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We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace can be estimated with the contaminated observations discarded. To this end, we employ a signal model which explicitly includes an interference term that is distinct from environmental noise. To detect when the interference term is nonzero, we estimate the interference term using an optimization problem with a sparsity-inducing group SLOPE penalty which accounts for simultaneous sparsity across all channels of the multichannel signal. We propose an iterative algorithm which efficiently computes the observations estimated to contain interference. Theoretical support for the accuracy of our interference estimator is provided by bounding its false discovery rate, the expected proportion of uncontaminated observations among those estimated to be contaminated. Finally, we demonstrate the empirical performance of our contributions in a number of simulated experiments. [ABSTRACT FROM AUTHOR]

In this paper, a novel weighted block sparse method based on the signal subspace is proposed to realize the Direction-of-Arrival (DOA) estimation under unknown mutual coupling in the uniform linear array. Firstly, the signal subspace is obtained by decomposing the eigenvalues of the sampling covariance matrix. Then, a block sparse model is established based on the deformation of the product of the mutual coupling matrix and the steering vector. Secondly, a suitable set of weighted coefficients is calculated to enhance sparsity. Finally, the optimization problem is transformed into a second-order cone (SOC) problem and solved. Compared with other algorithms, the simulation results of this paper have better performance on DOA accuracy estimation. [ABSTRACT FROM AUTHOR]

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

In order to improve the DOA estimation accuracy of mixed signals and reduce array aperture loss, a high-precision DOA estimation algorithm based on oblique projection operator is proposed. The proposed algorithm estimates the independent and coherent signals of the mixed signals in two stages. Firstly, the covariance matrix of the data received by the array element is processed by the estimating signal parameter via rotational invariance techniques(ESPRIT), and the DOA estimates of the independent signals in the mixed signals are calculated. Then, the algorithm uses the oblique projection operator to remove the independent signal information in the mixed signals to obtain a new covariance matrix. The signal subspace of the newly obtained covariance matrix is used for decoherence processing. Finally, the ESPRIT algorithm is used to calculate the DOA estimates of the coherent signals. Simulation results show that the proposed algorithm has higher accuracy than traditional mixed signal DOA estimation algorithms in the case of low signal-to-noise ratio and small signal incidence interval, and effectively reduces array aperture loss. Under the condition of different sampling snapshot numbers, the proposed algorithm also shows stronger robustness. [ABSTRACT FROM AUTHOR]

Abstract Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished.

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished. [ABSTRACT FROM AUTHOR]

Performance of direction of arrival (DOA) estimation is one of the most important issues in array signal processing. Subspace-based algorithms provide a good compromise between the estimation accuracy and computational complexity. However, these methods are exposed to performance breakdown at low SNR scenarios. A major reason for such performance breakdown is the subspace swap phenomenon (intersubspace leakage). In this article, we elaborate on a novel modified signal subspace model through exploiting a supervised index for the estimation of DOA. With the developed model we refine the signal subspace so as to enhance the performance of the DOA estimation. In the proposed scheme, we define a fuzzy similarity matrix for the eigenvalues of the array output correlation matrix to capture the distribution of the eigenvalues. Then, we build up a transformation matrix between the fuzzy similarity matrix and the eigenspace of the correlation matrix, and construct a nonlinear transformation function to adjust the fuzzy similarity matrix. Subsequently, we define a supervised evaluation index named signal subspace reconstruction error for DOA estimation and construct a cost function of the signal subspace to develop a supervised model for the signal subspace. The signal subspace can be modified through adjusting the parameter in the nonlinear transformation function and optimizing the abovementioned cost function. Finally, the performance of DOA estimation can be enhanced with the modified signal subspace. The main characteristic of the proposed model is circularly applied feedback of the estimated DOA for refining the estimated subspace. It is a closed loop and supervised method not reported before. This article opens a specific way for improving the performance of the DOA estimation in array signal processing by a supervised index. However, the proposed method is still unsatisfying in some scopes of signal-to-noise ratio. We believe that exploiting a validity index for DOA estimation in array signal processing is still a general and interesting problem. [ABSTRACT FROM AUTHOR]

ObjectiveIn biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain.ApproachIt defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.

ObjectiveIn functional electrophysiological imaging, signals are often contaminated by interference that can be of considerable magnitude compared to the signals of interest. This paper proposes a novel algorithm for removing such interferences that does not require separate noise measurements.ApproachThe algorithm is based on a dual definition of the signal subspace in the spatial- and time-domains. Since the algorithm makes use of this duality, it is named the dual signal subspace projection (DSSP). The DSSP algorithm first projects the columns of the measured data matrix onto the inside and outside of the spatial-domain signal subspace, creating a set of two preprocessed data matrices. The intersection of the row spans of these two matrices is estimated as the time-domain interference subspace. The original data matrix is projected onto the subspace that is orthogonal to this interference subspace.Main resultsThe DSSP algorithm is validated by using the computer simulation, and using two sets of real biomagnetic data: spinal cord evoked field data measured from a healthy volunteer and magnetoencephalography data from a patient with a vagus nerve stimulator.SignificanceThe proposed DSSP algorithm is effective for removing overlapped interference in a wide variety of biomagnetic measurements.

The environmental parameters are usually uncertain in complex shallow ocean environment and restrict the performance of the matching model-like method. Therefore, we need a more tolerant detection method for detecting underwater targets in the uncertain shallow ocean environment. The previous mode-subspace detection method has the characteristics of both high performance and robustness. However, the robust mode-subspace detector is suitable for vertical arrays and its performance is limited by shallow ocean environment. Therefore, we propose the tolerant detection method for estimating the robust signal subspace with horizontal arrays. We estimate the robust signal subspace by bringing uncertain parameters into the observation matrix of a horizontal array. Combined with the robust signal subspace estimation, we propose a subspace detector that tolerates uncertain parameters. The results on simulation in a uncertain shallow ocean environment show that the detector we proposed has a high average detection capability and a certain tolerance for uncertain parameters.

The demand for accurate indoor localization has become more and more urgent in location-based services (LBS). Since the traditional indoor localization is based on a single fingerprint, which is susceptible to environmental changes, it is hard to obtain high accuracy. In order to fill this gap, we propose a new multiple fingerprints method used in the indoor environment without extra measurement, and it can reduce the uncertainty caused by a single fingerprint. The multiple fingerprints are based on the signal Subspace and the received signal strength index (RSSI) and others, where the signal Subspace represents the characteristic representation of the received array signal and the RSSI represents the signal strength. First, we propose an algorithm named Subspace gradient boost decision tree (Subspace-GBDT) to obtain a strong classifier, which can make a successful prediction. Second, we propose another algorithm named double threshold assisted mode (DTAM) to combine multiple fingerprints. It can achieve accurate prediction by setting two different threshold parameters, the threshold of samples number and classifiers number, and reduce errors of matching. The experiment results show that the proposed method can obtain higher cumulative distribution function (CDF) value and localization accuracy than the traditional methods.

We present a novel and computationally simple solution to the problem of detecting the number of signals, which is applicable to both white and colored noise, and to a very small number of samples. The solution is based on a novel and non-asymptotic goodness-of-fit metric, referred to as signal subspace matching (SSM), which is aimed at matching a model-based signal subspace to its sampled-data-based counterpart. We form a set of hypothesized signal subspace models, with the k-th model being a projection matrix composed of the k leading eigenvectors of the sample-covariance matrix. This set of hypothesized models is compared to their sampled-data-based counterpart – a projection matrix constructed from the sampled data – via the SSM metric, and the model minimizing this metric is selected. We show that this solution involves the principal angles between the column span of the model and the column span of the model. We prove the consistency of this solution for the high signal-to-noise-ratio limit and for the large-sample limit. The large-sample consistency is shown to be conditioned on the signal-to-noise ratio (SNR) being higher than a a certain threshold. Simulation results, demonstrating the performance of the solution for both colored and white noise, are included. [ABSTRACT FROM AUTHOR]

We present a novel solution to the problem of estimating the array response of the signal of interest (SOI) in case it is constrained to lie in a known subspace, aimed at coping with model errors in the known subspace. The solution is based on a novel formulation of the problem, targeted at matching the error-contaminated model-based signal subspace to its sampled-data counterpart. The solution turns out to minimize the angle between these two subspaces, which is intuitively very pleasing. We solve the problem for three different characterization of the spatial interference: (i) the spatial interference is known, (ii) the spatial interference is unknown, and (iii) the spatial interference is constrained to lie in a known subspace. We present a closed-form solution for the first case and iterative solutions for the other two cases. Based on these solutions, we derive the corresponding estimators for the SOI’s waveform and their signal-to-interference+noise ratio (SINR). Simulation results, demonstrating the superiority of the derived solutions over the corresponding deterministic maximum likelihood (DML) solutions, are included. [ABSTRACT FROM AUTHOR]

The weighting subspace fitting (WSF) algorithm performs better than the multi-signal classification (MUSIC) algorithm in the case of low signal-to-noise ratio (SNR) and when signals are correlated. In this study, we use the random matrix theory (RMT) to improve WSF. RMT focuses on the asymptotic behavior of eigenvalues and eigenvectors of random matrices with dimensions of matrices increasing at the same rate. The approximative first-order perturbation is applied in WSF when calculating statistics of the eigenvectors of sample covariance. Using the asymptotic results of the norm of the projection from the sample covariance matrix signal subspace onto the real signal in the random matrix theory, the method of calculating WSF is obtained. Numerical results are shown to prove the superiority of RMT in scenarios with few snapshots and a low SNR. [ABSTRACT FROM AUTHOR]

Antenna arrays are widely used in radar systems and mobile networks in the physical layer to mitigate interference as well as to enhance the reliability and the capacity of the system. The performance of beamforming algorithms depends on the channel realisation and its associated micro‐parameters (angle of arrivals, multi‐path components, fading) plus the array geometry. The multiplicity of these micro‐parameters makes it difficult to establish a tractable characterisation of the overall performance. In this Letter, a new parameter, an algebraic angle cosine between the signal subspace and the interference subspace, is introduced to characterise the interference impact. It allows the derivation of a lower bound on the signal‐to‐interference‐plus noise ratio of the Capon beamformer. Outside two regions where the interferers are quasi‐orthogonal or quasi‐aligned with the desired user, the lower bound decreases linearly with this parameter. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The small aperture microphone array becomes more and more popular in the consumer electronics. However, the small aperture usually limits the performance of the traditional DoA estimation methods. The differential microphone array (DMA) has attracted much attention, recently. The DMA has the frequency-independent beampatterns owing to the small size and the dipole is one of the basic types. In this paper, we investigate the relationship between the direction-of-arrival (DoA) and the dipole beampatterns. It shows that the DoA can be directly yielded by an orthogonal dipole pair for the small aperture microphone array. Based on this relationship, we propose a speaker DoA estimation method with orthogonal dipoles (OD). The OD exhibits a good performance to DoA estimation. Nevertheless, it is vulnerable to the axial directions in the reverberant environment. To increase the robustness to the axial directions, we introduce the anti-reverberation function in OD and propose the improved OD method. Both simulations and experiments show that the proposed methods not only significantly outperform the traditional methods but also are much more computationally efficient without the spatial spectrum search. [ABSTRACT FROM AUTHOR]

The separation of signal-and-noise subspaces is a crucial step in many array signal processing applications, since the performance of most high-resolution methods mainly depends on the accuracy of separated signal-and-noise subspaces. If the resulting signal subspace is inaccurately estimated, high-resolution subspace-based algorithms would most likely fail. In this paper, we propose a high-accuracy method to complete the separation of signal-and-noise subspaces. In the developed scheme, eigenvalues of the covariance matrix of the data received by the uniform linear array are first employed to construct an ideal sample space using the Schur product of matrices. Then, the Gaussian kernel is introduced to map the sample space into a new high-dimensional feature space, where the resulting structure becomes linearly separable. In the sequel, we propose two fuzzy set-based methods to divide the feature space into two subspaces, which correspond to the signal-and-noise subspaces. In this way, the signal subspace becomes separated. Experimental results show that, compared with the results produced by five other commonly used algorithms, the proposed method yields much higher accuracy, especially for low signal-to-noise ratio thresholds and small snapshots. [ABSTRACT FROM AUTHOR]

The dimension of the right null space is only one for traditional signal space alignment with the minimum configuration of antennas. Then, the direction of a pair of alignment signal space is fixed and cannot be flexibly adjusted. Although the different alignment directions are mutually independent to facilitate relay decoding, the minimum Euclidean distance between modulated signals code words is small, which affects the decoding accuracy. In this paper, we design a novel alignment signal transmission scheme using degrees of freedom of null space generated by redundant antennas. The scheme selects the mutually orthogonal space dimension in the redundant null space as the signal alignment direction. It optimizes the minimum Euclidean distance in the system by maximizing the minimum constellation point distance. Simulation results show that the distances between the constellation points of different code symbols become significantly larger. The larger constellation distance of different coded symbols can improve the decoding accuracy. By optimizing the distance between the minimum constellation points, the transmission performance of each link is balanced and the whole system performance is improved. [ABSTRACT FROM AUTHOR]

Compared with the standard estimation of signal parameters via rotational invariance technique (ESPRIT) for direction of arrival estimation, the propagator‐based ESPRIT is a more computationally efficient method since it requires no eigenvalue decomposition when calculating the signal subspace. In this study, the propagator‐based ESPRIT method is analysed by deriving its theoretical asymptotic error. With first‐order perturbation analysis, it is shown that both propagator‐based ESPRIT and standard ESPRIT have the same asymptotic error with high signal‐to‐noise ratio. Simulation results of both the propagator‐based ESPRIT and the standard ESPRIT are presented, and they are shown to be consistent with the theoretical derivations. [ABSTRACT FROM AUTHOR]

Wideband direction of arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical, and multimedia applications. Many state-of-the-art wideband DOA estimators coherently process frequency binned array outputs by approximate maximum likelihood (ML), weighted subspace fitting, or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and changes of the array response with frequency within the bin create ghost sources dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning are not consistent even when the array response is perfectly known. In this paper, under a more realistic array model, which still has finite rank under a space-time formulation, signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying space time, MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wideband, space-time sensor cross-correlation matrix. A novel, consistent ML-based ST-MUSIC subspace estimate is developed to estimate the number of sources active at each frequency by information theoretic criteria. Empirical ST-MUSIC subspaces are fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that this approach allows better performance over binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor. [ABSTRACT FROM AUTHOR]