Forward-backward Spatial Smoothing Research Articles

An improved forward-backward spatial smoothing MUSIC algorithm for coherent signal direction finding

An improved forward-backward spatial smoothing MUSIC algorithm for coherent signal direction finding

Forward-backward spatial smoothing for snapshot matrix construction of blade tip timing signal

Forward-backward spatial smoothing for snapshot matrix construction of blade tip timing signal

Inductive Matrix Completion and Root-MUSIC-Based Channel Estimation for Intelligent Reflecting Surface (IRS)-Aided Hybrid MIMO Systems

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)-aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC-based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.

Source Detection With Multi-Label Classification

Radio source detection through conventional algorithms has been unreliable when trying to solve for large number of sources in the presence of low SINR and less number of snapshots. We address this by reformulating source detection as a multi-class classification problem solved using deep learning frameworks. Incoming waveforms are sampled using a centro-symmetric linear array with omni-directional elements and the normalized upper triangle of the autocorrelation matrix is extracted as the input feature to a modified convolutional neural network with uni-dimensional filters, trained to detect the sources in the presence of both uncorrelated and correlated signals. Two detection algorithms are introduced and referred to as CNNDetector and RadioNet, and subsequently benchmarked against the conventional source detection algorithms. By including pre-processing in forward backward spatial smoothing, RadioNet can also resolve the number of uncorrelated sources in the presence of correlated paths. Finally, the algorithms are stress tested under challenging operational conditions and extensive evaluations are presented showing the efficacy and contributions of the introduced predictive models. To the best of our knowledge, this is the first time the source detection problem has resolved L-1 sources, for an antenna array of L elements using a deep learning framework.

Direction-of-Arrival Estimation for Coherent Signals Exploiting Moving Coprime Array

In this letter, we propose a novel algorithm to estimate the direction-of-arrival (DOA) for coherent signals exploiting the moving coprime array (MCA). Firstly, we construct a decoherent covariance matrix by utilizing the data vectors received at specific time instants, whose structure is similar to that of the covariance matrix under the condition of uncorrelated signals. Then we use vectorization, array interpolation and matrix completion technologies to reconstruct the data vector received by the augmented uniform linear array (ULA). Afterwards, forward/backward spatial smoothing (FBSS) and root-MUSIC are applied for DOA estimation. Simulation results demonstrate the effectiveness and superiority of the proposed algorithm when processing coherent signals.

MIMO transmission diversity and spatial smoothing: A joint decorrelation effect study

To improve the performance of high-resolution bearing estimation algorithms in the presence of coherent targets, we investigate the joint decorrelation effect produced by the multiple-input-multiple-output (MIMO) based transmission diversity smoothing (TDS) and the spatial smoothing (SS). We utilize the degree of freedom (DOF) of smoothing (i.e., the number of covariance matrix averaged for smoothing) to evaluate the decorrelation effect quantitatively. Investigating the Hermitian square root of the jointly smoothed echo covariance matrix, we find the smoothing DOFs by the joint decorrelation processing is a product of that of SS and TDS. Due to the remarkably increased smoothing DOFs, the joint decorrelation processing provides great potentials to improve the decorrelation effect. Moreover, sparsely placing transmitters helps fully utilize the obtained smoothing DOFs to strengthen the non-singularity of the echo covariance matrix, and thus improves the joint decorrelation effect. Besides, introducing forward-backward spatial smoothing contributes to further improve the decorrelation effect. By balancing the subarray aperture and the smoothing DOFs, an upper limit of the subarray number and the maximum resolvable number of coherent targets are concluded for MIMO array design and performance evaluation. Numerical simulations validate the effectiveness of the joint decorrelation processing and its robustness against the transmit manifold errors.

A novel co-prime MIMO radar model for DOA estimation

In this paper, we propose a novel co-prime multiple-input multiple-output (MIMO) radar model based on the transmit energy focusing (TEF) technique for direction of arrival (DOA) estimation. Compared with omnidirectional radiation of the transmit energy of the traditional co-prime MIMO radar, the proposed model can focus the transmit energy in the desired spatial sector. To obtain more degrees of freedom (DOFs), we design the transmit beamspace matrix with a specific structure. Then, the sum and difference co-array (SDC) is given by vectorizing the sampling covariance matrix of the received data. Subsequently, the maximum number of consecutive lags and unique lags for SDC is derived. Besides, we also derive the Cramer–Rao bound (CRB) of our model. Moreover, the DOA estimation performance of the TEF-based co-prime MIMO radar and traditional co-prime MIMO radar is compared by using forward-backward spatial smoothing (FBSS), sparse recovery (SR), and fast iterative interpolated beamformer (FIIB) algorithms. Simulation results show the superiority of the proposed model.

Deep Learning-Aided Coherent Direction-of-Arrival Estimation With the FTMR Algorithm

In this work, we apply deep learning to estimate the direction-of-arrival (DoA) of multiple narrowband signals with a uniform linear array in a coherent environment. First, the logarithmic eigenvalue-based classification network (LogECNet) is introduced to enhance signal number detection accuracy in challenging scenarios, such as the low signal-to-noise (SNR) regime and limited snapshots. Next, a multi-label classification model called the root-spectrum network (RSNet) is devised to estimate the DoAs using the signal number inferred by LogECNet. In the proposed architecture, the full-row Toeplitz matrices reconstruction (FTMR), which exploits all rows of the signal covariance matrix (SCM), is combined with LogECNet and RSNet to inversely map the SCM to the numerical DoAs in the coherent scenario. It is shown that the eigenvalues factorized from the FTMR output matrix become more robust sources for signal enumeration than those of the forward/backward spatial smoothing (FBSS) algorithm. Furthermore, the logarithmic scaling of the eigenvalues of the FTMR results in LogECNet outperforming other detectors. The simulation results show our proposed method not only improves the signal number detection and angular estimation performance, but also achieves the complexity reduction with respect to the prior schemes.

Spatially Smoothed TF-Root-MUSIC for DOA Estimation of Coherent and Non-Stationary Sources Under Noisy Conditions

This paper proposes a method for efficient Direction-of-Arrival (DOA) estimation of coherent and non-stationary sources under adverse noise conditions. The method consists of three main parts: 1) derivation of Spatial Time-Frequency Distribution (STFD) matrix; 2) application of the forward-backward spatial smoothing technique; 3) estimating the angles of arrival by solving for the roots of the polynomial. The key significance of the proposed method is that the combination of existing methods and techniques allows an estimation of DOA angles for both coherent and non-stationary source signals under noise. Whereas the individual use of the existing methods does not show adequate performance under these conditions. The experiments allow studying the performance of the proposed method for 1) both coherent and non-coherent clean sinusoidal signals; 2) noisy non-stationary chirp signals; 3) coherent and non-stationary signals under noise. Furthermore, extensive simulations have been carried out to compute the root mean square error (RMSE) performance of the proposed method in comparison with the existing ones. The experiments have been designed for varying number of microphones, level of noise, and value of the time-frequency threshold. As a result of the experiments, we observe the efficacy of the proposed method in comparison with the conventional Root-MUSIC and Time-Frequency MUSIC (TF-MUSIC) methods.

Model-Aided Deep Neural Network for Source Number Detection

Source number detection is a critical problem in array signal processing. Conventional model-driven methods e.g., Akaikes information criterion (AIC) and minimum description length (MDL), suffer from severe performance degradation when the number of snapshots is small or the signal-to-noise ratio (SNR) is low. In this paper, we exploit the model-aided based deep neural network (DNN) to estimate the source number. Specifically, we first propose the eigenvalue based regression network (ERNet) and classification network (ECNet) to estimate the number of non-coherent sources, where the eigenvalues of the received signal covariance matrix and the source number are used as the input and the supervise label of the networks, respectively. Then, we extend the ERNet and ECNet for estimating the number of coherent sources, where the forward-backward spatial smoothing (FBSS) scheme is adopted to improve the performance of ERNet and ECNet. Numerical results demonstrate the outstanding performance of ERNet and ECNet over the conventional AIC and MDL methods as well as their excellent generalization capability, which also shows their great potentials for practical applications.

DOA estimation method for multi‐path targets based on TR MIMO radar

To reduce the large errors for direction of arrival (DOA) estimation in the multipath condition, a DOA estimation method for multipath targets based on time reversal (TR) multi-input multi-output (MIMO) radar is proposed. First, the proposed algorithm combines the focusing characteristic of TR technology with the waveform diversity and symmetry characteristic of MIMO radar, obtaining the virtual sub-arrays of echo signal. Then, the authors multiplex the rows and columns and apply forward–backward spatial smoothing algorithm to remove the coherence of the virtual sub-arrays, effectively improving the DOA estimation accuracy for multipath targets. Simulation results verify the validity of the proposed method.

Efficient Cumulant-Based Methods for Joint Angle and Frequency Estimation Using Spatial-Temporal Smoothing

Most non-Gaussian signals in wireless communication array systems contain temporal correlation under a high sampling rate, which can offer more accurate direction of arrival (DOA) and frequency estimates and a larger identifiability. However, in practice, the estimation performance may severely degrade in coloured noise environments. To tackle this issue, we propose real-valued joint angle and frequency estimation (JAFE) algorithms for non-Gaussian signals using fourth-order cumulants. By exploiting the temporal correlation embedded in signals, a series of augmented cumulant matrices is constructed. For independent signals, the DOA and frequency estimates can be obtained, respectively, by leveraging a dual rotational invariance property. For coherent signals, the dual rotational invariance is constructed to estimate the generalized steering vectors, which associates the coherent signals into different groups. Then, the coherent signals in each group can be resolved by performing the forward-backward spatial smoothing. The proposed schemes not only improve the estimation accuracy, but also resolve many more signals than sensors. Besides, it is computationally efficient since it performs the estimation by the polynomial rooting in the real number field. Simulation results demonstrate the superiorities of the proposed estimator to its state-of-the-art counterparts on identifiability, estimation accuracy and robustness, especially for coherent signals.

Unitary Matrix Completion-Based DOA Estimation of Noncircular Signals in Nonuniform Noise

In this paper, a novel direction-of-arrival (DOA) estimation algorithm is proposed for noncircular signals with nonuniform noise by using the unitary matrix completion (UMC) technique. First, the proposed method utilizes the noncircular property of signals to design a virtual array for approximately doubling the array aperture. Then, the virtual complex-valued covariance matrix with the unknown nonuniform noise is transformed into the real-valued one by utilizing the unitary transformation to improve the computational efficiency. Next, a novel UMC method is formulated for the DOA estimation to remove the influence of nonuniform noise. Finally, the DOA without the influence of the unknown noncircularity phase is obtained by using the modified estimation of signal parameters via rotational invariance technique (ESPRIT). Especially, for handling the coherent sources, the forward–backward spatial smoothing technique is utilized to reconstruct a full-rank covariance matrix so that the signal subspace and the noise subspace can be correctly separated. Due to utilizing the extended array aperture and the unitary transformation, the proposed method can identify more sources than the number of physical sensors and provides higher angular resolution and better estimation performance. Compared with the existing DOA estimation algorithms for noncircular signals, the proposed one can effectively suppress the influence of the nonuniform noise. The simulation results are provided to verify the effectiveness and superiority of the proposed method.

Direction of Arrival Estimation of Acoustic Echoes Using Source Elimination Method

A new method for the direction of arrival (DOA) estimation for a single narrowband acoustic source with multiple low power echoes is proposed. The mathematical relations between the signal covariance matrix, the sources steering vectors, and the power of the sources are developed in order to expose the contribution of each source. Algorithms to find each of the source's DOA and their respective power are presented. The source elimination method (SEM), based on the elimination of the contribution of each source to improve the DOA estimation, is developed. Monte Carlo simulations are presented, showing that SEM yields more accurate results than multiple signal classification (MUSIC) with forward-backward spatial smoothing (FBSS) to find the echoes' DOA with an echo-to-noise ratio between -13 and -17 dB. Experimental results show that for a small array and two sources with different power, SEM outperforms MUSIC with FBSS.

Sequential DOA estimation method for multi-group coherent signals

In order to cope with multi-group coherent signals induced by multipath propagation, this paper presents a novel approach to estimate the direction of arrivals (DOAs) of each group sequentially. For each time, we just estimate the DOAs of one group which has the minimum coherent signals based on forward spatial smoothing (FSS), and the information of this group is eliminated from the array covariance matrix with oblique projection technique. Then we estimate the next group similarly until all groups are estimated. Afterwards, we use the forward/backward spatial smoothing (FBSS) to further improve the estimation accuracy of the DOAs in each group separately. The new method not only utilizes less array sensors to resolve multi-group coherent signals, but also estimates the same DOAs from different groups. Simulation results are presented to demonstrate the effectiveness of the proposed method especially in low signal-to-noise ratio (SNR) and small number of snapshots.

Estimation of source location and ground impedance using a hybrid multiple signal classification and Levenberg–Marquardt approach

A microphone array signal processing method for locating a stationary point source over a locally reactive ground and for estimating ground impedance is examined in detail in the present study. A non-linear least square approach using the Levenberg–Marquardt method is proposed to overcome the problem of unknown ground impedance. The multiple signal classification method (MUSIC) is used to give the initial estimation of the source location, while the technique of forward backward spatial smoothing is adopted as a pre-processer of the source localization to minimize the effects of source coherence. The accuracy and robustness of the proposed signal processing method are examined. Results show that source localization in the horizontal direction by MUSIC is satisfactory. However, source coherence reduces drastically the accuracy in estimating the source height. The further application of Levenberg–Marquardt method with the results from MUSIC as the initial inputs improves significantly the accuracy of source height estimation. The present proposed method provides effective and robust estimation of the ground surface impedance.

Direction-of-Arrival Estimation of Virtual Array Signals Based on Doppler Effect

The estimation accuracy of direction-of-departure (DOD) and direction-of-arrival (DOA) is reduced because of Doppler shifts caused by the high-speed moving sources. In this paper, an improved DOA estimation method which combines the forward-backward spatial smoothing (FBSS) technique with the MUSIC algorithm is proposed for virtual MIMO array signals in high mobility scenarios. Theoretical analysis and experiment results demonstrate that the resolution capability can be significantly improved by using the proposed method compared to the MUSIC algorithm for the moving sources with limited array elements, especially the DOA which can still be accurately estimated when the sources are much closely spaced.

A coherent direction of arrival estimation method using a single pulse

This paper addresses the problem of coherent direction of arrival (DOA) estimation in monostatic multi-input multi-output (MIMO) radar using a single pulse, and links the trilinear model to derive a coherent DOA estimation method. We use the received data to construct a set of Toeplitz matrices through which a trilinear model is formed, and then the trilinear decomposition is used to attain the DOAs of sources. The proposed algorithm is effective for a single pulse. Compared to the forward backward spatial smoothing estimation method of signal parameters via rotational invariance techniques (ESPRIT), the ESPRIT-like of Han, and the ESPRIT-like of Li algorithms, our method has better angle estimation performance. Numerical simulations present the effectiveness and improvement of our approach.

A RD-ESPRIT algorithm for coherent DOA estimation in monostatic MIMO radar using a single pulse

This paper discusses the problem of coherent direction of arrival (DOA) estimation in a monostatic multi-input multi-output (MIMO) radar using a single pulse, and proposes a reduced dimension (RD)-estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. We reconstruct the received data and then utilise it to construct a set of Toeplitz matrices. After that, we use RD-ESPRIT to obtain the DOAs of the sources. The proposed algorithm is effective for coherent angle estimation based on a single pulse, and it has much better angle estimation performance than the forward backward spatial smoothing (FBSS)-ESPRIT algorithm and the ESPRIT-like of Li, as well as very close angle estimation performance to the ESPRIT-like of Han. For complexity comparison, our algorithm has very close complexity to the FBSS-ESPRIT algorithm, and lower complexity than the ESPRIT-like of Han and the ESPRIT-like of Li. Simulation results present the effectiveness and improvement of our approach.

A PARALIND Decomposition-Based Coherent Two-Dimensional Direction of Arrival Estimation Algorithm for Acoustic Vector-Sensor Arrays

In this paper, we combine the acoustic vector-sensor array parameter estimation problem with the parallel profiles with linear dependencies (PARALIND) model, which was originally applied to biology and chemistry. Exploiting the PARALIND decomposition approach, we propose a blind coherent two-dimensional direction of arrival (2D-DOA) estimation algorithm for arbitrarily spaced acoustic vector-sensor arrays subject to unknown locations. The proposed algorithm works well to achieve automatically paired azimuth and elevation angles for coherent and incoherent angle estimation of acoustic vector-sensor arrays, as well as the paired correlated matrix of the sources. Our algorithm, in contrast with conventional coherent angle estimation algorithms such as the forward backward spatial smoothing (FBSS) estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, not only has much better angle estimation performance, even for closely-spaced sources, but is also available for arbitrary arrays. Simulation results verify the effectiveness of our algorithm.