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We present a subspace-based polynomial rooting algorithm to estimate the frequency bias (FB) of generalized frequency division multiplexing (GFDM) systems employing null subcarriers and repetitive sub-symbols. The estimation process is classified into fractional FB (FFB) and integer FB (IFB) estimation. The use of repetitive sub-symbols creates a quasi-periodic structure in the FB-distorted received signal, allowing the proposed algorithm to estimate the FFB using the root-MUSIC algorithm. Based on this, the proposed algorithm compensates for the FFB in the received signal and then estimates the null subcarrier pattern (NSP) in the frequency domain. As a result, the IFB estimate can be obtained in a maximum likelihood (ML) manner. Before the NSP estimation, this study uses a sub-symbol combiner to enhance signal strength of the FFB-aligned signal, ensuring the reliability of the IFB estimate. Computer simulations show that the proposed subspace-based algorithm has several advantages over traditional FB estimation methods: 1. Unlike some existing algorithms that use a training sequence to estimate FB, the proposed approach is a semi-blind algorithm because it can deliver information through repeated sub-symbols while estimating FB; 2. The proposed algorithm demonstrates excellent estimation accuracy compared to most traditional FB estimation algorithms; and 3. The proposed algorithm is computationally efficient, making it applicable to real-time applications in future communication systems. [ABSTRACT FROM AUTHOR]

We present a subspace-based polynomial rooting algorithm to estimate the frequency bias (FB) of generalized frequency division multiplexing (GFDM) systems employing null subcarriers and repetitive sub-symbols. The estimation process is classified into fractional FB (FFB) and integer FB (IFB) estimation. The use of repetitive sub-symbols creates a quasi-periodic structure in the FB-distorted received signal, allowing the proposed algorithm to estimate the FFB using the root-MUSIC algorithm. Based on this, the proposed algorithm compensates for the FFB in the received signal and then estimates the null subcarrier pattern (NSP) in the frequency domain. As a result, the IFB estimate can be obtained in a maximum likelihood (ML) manner. Before the NSP estimation, this study uses a sub-symbol combiner to enhance signal strength of the FFB-aligned signal, ensuring the reliability of the IFB estimate. Computer simulations show that the proposed subspace-based algorithm has several advantages over traditional FB estimation methods: 1. Unlike some existing algorithms that use a training sequence to estimate FB, the proposed approach is a semi-blind algorithm because it can deliver information through repeated sub-symbols while estimating FB; 2. The proposed algorithm demonstrates excellent estimation accuracy compared to most traditional FB estimation algorithms; and 3. The proposed algorithm is computationally efficient, making it applicable to real-time applications in future communication systems.

Abstract This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method.

This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method. [ABSTRACT FROM AUTHOR]

The direction-finding (DF) problem for unfolded co-prime linear array (UCLA) is researched. Specifically, there is a need to address the critical issue of non-trivial ambiguity in estimating the angle-of-arrival (AOA) parameter. To address this issue, an improved polynomial rooting-based method is proposed. A polynomial function is derived based on the orthogonality between the noise subspace singular vectors and array response vectors. In order to select the signal roots that are related to true AOAs over ambiguous roots, a maximum signal power function is proposed based on spatial filtering and second-order differential. The proposed method overcomes the non-trivial ambiguity and estimates the true AOAs successfully with improved estimation performances in terms of reliability, accuracy and angular resolution involving low computational cost. Simulations have been performed to show the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the problem of direction-of-arrival (DOA) estimation using uniform linear arrays (ULAs) composed of two-component electromagnetic vector-sensors. Quaternions are utilized as a primitive tool for our design. Using the elegant quaternion modeling of the received data, a useful orthogonality criterion between the noise subspace eigenvectors and the spatial steering vector of the array is derived. This criterion enables us to utilize the Vandermonde structure of the spatial steering vector of a ULA to develop a polynomial rooting-based DOA estimation algorithm, denoted by Q-Root-MUSIC. The proposed method replaces the need for a search procedure over the DOA and the polarization parameters with a polynomial rooting procedure which significantly reduces the computational burden of the method. Simulations are conducted to demonstrate the performance of the proposed method. The simulation results show that the proposed method provides improved resolution capabilities for closely-spaced sources in the low signal-to-noise ratios with dramatically lower computational complexity. [ABSTRACT FROM AUTHOR]

Abstract A novel Toeplitz fourth-order cumulant (FOC) orthonormal propagator rooting method (TFOC ‐ OPRM) of direction-of-arrival (DOA) estimation for uniform linear array (ULA) is proposed in this paper. Specifically, the modified (i.e., reduced-dimension) FOC (MFOC) matrix is achieved at first via removing the redundant information encompassed in the primary FOC matrix; then, the TFOC matrix which possesses Toeplitz structure can be recovered by utilizing the Toeplitz approximation method. To reduce the computational complexity, an effective method based on the polynomial rooting technology is adopted. Finally, the DOAs of incident signals can be estimated by exploiting orthonormal propagator rooting method. The theoretical analysis coupled with simulation results show that the proposed resultant algorithm can reduce the computational complexity significantly, as well as improve the estimation performance in both spatially white noise environment and spatially color noise environment.

Generally, multi-dimensional spectral peak search (SPS) in parameter estimation for polarization sensitive coprime linear arrays (PS-CLAs) requires heavy computational burden. To resolve this problem, we propose a search-free algorithm for multi-parameter estimation with PS-CLAs in this paper. Specifically, different from the decomposition algorithms, we first reconstruct the total received signal of PS-CLA as the signal extracted from a large uniform linear array, which enables to offer a spectrum function only with regard to direction of arrival (DOA) by utilizing rank reduction estimator. Subsequently, we employ the polynomial root finding technique instead of one-dimensional SPS to directly calculate the DOA estimates. Furthermore, a quadratic optimization problem is established for the polarization parameters and in particular, the closed-form solutions are provided by utilizing Lagrange multiplier approach. Finally, numerical simulations illustrate that the proposed search-free algorithm can obtain improved estimation accuracy with remarkably low complexity. [ABSTRACT FROM AUTHOR]

In this study, the problem of low-complexity direction-of-arrival (DOA) estimation is addressed, and a novel real-valued propagator method (PM) is presented with a uniform linear array. The covariance matrix is divided into two subarrays and an equivalent noise subspace is obtained by exploiting the standard PM algorithm without eigenvalue decomposition. By a coordinate mapping technique, the complex PM cost function has been converted into a real-valued polynomial whose order only rely on the number of arrays. Using such a mathematical fact, source DOAs can be estimated by polynomial rooting instead of peak searching. The proposed method is able to reduce significant complexity with comparable root-mean-square error performance to the standard PM, which is finally verified by numerical simulations. [ABSTRACT FROM AUTHOR]

• The article discusses the ability of polarimetric multiple-input multiple-output (MIMO) radar to operate data in joint spatial and polarization domains. • The article explores the non-ideal factors that may exist in practical polarimetric MIMO radar and points out that many existing methods cannot handle these factors. • The article proposes a joint direction-of-arrival (DOA) and polarization parameter estimation method, termed PMS2, which incorporates the polarimetric manifold separation (PMS) technique and requires no pair matching or spectral peak searching procedures. The proposed PMS2 approach can perform joint DOA and polarization estimation for polarimetric MIMO radar with various non-ideal factors for an array, such as gain error, phase error, and position error. • The article provides the Cramér-Rao lower bound for the multi-dimensional parameters involved in the estimation problem. • The article presents simulation results that demonstrate the performance advantages of the proposed PMS2 approach, which is attributed to the compact structure of polarimetric transceivers and the ability of the PMS2 approach to handle the polarimetric properties of signals. Compared with conventional multiple-input multiple-output (MIMO) radar, polarimetric MIMO radar has been proven to hold the additional capability to operate data in the joint spatial and polarization domains. However, practical transceivers may involve antenna arrays with classical non-ideal factors (e.g., gain/phase/position errors) and polarimetric non-ideal factors (e.g., polarimetric antenna misorientation), and many current approaches cannot handle such non-ideal factors in real applications. In this study, polynomial rooting-based direction-of-arrival (DOA) and polarization parameter estimation is investigated for polarimetric monostatic MIMO radar with non-ideal transceivers. By incorporating the polarimetric manifold separation (PMS) technique, a joint DOA and polarization parameter estimation method, termed PMS2, is proposed with a closed-form solution. The Cramér-Rao bound for the multi-dimensional parameters involved in the estimation problem is also given. Simulation results demonstrate the performance advantages of the proposed PMS2 approach, which is attributed to the compact structure of polarimetric transceivers and the ability of the PMS2 approach to handle the polarimetric properties of signals. [ABSTRACT FROM AUTHOR]

In this study, the problem of low-complexity direction-of-arrival (DOA) estimation is addressed, and a novel real-valued propagator method (PM) is presented with a uniform linear array. The covariance matrix is divided into two subarrays and an equivalent noise subspace is obtained by exploiting the standard PM algorithm without eigenvalue decomposition. By a coordinate mapping technique, the complex PM cost function has been converted into a real-valued polynomial whose order only rely on the number of arrays. Using such a mathematical fact, source DOAs can be estimated by polynomial rooting instead of peak searching. The proposed method is able to reduce significant complexity with comparable root-mean-square error performance to the standard PM, which is finally verified by numerical simulations.

The problem of closed-form parameter estimation using a diversely polarized antenna array of arbitrary configurations is considered, under the coexistence of the circular and strictly noncircular signals used in the communication/radar systems. By incorporating the noncircularity difference and polarization diversity of the signals with the augmented polarimetric manifold decoupling, the conventional polynomial rooting polarimetric element space subspace technique is enhanced for direction-of-arrival, polarization, and noncircularity phase (for strictly noncircular sources) estimation. A subspace constraint method is also presented to improve parameter estimation of the strictly noncircular sources. Simulation results are included to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

To increase the computing speed of the angle of direction of arrival (DOA) estimation algorithm，on the bases of analysis of the MUSIC symmetric compression algorithm and on the basis of using the structure of conjugate noise subspace and intersection of the noise subspace and conjugate noise subspace for singular valve decomposition， equivalent to add image source ideas，this paper proposed the construction of polynomials of MSCS algorithm，which MSCS algorithm was polynomial roots. The algorithm kept the image characteristics of MSCS algorithm，and didn't need to be carried out traversal search within the half spectrum，only needed to seek the root processing in a half spectrum. Theoretical analysis and simulation experiments show that the algorithm further improves the operation speed of the MSCS algorithm，with respect to the root MUSIC algorithm，the algorithm improves the DOA estimation accuracy，which proves the validity of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of sparsity-inducing direction-of-arrival (DOA) estimation in the context of array covariance vectors when a recently proposed nested array structure is utilized. The proposed approach is based on a Sparse Bayesian learning (SBL) perspective while the off-grid effects inherent in traditional sparse recovery algorithms are taken into account simultaneously. Specifically, the notable advantages of the developed approach can be attributed to two aspects. First, through a linear transformation, the unknown noise variance can be eliminated effectively and the estimation error between the actual and sample covariance matrix can be normalized to an identity matrix, thereby facilitating a noise-free sparse representation. Second, a computationally tractable polynomial rooting procedure is introduced to calculate the discretized sampling grid error one by one based on the reconstructed spatial power spectrum, thus this novel algorithm can maintain high estimation accuracy even under a coarse sampling grid. Extensive simulation results finally demonstrate the superiority of the proposed approach in terms of DOA estimation precision and computational efficiency over off-the-shelves techniques. [ABSTRACT FROM AUTHOR]

The extended signal subspace was constructed to reduce the computation load of former data processing of bistatic MIMO radar.According to the characteristic of this signal subspace,the polynomial rooting-spatial filtering algorithm was proposed to estimate the direction of arrivals (DOA) and direction of departure (DOD).It avoided the conventional two-dimensional spectrum searching and the estimated parameters were paired automatically without extra pairing operation.Furthermore,Cramer-Rao bounds (CRB) for DOA and DOD estimation were derived under multi-target and single target in bistatic MIMO radar.The results illustrate that when spatial sector is filt the higher order of the Taylor series expansion,the better angular accuracy of targets can be derived.The proposed algorithm can get good estimation performance even when the DODs of targets are close to each other.And the polynomial rooting-spatial filtering algorithm can perform better than ESPRIT algorithm in resolution in SNR,and both of them are close to the CRB in the high SNR.

This paper deals with direction of arrival (DOA) and direction of departure (DOD) estimation of existing targets based on polynomial root finding estimators with minimum variance distortionless response (MVDR) criterion in bistatic multi-input multi-output radar systems. First, the presented estimator transforms the conventional two-dimensional searching approach into double one-dimensional polynomial root-MVDR approach for DOA and DOD estimation. Thus, the pairing operation can be obtained automatically. Second, to mitigate the influence of noise corruption and the estimate radial bias, we also presented a differential polynomial root-MVDR estimator to obtain more accuracy estimation performance. Finally, simulation results are provided to verify the efficiency of the proposed estimators. [ABSTRACT FROM AUTHOR]

Two adaptive Capon methods that jointly estimate the azimuth-angle and polarization of the sources in a closed-form are proposed. It is shown that the azimuth-angles of the sources may be estimated from the roots of a complex-valued polynomial or by rooting a real-valued polynomial, instead. The latter method is particularly useful in tracking arbitrarily polarized sources in a sequential snapshot-by-snapshot manner using root-tracking techniques. The proposed polynomial rooting based methods are applicable to polarization sensitive arrays regardless of the array geometry including conformal arrays, and take into account array nonidealities. A large-sample analysis of the polarimetric Capon method is also provided showing that it converges, up to a multiplicative factor that depends on the interference-plus-noise power, to the polarimetric MUSIC method in the high SINR regime. Such a result gives a new insight into the well-known Capon and MUSIC methods. This paper also shows that employing manifold separation in robust Capon beamforming as well as in transmit beamforming schemes leads to improved performance in terms of received SINR when array calibration measurements are used. Extensive numerical results employing real-world polarimetric arrays are given. Results show that employing manifold separation leads to improved performance in many array processing tasks. [ABSTRACT FROM PUBLISHER]

In the present paper, we propose a novel method for estimating one-dimensional damped and undamped harmonics. Our method utilizes the multiple shift-invariance property comprised in the signal model. We develop a new rank-reduction estimator which is formed as the weighted sum of the individual matrix polynomials obtained from individual shift-invariance equations. The uniqueness conditions for the proposed rank-reduction criteria are derived under the assumption that all samples are available. Moreover, a novel technique for the incomplete data case, where some samples are missing, is presented. In this case, the rank-reduction estimator may suffer from ambiguities. To overcome this problem, we propose an extension of the rank-reduction estimator that is based on polynomial intersection and the properties of the Sylvester matrix. The latter algorithm yields unique estimates of the damped harmonics. The proposed high-resolution techniques are search-free and therefore, they enjoy moderate computational complexity. [ABSTRACT FROM PUBLISHER]

Abstract: A direction of the arrival (DOA) estimation method utilizing polynomial rooting is developed for monostatic MIMO radar. Utilizing the redundancy of the received data, a reduced-dimensional matrix is firstly performed to alleviate the temporal snapshots requirement and the computational burden resulting from the inversion of the covariance matrix. To further alleviate the complexity burden, a polynomial rooting method is proposed to identify the extreme values of Capon spatial spectrum. Since the target DOA lies in the set of all extreme values, DOA estimation method can be performed based only on the candidate angles around those extreme values. Numerical results verify the effectiveness of this method. [Copyright &y& Elsevier]

Abstract: A fast and highly accurate algorithm for solving quartic equations is introduced. This new algorithm is more than six times as fast and several times more accurate than the quasi-standard Companion matrix eigenvalue quartic solver. Moreover, the method is exceptionally robust in cases of extreme root spread. The new algorithm is based on a factorization of the quartic in two quadratics, which are solved in closed form. The performance key at this point is a fixed-point iteration based fitting algorithm for backward optimization of the underlying quartic-to-quadratic polynomial decomposition. Detailed experimental results confirm our claims. [Copyright &y& Elsevier]

A new polynomial root-finding-based method for two-dimensional (2-D) angles of arrival (AOAs) estimation is proposed, which uses two parallel uniform linear arrays. The method takes the special structure of the array that enables decoupling the 2-D AOA estimation problem into two successive one-dimensional (1-D) AOA estimation problems, thereby increases the array aperture to estimate more sources than those of 2-D ESPRIT and DOA matrix methods. The computation complexity of the proposed method is evaluated and a relevant Cramer-Rao bound of the proposed method is derived. Numerical examples are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The blind carrier frequency offset estimation problem has been well studied by exploiting the virtual carriers existing in practical orthogonal frequency division multiplexing transmissions. A highly efficient approach by rooting a polynomial has been proposed in the literature. However, this rooting method is suboptimal when noise is present. In this letter, we propose an improved polynomial rooting method that is shown to be the maximum likelihood estimator for both the noisy and the noise-free case. [ABSTRACT FROM AUTHOR]