Fourth-order Cumulant Research Articles

Passive direction finding with a pair of acoustic vector sensors using fourth-order cumulants

In this paper, an elevation-azimuth direction finding algorithm with the use of a pair of identically oriented acoustic vector sensors, which can be arbitrarily deployed at unknown locations, is proposed. Two fourth-order cumulant (FOC) matrices, which impose the so-called translational invariance property in the coarray domain, are defined. Such invariant structure allows recovering the coarray steering vectors of the acoustic vector sensors in closed-form from the generalized eigenvectors of the matrix pencil, which is built from the two defined FOC matrices. The identifiability performance of the proposed algorithm is further investigated. It is shown that up to 9 sources can be uniquely identified. The extension of the proposed algorithm for accommodating arbitrary AVS arrays with unknown sensor locations is also addressed. Afterward, the asymptotic performance bound of the considered problem is derived. Finally, the efficacy of the proposed algorithm is verified by numerical examples.

A Two-Stage High-Order Modulation Recognition Based on Projected Accumulated Constellation Vector in Non-Cooperative B5G OSTBC-OFDM Systems

Blind modulation recognition (BMR) is a pivotal signal processing technology for cognitive receivers to reduce signaling overhead and improve transmission efficiency. Although BMR techniques have been extensively explored for single-carrier systems, only a few research have been published for OSTBC-OFDM systems. More troubling is that high-order modulation types will make the BMR harder because the constellation points are overcrowded. To remedy these flaws, we propose a two-stage high-order BMR approach that leverages low-complexity cumulants and projected accumulated constellation vector (P-ACV) to recognize high-order modulation types (e.g., 2048QAM). Firstly, zero-forcing blind equalization is employed to recover the damaged signal and enhance its feature representation. Next, the first-stage recognition module leverages the fourth-order cumulants to classify 13 modulation types into three groups, including PSK&PAM, square-shaped QAM and cross-shaped QAM groups. Finally, the second-stage recognition module distinguishes the inter-class signal in each group by P-ACV features. The temporal convolution network is built to tap the potentialities of P-ACV and speed up online inference. Numerical results demonstrate that our two-stage algorithm obtains a recognition accuracy of 97.37% when signal-to-noise-ratio (SNR) ≥ 12 dB and performs six times faster than the suboptimal method. Notably, it does not require prior knowledge, such as channel state information (CSI) and SNR conditions.

Cumulant methods for electron-phonon problems. I. Perturbative expansions

In this work we investigate the ability of the cumulant expansion (CE) to capture one-particle spectral information in electron-phonon coupled systems at both zero and finite temperatures. In particular, we present a comprehensive study of the second- and fourth-order CE for the one-dimensional Holstein model as compared with numerically exact methods. We investigate both finite sized systems as well as the approach to the thermodynamic limit, drawing distinctions and connections between the behavior of systems in and away from the thermodynamic limit that enable a greater understanding of the ability of the CE to capture real-frequency information across the full range of wave vectors. We find that for zero electronic momentum, the spectral function is well described by the second-order CE at low and high temperatures. However, for non-zero electronic momenta, the CE is only accurate at high temperature. We analyze the fourth-order cumulant, and find that while it improves the description of the short-time dynamics encoded in the one-particle Green's function, it can introduce divergences in the time domain as well as unphysical negative spectral weight in the spectral function. When well-behaved, the fourth-order CE does provide notable accurate corrections to the second-order CE. Finally, we use our results to comment on the use of the CE as a tool for calculating transport behavior in the realistic ab initio modeling of materials.

A novel sparse linear array based on fourth‐order cumulants for improved direction‐of‐arrival estimation

Owing to increased degrees of freedom (DOFs) and reduced mutual coupling effect, sparse linear arrays can improve the performance of direction-of-arrival estimation compared with uniform linear arrays. In this study, a novel sparse linear array is presented based on fourth-order cumulants, which consists of five sparse sub-arrays. The sensor locations of the five sub-arrays are determined by a closed-form expression. Closed-form expressions of DOFs for the proposed array with any number of sensors are also derived. By optimising the allocation of sensors in each sub-array, the DOFs of the proposed array with M sensors achieve O M 4 . Because each sub-array is sparse, the number of pairwise sensors with small separation is significantly alleviated. Theoretical analysis shows that the proposed array can provide a higher number of DOFs and is more robust in scenarios with heavy levels of mutual coupling than most sparse linear arrays. Numerical simulations are conducted to demonstrate the merits of the proposed array over other sparse linear arrays.

Estimation Method for Mixed Near-Field and Far-Field Sources Based on Four-Order Cumulant and Polarization Sensitive Array

A new multidimensional parameters joint estimation method of mixed near-field and far-field sources based on polarization sensitive array, fourth-order cumulant, joint diagonalization technology, and propagator method is presented, which can realize the joint estimation of DOA (Direction of Arrival), range, frequency, polarization auxiliary angle, and polarization phase difference without multidimensional spectral peak searching and parameter pairing, and it is suitable for any additive Gaussian noise environment and effective for reducing the loss of array aperture. The algorithm skillfully constructs the fourth-order cumulant matrix by using the output on the label of specific dipole pairs of the received array, which effectively avoids the matrix rank reduction caused by the far-field sources coexistence situation. In addition, the presented algorithm utilizes the orthogonal propagation algorithm for subspace decomposition and uses the total least square solution to replace the orthogonal solution of singular value decomposition, which effectively reduces the computational complexity. The experiment proved the effectiveness of the proposed algorithm.

A Gridless Fourth-Order Cumulant-Based DOA Estimation Method Under Unknown Colored Noise

To reduce the adverse impacts of the unknown colored noise on the performance degradation of the direction-of-arrival (DOA) estimation, we propose a new gridless DOA estimation method based on fourth-order cumulant (FOC) in this letter. We first introduce the non-redundancy single measurement vector (SMV) through FOC, which is capable of suppressing the Gaussian colored noise. Next, we analyze the distribution of the estimation error and design an estimation error tolerance scheme for it. We then combine the atomic norm minimization of the non-redundancy SMV with the above constraint scheme. This combination poses the stability of the sparsest solution. Finally, the DOA estimation is retrieved through rotational invariance techniques. Moreover, this method extends the gridless DOA estimation to the sparse linear array. Numerical simulations validate the effectiveness of the proposed method.

Location Parameter Estimation of Moving Aerial Target in Space–Air–Ground-Integrated Networks-Based IoV

Estimating the location parameters of moving target is an important part of intelligent surveillance for the Internet of Vehicles (IoV). Satellite has the potential to play a key role in many applications of space–air–ground-integrated networks (SAGINs). In this article, a novel passive location parameter estimator using multiple satellites for the moving aerial target is proposed. In this estimator, the direct wave signals in reference channels are first filtered by a band-pass filter, followed by a sequence cancelation algorithm to suppress the direct-path interference and multipath interference. Then, the fourth-order cyclic cumulant cross ambiguity function (FOCCCAF) of the signals in the reference channels and the four-weighted fractional Fourier transform FOCCCAF (FWFRFT-FOCCCAF) of signals in the surveillance channels are derived. Using them, the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) are estimated and the distance between the target and the receiver and the velocity of the moving aerial target are estimated by using multiple satellites. Finally, the Cramer–Rao lower bounds of the proposed location parameter estimators are derived to benchmark the estimator. The simulation results show that the proposed method can effectively and precisely estimate the location parameters of the moving aerial target.

Through-the-wall high-dimensional imaging of human vital signs by combining multiple enhancement algorithms using portable LFMCW-MIMO radar

Radar-based life imaging technology has been widely applied in both civilian and military applications. Wall penetration attenuation degrades the signal-to-clutter-and-noise ratio (SCNR) and radar portability restricts the spatial resolution of the high-dimensional image. In this study, we constructed a portable linear-frequency continuous-wave(LFMCW) multiple-inputmultiple-output(MIMO) radar system, and we presented a novel high-dimensional imaging framework. We combined the maximum spectrum peak, fourth-order cumulant (FOC) and 3D coherent factor (CF) to enhance vital signs based on attention mechanism. We improve resolution by deconvolution algorithm using the data from a human dummy. Visualization-enhanced 4D point clouds images were created by mapping micro-doppler-frequency to color. We employed a series of experiments to validate the proposed method, including human and beagle imaging in free space, and short-range and long-range (16 m) human imaging through a wall. These high-dimensional imaging results validated the portable radar system’s potential in detection, identification, interpretation of human targets.

Parameter Estimation of Non-Gaussian Signals for Polarization-Sensitive Augmented Coprime Array: Fourth-Order Cumulant Reduced-Dimensional Capon Algorithm

In this paper, we investigate the problem of direction of arrival (DOA) and polarization estimation for non-Gaussian signal in polarization-sensitive augmented coprime array. Instead of the second-order cumulant statistics, the fourth-order cumulant statistics of the received signals are used for parameter estimation because they can detect more information of the non-Gaussian signal. First, polarization-sensitive augmented coprime array is designed, where each sensor element is equipped with a pair of orthogonal electric dipoles. Furthermore, a low-complexity reduced-dimensional Capon algorithm which uses the fourth-order cumulant of the received array signal is proposed for DOA and polarization estimation. Only one-dimensional peak search is required by reconstructing peak search function. Theoretical analysis has proven the effectiveness of the algorithm, and simulation results demonstrate that the proposed fourth-order cumulant reduced-dimensional Capon algorithm outperforms the other algorithms.

Localisation and classification of mixed far‐field and near‐field sources with sparse reconstruction

A sparse reconstruction algorithm for the localisation of mixed near-field and far-field sources (MFNS) based on four-order statistics is proposed in this study. First, utilising the structural characteristics of a uniform symmetric linear array, a fourth-order cumulant (FOC) matrix is constructed, which decouples the angular information from the range parameters. Based on the sparse representation framework, a weighted l1-norm minimisation algorithm is developed to obtain the direction of arrivals (DOAs) of the MFNS. However, the existing selection strategy of the tuning factor is not adaptive to different observation scenarios. So a closed-form expression of the tuning factor based on the FOC estimation error is presented. Then, another FOC matrix is constructed, which includes both the DOA and range information of the MFNS. With the DOA estimates, the two-dimensional spatial dictionary can be reduced into a one-dimensional dictionary, which only depends on the range parameters. Using the similar sparse reconstruction method, the range estimates of the MFNS can be obtained, and the types of the sources can be distinguished according to their range parameters. According to numerical simulations, the estimation performance of the proposed algorithm approaches the CRB in the high signal-to-noise ratio region, which successfully circumvents the saturation problem due to the fixed tuning factor.

A High-Precision Algorithm for DOA Estimation Using a Long-Baseline Array Based on the Hearing Mechanism of the Ormia Ochracea.

Inspired by the Ormia Ochracea hearing mechanism, a new direction of arrival estimation using multiple antenna arrays has been considered in spatially colored noise fields. This parasitoid insect can locate s cricket’s position accurately using the small distance between its ears, far beyond the standard array with the same aperture. This phenomenon can be understood as a mechanical coupled structure existing between the Ormia ears. The amplitude and phase differences between the received signals are amplified by the mechanical coupling, which is functionally equivalent to a longer baseline. In this paper, we regard this coupled structure as a multi-input multi-output filter, where coupling exists between each pair of array elements. Then, an iterative direction-finding algorithm based on fourth-order cumulants with fully coupled array is presented. In this manner, the orientation of the mainlobe can direct at the incident angle. Hence, the direction-finding accuracy can be improved in all possible incident angles. We derive the Cramér-Rao lower bound for our proposed algorithm and validate its performance based on simulations. Our proposed DOA estimation algorithm is superior to the existing biologically inspired direction-finding and fourth-order cumulants-based estimation algorithms.

DOA Estimation Method of Weak Signal under the Compound Background of Strong Interference and Colored Noise

The traditional algorithm performing direction of arrival (DOA) estimation under the background of strong interference and colored noise has the problems of low estimation accuracy and small measurement targets. Based on the construction of a fourth-order cumulant (FOC) matrix to suppress colored noise, this paper adopts the extended noise subspace (ENS) algorithm and the fixed projection blocking (FPB) algorithm to estimate the DOA of weak targets. Firstly, a FOC matrix of the received signal vector is established to curb the noise component, and the eigenvalue decomposition is performed. Then, two approaches of weak signal DOA estimation are proposed. One approach is to merge the space where the strong interference steering vector lies into the noise subspace to construct an extended noise subspace, and then, the multisignal classification (MUSIC) algorithm is used to obtain the DOA estimation of the weak signal on the basis of the extended noise subspace. Another approach is to build the orthogonal projection matrix of the interference subspace as the interference blocking matrix, and the receiving array signal is preprocessed, and on the basis of it, the eigen decomposition is performed again to obtain the DOA information of the weak signal. Both algorithms make breakthroughs in the aperture limitation of the traditional algorithm, effectively expand the aperture, and promote the accuracy of estimation. The simulation tests the effectiveness of the proposed method.

Robust Adaptive Beamforming Algorithm for Sparse Array Based on Covariance Matrix Reconstruction Technology

When the array structure of the sparse arrays (SA) cannot be determined, the existing beamforming algorithms designed according to specific formations such as coprime arrays (CA), nested arrays (NA), etc. will fail. To solve this problem, we propose two algorithms that are suitable for a variety of SA. In the first method, assuming that the desired signal is a non-Gaussian signal, the desired signal direction vector (DSDV) is estimated using the fourth-order cumulant, and then the interference plus noise covariance matrix (INCM) is reconstructed by integrating the area outside the desired signal. When the desired signal is a Gaussian signal, we propose the second method. The second method estimates the power and direction of arrival (DOA) of the signals by performing eigenvalue decomposition on the sampled covariance matrix (SCM) and finally calculates the weight vector. However, this method needs to estimate the DOA of the signals, so it has certain requirements for the SA structure design. The simulation results show that the proposed method has good performance and strong robustness under different SA.

Non-Gaussian entanglement in gravitating masses: The role of cumulants

We develop an entanglement criterion with third- and fourth-order cumulants to detect the entanglement of non-Gaussian states. The efficiency of the entanglement criterion is investigated for gravitating mirrors in optomechanical systems. We show that the entangled regime of the mirrors is enlarged by the third- and fourth-order cumulants. We also discuss the limitations of the entanglement criterion for mirrors in a highly non-Gaussian state.

AoA Estimation Based on Fourth-Order Coarrays and Cumulants for Mmwave Systems

In radar applications, it is known that with a sparse array of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas, we can construct a virtual array of size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) using fourth-order coarrays and cumulants. Such a result is valid when the sources are not Gaussian. In this paper, we consider the estimation of angles of arrival (AoA) for mmWave channels using fourth-order coarrays. An mmWave system usually has a large number of antennas but few RF chains, which restricts the effective antenna size. The angle estimation problems of mmWave and radar systems are similar, but there are differences. In particular, in the problem formulation of angle estimation for mmWave systems, we have path gains instead of source symbols. The path gains in mmWave channels are typically modeled as Gaussian random variables. We show that the critical non-Gaussian assumption for using fourth-order coarrays can be circumvented by using a submatrix of a banded Toeplitz matrix for analog combining. The combiner can be designed so that the conditions for applying fourth-order coarrays are satisfied asymptotically. A virtual array of size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) can be constructed when there are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> RF chains.

Design and Testbed Implementation of Blind Parameter Estimated OFDM Receiver

Designing an intelligent or adaptive transceiver system is becoming a promising technology for upcoming generations of wireless communication systems due to its adaptivity, spectrum efficiency, and low-latency characteristics. However, there is no work available until now that characterizes and demonstrates complete adaptation in the physical layer for orthogonal frequency-division multiplexing (OFDM) systems. In this article, we propose and implement sequential blind parameter estimation methods for OFDM signals using radio frequency (RF) testbed setup in a realistic scenario. The estimations include the number of subcarriers, symbol duration, cyclic prefix, oversampling factor, symbol timing offset (STO), and carrier frequency offset (CFO). The proposed algorithms also include blind modulation classification for linearly modulated signals over a frequency-selective fading channel. The parameter estimation has been carried out through a cyclic cumulant process. The modulation formats are classified by using normalized fourth-order cumulant in the frequency domain. The STO and CFO are estimated by a proposed modified maximum likelihood algorithm. The performances of parameter estimations, modulation classification, and synchronization are measured through analytical, simulation, and measurement studies. The overall performance of the OFDM system is provided in terms of the received constellation diagram and bit error rate (BER) over an indoor propagation environment.

Azimuth-Elevation Direction Finding With a Pair of Acoustic Vector Sensors in the Presence of a Reflecting Boundary

This paper is aiming at addressing an azimuth-elevation direction-finding algorithm using a pair of identically oriented acoustic vector sensors located near a reflecting boundary. Two fourth-order cumulant matrices related in terms of a translationally invariant structure are formed for recovering the acoustic vector sensor steering vectors in the particle-velocity coarray domain. Afterward, source azimuth-elevation directions are extracted in closed-form from the estimates of the coarray steering vectors. The identifiability study shows that the algorithm proposed herein can uniquely resolve up to 13 sources, thereby being applicable to underdetermined scenarios, where the number of sources exceeds that of the sensors. This capability constitutes the primary advantage over the many seminal works Hawkes and Nehorai (2000); Wu et al. (2016); Ahmadi-Shokouh and Keshavarz (20007); Tao et al. (2007); Xu and Liu (2007) that pioneered AVS array processing involving reflecting boundaries. Finally, numerical examples are provided to verify the theoretical analysis and demonstrate the efficacy of the proposed algorithm.

Plastic Pipeline Leak Localization Based on Wavelet Packet Decomposition and Higher Order Cumulants

This paper presents a plastic pipeline leak localization method based on wavelet packet decomposition and higher order cumulants. The hydrophone sensors are used to capture the acoustic signals generated by the water leakage in the plastic pipe. The feature frequency band containing the most leak information is subsequently extracted by performing wavelet packet decomposition on the signals. The most suitable wavelet packet basis function for leak signals is obtained by comparing the effects of varieties of wavelet packet basis functions. Furthermore, the higher order cumulant method is used to estimate the time delay between the two sensors signals, from which the leak hole can be located. The simulation and experimental results show that, compared with the basic cross-correlation method (BCC) and the generalized cross-correlation method (GCC), the higher order cumulant method has higher leak localization accuracy. The relative error of the third-order cumulant method is 2.99% in experiment 1 and 7.58% in experiment 2, while the relative localization error of the fourth-order cumulant method is 1.96% in experiment 1 and 1.23% in experiment 2.

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.

Fixed point behavior of cumulants in the three-dimensional Ising universality class

High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics, the temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.