estimation with feasible computational complexity. The two‐stage algorithm is composed of a detection network and a series of parallel DOA estimation networks: the multilayer perceptron is trained to detect the presence of one or more sources in an angular sector at the first stage, the DOA estimation networks then estimate their respective DOAs at the second stage. When a single type of array imperfection is considered, numerical results reveal that the DNN‐based method can obtain DOA estimates with much higher precision than the existing techniques for significant location errors and gain/phase perturbations, they also illustrate the potential usefulness of the proposed algorithm towards better DOA estimation accuracy for mutual coupling as the mutual coupling matrix is not simplified. Moreover, the proposed method is finally extended to deal with the DOA estimation problem when multiple types of array perturbations coexist.

Joint estimation of DOA and mutual coupling via imposing an annihilation constraint

The mutual coupling between elements degrades the direction-of-arrival (DOA) estimation performance. This paper considers jointly estimating the DOA and mutual coupling. Firstly, based on the fact that the noiseless array output without mutual coupling consists of complex exponential sums, an annihilation relation is obtained. Then, an optimization problem is proposed by combining a cost function derived from the maximum likelihood principle and a constraint formed by the annihilation relation. The optimization problem is solved by the sequential quadratic programming (SQP) method, where the Jacobian matrix is derived via exploiting the symmetric Toeplitz structure of the mutual coupling matrix. At last, a post-processing method is proposed for further improving the accuracy of mutual coupling estimation. The new method can handle single snapshot estimation, and it is gridless while utilizing the whole aperture. It is also insensitive to overestimation of the degree of mutual coupling. The method has been verified by simulations and compared with representative methods regarding accuracy and efficiency.

Rapid Subentire-Domain Basis Functions Method Based on Adaptive Artificial Neural Networks

The subentire-domain (SED) basis functions method has shown its efficiency in solving the electromagnetic problem of large-scale finite periodic structures (LFPSs). However, calculating the expansion coefficients of SED basis functions is very time-consuming due to the consideration of the mutual coupling between all the elements in LFPSs, even after accelerated by conjugate-gradient fast Fourier transform (CG-FFT) and/or fast multipole method (FMM). In this article, based on the physics locations of observation cells, the adaptive artificial neural networks (AANNs) have been employed to rapidly predict the expansion coefficients of SED basis functions on interior cells, edge cells, and corner cells. By involving the AANNs, the mutual coupling between all the elements can be accounted into the neural networks without the construction of the mutual coupling matrix, and the expansion coefficients of SED basis functions can be obtained rapidly. Numerical experiments prove the accuracy and efficiency of the AANN-assisted SED basis functions method.

Multi-UAV Cooperative Localization for Marine Targets Based on Weighted Subspace Fitting in SAGIN Environment

As an indispensable part of the Internet of Vehicles (IoV), unmanned aerial vehicles (UAVs) can be deployed for target positioning and navigation in the space–air–ground-integrated network (SAGIN) environment. Maritime target positioning is very important for the safe navigation of ships, hydrographic surveys, and marine resource exploration. Traditional methods typically exploit satellites to locate marine targets in the SAGIN environment, and the location accuracy does not satisfy the requirements of modern ocean observation missions. In order to localize the marine target, we develop a system architecture in this article, which contains UAVs integrated with monostatic multiple-input–multiple-output (MIMO) radars. The main thrust is to estimate the direction-of-arrival (DOA) via MIMO radar. Herein, we consider a general scenario that unknown mutual coupling exist and a novel sparse reconstruction algorithm is proposed. The mutual coupling matrix (MCM) is adopted with the help of its special structure, we formulate the data model as a sparse representation form. Then, two novel matrices, a weighted matrix, and a reduced-dimensional matrix are constructed to reduce the computational complexity and enhance the sparsity, respectively. Thereafter, a sparse constraint model is constructed using the concept of optimal weighted subspace fitting (WSF). Finally, the DOA estimation of maritime targets can be achieved by reconstructing the support of a block sparse matrix. Based on the DOA estimation results, multiple UAVs are used to cross-locate marine targets multiple times, and an accurate marine target position is achieved in the SAGIN environment. Numerical results are carried out, which demonstrates the effectiveness of the proposed DOA estimator, and the multi-UAV cooperative localization system can realize accurate target localization.

Robust Sparse Bayesian Learning Scheme for DOA Estimation with Non-Circular Sources

In this paper, a robust DOA estimation scheme based on sparse Bayesian learning (SBL) for non-circular signals in impulse noise and mutual coupling (MC) is proposed. Firstly, the Toeplitz property of the MC matrix is used to eliminate the effect of array MC, and the array aperture is extended by using the properties of the non-circular signal. To eliminate the effect of impulse noise, the outlier part of the impulse noise is reconstructed together with the original signal in the signal matrix, and the DOA coarse estimation is obtained by balancing the accuracy and efficiency of parameter estimation using the alternating SBL update algorithm. Finally, a one-dimensional search is used in the vicinity of the searched spectral peaks to achieve a high-precision DOA estimation. The effectiveness and robustness of the algorithm for dealing with the above errors are demonstrated by extensive simulations.

Underdetermined DOA estimation for moving array with reduced mutual coupling in unknown nonuniform noise environment

In practice, direction of arrival (DOA) estimation methods will suffer from significant performance degradation due to limited physical sensors, mutual coupling effect and unknown nonuniform noise. To improve the performance of underdetermined DOA estimation in the case, this paper proposes a moving sparse uniform linear array (ULA) for more degrees of freedom (DOF) and lower mutual coupling, and then provides an estimation algorithm with unknown nonuniform noise mitigation. There is a systematic procedure to determine the inter-sensor spacing of the original array and number of shifted arrays for the synthetic ULA, for achieving increased DOF. The construction and analysis of mutual coupling matrix are exploited to show the reduced mutual coupling in the synthetic array. A procedure of nonuniform noise suppression for the synthetic array is given by averaging the noise power from the original array, and then root-MUSIC is employed for DOA estimation with low-complexity. Simulation results are given to demonstrate the superiority of the proposed array and algorithm in terms of DOF enhancement, mutual coupling reduction and nonuniform noise mitigation.

Off-Grid DOA Estimation With Mutual Coupling via Block Log-Sum Minimization and Iterative Gradient Descent

Mutual coupling (MC) effect between antennas can deteriorate the direction of arrival (DOA) estimation performance. Block sparse signal representation (BSSR) is an effective solution to mitigate the MC effect. Nevertheless, continuous angle space has to be discretized into a finite set of grid points, which lead to the grid mismatch. In this paper, we present an iterative block sparsity reconstruction algorithm for off-grid DOA estimation with MC. First, by exploiting the banded symmetric Toeplitz structure of MC matrix, a reduced BSSR model is formulated to preferably mitigate the MC effect. Then, an iterative block sparsity reconstruction algorithm with multiple measurement vectors (MMV) is proposed. Due to the NP-hard property of block l0 norm minimization, a block log-sum minimization method is developed to encourage sparsity for such a block sparse recovery problem, and a surrogate objective function is derived via the majorization-minimization approach. Finally, an iterative gradient descent algorithm is explored to refine the DOAs. Simulations verify that the proposed off-grid algorithm has robustness under limited snapshots and coherent sources.

Robust beamforming for non-circular signals in uniform linear arrays with unknown mutual coupling

The performance of widely linear beamformer (WLB) is seriously degraded by any uncalibrated mutual coupling between antenna elements. In this paper, we propose an architecture to mitigate the unknown mutual coupling mismatch in uniform linear arrays and design a robust WLB for non-circular signals. We exploit the fourth-order cumulants method and the steering vector property of a uniform linear array to estimate the directions of incident signals as well as the mutual coupling coefficients. We decouple the received signals by using the mutual coupling matrix so that the powers and non-circularity coefficients of incident signals can be estimated appropriately. This allows us to reconstruct a so-called decoupled augmented interference-plus-noise covariance matrix (AINCM). We minimize the variance of beamformer with the subspace constraint to estimate the steering vector mismatch. Meanwhile, the extended steering vector (ESV) mismatch is estimated by minimizing the variance of WLB with the extended subspace constraint. Therefore, the ESV of signal-of-interest can be estimated accurately. Numerical simulations illustrate that the proposed WLB is robust against the unknown mutual coupling mismatch and significantly outperforms some of the state-of-the-art WLBs.

Performance Analysis of Dipole Antenna Based Planar Arrays With Mutual Coupling and Antenna Position Error in mmWave Hybrid System

In this work, a hybrid architecture called fully connected sub-array (FCSA) is considered for uplink data decoding with mutual coupling and space constraints at the base station (BS). The above architecture achieves the same system performance with a lower hardware complexity than a fully connected array. The packing of many antenna elements on a small surface area leads to the mutual coupling effect. Moreover, having antenna elements at the BS with finite directivity is more practical than having isotropic antenna elements at the BS. In the present work, we have considered uplink data decoding with dipole antennas arranged in a uniform planar array (UPA) grid at the BS with the error in separation between the antenna elements and mutual coupling as additional impairments. An approximate expression for the mutual coupling matrix (MCM) is derived and verified. A geometry-based stochastic model (GBSM) for the channel is considered between the user equipment (UE) and the BS. The performance of the hybrid architecture in terms of spectral efficiency (SE) and bit error rate (BER) of the system, with the mutual coupling effect and antenna separation error, is analyzed. Numerical simulations show that when the BS has no information on the MCM, SE and the system's BER performances with the FCSA architecture degrade. In the absence of any information on the coupling effect, the system performs better when a more extensive array size is used at the BS. Both the SE and BER degraded when longer dipoles were used in the array.

Wideband Electromagnetic Field Vector Antenna Array Technique and Direction Finding Algorithm

Wideband (UWB) technology has been widely used in ultra-wideband wireless communication, radar detection and other fields because of its advantages such as wide working frequency band, fast transmission rate and accurate positioning. This paper mainly studies the broadband electromagnetic field vector antenna array technology and direction finding algorithm. In this paper, the structure of a broadband resonant antenna unit is designed. The antenna unit adopts the form of printed antenna, which has both the advantages of planar antenna structure and wider bandwidth. For array antenna amplitude-phase error exists when the ideal direction, of the environment theory analyzes the mutual coupling and antenna array yuan border effect influence on beam shaper MUSIC algorithm, this paper proposes a anti-interference antenna phase characteristic difference of the calibration method of using 3 d electromagnetic simulation software HFSS, the mutual coupling matrix calculation, the amplitude-phase error correction, and has carried on the MATLAB simulation, the simulation results show that the method of direction finding pitching Angle error of less than 1, the direction finding azimuth error is less than 2, can be used for the beidou anti-interference antenna of direction finding.

Antenna Array Calibration Using a Sparse Scene

In radar systems, antenna arrays acquire direction-dependent information to localize targets or create images of the environment. However, because of unknown complex amplitudes per channel and mutual coupling, a calibration is necessary for good performance. Common calibration approaches measure to targets under known angles in a multipath-free far-field environment, which often can only be provided by anechoic chambers. Therefore, this process is not suitable for low-cost and frequent calibration. To overcome these limitations, this paper proposes a novel calibration approach using an unknown but sparse target scene. Multiple measurements at known relative positions of the radar are combined to a synthetic aperture. Then, the full mutual coupling matrix is estimated simultaneously with the unknown target scene. The method requires neither target position information, far-field conditions, nor an anechoic chamber because multipath propagation can be suppressed easily for targets located in the near-field. The proposed calibration approach is validated by measurements of a commercial 77GHz radar. The performance is evaluated by comparing the achieved image quality using the calibration results of this work and the radar’s ex-factory calibration data. The proposed novel calibration procedure improves the image quality, while considerably lowering the demands on the calibration measurements and environment.

How Varying the Dipole Lengths of a Uniform Linear Array Affects the Performance of an ESPRIT based Direction Finding Algorithm

Popularly used to collect data for the direction-of-arrival estimation of an incident source. Since the dipole elements of the uniform linear array are electromagnetically and mutually coupled, the presence of mutual coupling may degrade the performance of any direction finding algorithms. In order to mitigate mutual coupling, several references introduced modifications of the well-known ESPRIT algorithm. These modifications involve discarding the data collected by linear array at the two ends. However, the assumption of several literature that the mutual coupling matrix to be both Toeplitz and banded are invalid. This is pointed out by the “method of moments” based computer simulation tool used in this paper. The Toeplitz-and-banded coupling-matrix assumption leads to the mutual coupling being mis-modeled. Furthermore, previous studies failed to consider how varying the dipoles’ electrical length affect the performance of the direction-of-arrival estimation under mutual coupling.

Element phase centre and orientation compensation in conformal arrays during continuous deformations based on spherical mode expansion

Radiation field of conformal arrays can be obtained by simulation computation. There must be a trade-off between computation accuracy and complexity. With respect to applications where both high efficiency or even real-time applications and accuracy are required, such as adaptive beamformers together with time-varying array structures due to deformations or vibrations, more effective methodologies have to be employed for precise mainlobe direction maintenance and rigorous suppression of existing interferences. A method combining spherical mode expansion, rotation and translation of spherical waves, spatial displacement phase compensation, and approximations of constant element radiation patterns in local coordinate systems is proposed here, featuring one-time numerical effort for isolated element radiation patterns, fast coupling matrix calculation based on updated array configuration, and analytical radiation field expressions with limited eigenmode expansion coefficients storage requirements. Adaptive beamformers are utilised to validate the effects of remaining approximations including constant element patterns in local coordinate systems and constant mutual coupling matrix, proving the proposed method has the potential for aircraft-borne conformal antenna array radiation field analysis where deformations and vibrations occur continuously.

Direction-of-Arrival Estimation of Coherent Signals Under Direction-Dependent Mutual Coupling

In this letter, we develop an effective algorithm for direction-of-arrival (DOA) estimation of coherent signals in the presence of direction-dependent mutual coupling. Based on the structure feature of mutual coupling matrix, we firstly eliminate the mutual coupling effect by selecting the middle subarray outputs. Subsequently, we exploit a linear combination of the subarray manifolds to formulate forward/backward linear prediction models. Finally, the DOAs of coherent signals are extracted from the phase factors of the roots that make the prediction polynomial to be zero. Without any array calibration, the proposed algorithm can accurately estimate the DOAs of coherent signals under direction-dependent mutual coupling. Numerical results demonstrate the effectiveness of the proposed algorithm.

Robust Sparse Representation for DOA Estimation With Unknown Mutual Coupling Under Impulsive Noise

A variety of approaches have been exploited for DOA estimation with unknown mutual coupling in recent years. However, they usually suffer performance degradation under impulsive noise. To overcome this problem, an improved method for DOA estimation in the presence of unknown mutual coupling is proposed. Firstly, a sparse representation of the received signals is created by the aid of the structure of mutual coupling matrix (MCM). Subsequently, a Cauchy-score based cost function is utilized to reconstruct the sparse model and realize DOA estimation. Numerous experiments are carried out to evaluate the algorithms and simulation results confirm that our method shows superior performance than existing methods.

Calibration of antenna arrays using the extended manifold

Parametric calibration of antenna arrays uses mathematical models of the array manifold with adjustable parameters. In this study, the author shows that the standard model used in that array signal processing literature may not be capable of accurate calibration because of the mismatch between the assumed manifold and the true electromagnetic manifold. To improve calibration quality, the author uses the extended array manifold which employs a non-square coupling matrix instead of the square mutual coupling matrix used in the standard model. This new model makes it possible to increase array calibration accuracy to any desired level, at the cost of requiring more calibration sources.