A Multistage Space–Time Equalizer for Blind Source Separation

DOA (Direction of Arrival) estimation is a major problem in array signal processing applications. Recently, compressive sensing algorithms, including convex relaxation algorithms and greedy algorithms, have been recognized as a kind of novel DOA estimation algorithm. However, the success of these algorithms is limited by the RIP (Restricted Isometry Property) condition or the mutual coherence of measurement matrix. In the DOA estimation problem, the columns of measurement matrix are steering vectors corresponding to different DOAs. Thus, it violates the mutual coherence condition. The situation gets worse when there are two sources from two adjacent DOAs. In this paper, an algorithm based on OMP (Orthogonal Matching Pursuit), called ILS-OMP (Iterative Local Searching-Orthogonal Matching Pursuit), is proposed to improve DOA resolution by Iterative Local Searching. Firstly, the conventional OMP algorithm is used to obtain initial estimated DOAs. Then, in each iteration, a local searching process for every estimated DOA is utilized to find a new DOA in a given DOA set to further decrease the residual. Additionally, the estimated DOAs are updated by substituting the initial DOA with the new one. The simulation results demonstrate the advantages of the proposed algorithm.

The direction of arrival (DOA) estimation is a key issue in array signal processing, and there are many well-known methods, e.g., Capon, MUSIC, Root-MUSIC and some other DOA estimation algorithms in the literature. Nevertheless, the effective DOA estimation for closely spaced multiple sources with large power differences is still a difficult problem due to the deteriorated resolution for the low power sources. In this paper, a novel DOA estimation method called Capon-MUSIC algorithm is proposed, which has a much higher resolution for closely spaced multiple sources with obvious power differences. Finally, some numerical experiments are provided to demonstrate the effectiveness of the proposed method.

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

Grid-less DOA estimation of coherent sources based on the covariance matrix recovery

In automotive millimeter-wave (MMW) radar systems, achieving high-precision direction of arrival (DOA) estimation with a limited number of array elements is a crucial research focus. Compressive sensing (CS) techniques have been demonstrated to offer superior performance in DOA estimation compared to spectral estimation methods. However, traditional CS methods suffer from an off-grid effect, which causes their reconstruction results to deviate from the actual positions of the signal sources, thereby reducing the accuracy. Currently, as a gridless method, atomic norm minimization (ANM) has shown effectiveness in DOA estimation for uniform linear arrays (ULAs). However, the performance of ANM is suboptimal in non-uniform linear arrays (NULAs), and their computational efficiency is not satisfactory. In this paper, we propose a novel algorithm for DOA estimation in NULA, drawing inspiration from the alternating descent conditional gradient algorithm framework. First, we construct an atomic set based on the observation scene and select the atoms with the highest correlation to the residuals as potential signal sources for global estimation. Then, we construct a mapping function for the signal sources in the continuous domain and perform conditional gradient descent in the neighborhood of each signal source, addressing the bias introduced by the off-grid effect. We compared the proposed algorithm with ANM, Iterative Shrinkage Thresholding (IST), and Multiple Signal Classification (MUSIC) algorithms. Simulation experiments validate that the proposed algorithm effectively addresses the off-grid effect and is applicable to DOA estimation in coprime and random arrays. Furthermore, real data experiments confirm the effectiveness of the proposed algorithm.

Deep learning (DL) based direction of arrival (DOA) estimation has drawn increasing attention recently because of its significant potential advantages. However, existing DL-based DOA estimation algorithms may have the problems of network training difficulty and low estimation accuracies for multiple signal sources. To address these issues, a DOA estimation algorithm using an interpretable spatial filtering network (SF-Net) and parallel small-scale two-dimensional (2D) convolutional neural networks (CNNs) is proposed. Based on matrix spatial filtering (MSF) theory and single-layer fully connected neural networks, an interpretable SF-Net with the same physical foundation to MSF is constructed to divide the array received data into different angle subregions. Then, parallel 2D CNNs are used to process the output data of SF-Net, obtaining the spatial spectrum estimation of each angle subregion. Finally, spatial spectra of different subregions are synthesized to achieve accurate DOA estimation of multiple sources. Experiment results show that the proposed algorithm can achieve higher multiple source DOA estimation performance with reduced dataset size and network training difficulty in comparison with the state-of-the-art DL-based estimation algorithms. Compared to the conventional estimation algorithms, the proposed algorithm has the advantages in the case of low signal-to-noise-ratio, small number of snapshots, and small source angle separation.

This paper addresses the source association (SA), direction of arrival (DOA), and fading coefficients (FCs) estimation problem in multipath environment. First, we establish a rank reduction property for a multipath signal model with the existence of multiple groups of coherent signals. Subsequently, based on this property, effective algorithms for SA, DOA, and FCs estimation have been developed. The proposed DOA and FCs estimation methods exploit the multipath structure information to achieve improved accuracy. The new DOA estimation methods work well even in the case that the DOAs of the multipath signals associated with different sources are (nearly) overlapped. Meanwhile, the new methods are applicable to arbitrary array geometry while without decreasing the effective array aperture. Then, the stochastic Cramér-Rao bound on DOA and FCs estimation of multipath model (MCRB) exploiting the multipath structure information is derived in closed form. Numerical simulations have been provided to demonstrate the effectiveness of the proposed methods.

This paper mainly introduces a novel estimation method for direction of arrival (DOA) estimation. Recently, direction-of-arrival (DOA) estimation has been widely employed in wireless communication networks, electromagnetic (EM) environment management, and radar tracking. However, traditional DOA estimation algorithms and systems are based on multiple digital receivers with expensive hardware. To overcome this challenge, we propose a novel DOA estimation method based on a space-time coding method and an easy-configurable antenna array. With this programmable L-shape antenna array and space-time coding method, a two-dimensional DOA estimation is realized.

Uniform linear array (ULA) geometry does not perform well for direction of arrival (DOA) estimation at directions close to the array endfires. Shirvani and Akbari solved this problem by displacing two elements from both ends of the ULA to the top and/or bottom of the array axis. Shirvani-Akbari array (SAA) presents a considerable improvement in the DOA estimation of narrowband sources arriving at endfire directions in terms of DOA estimation accuracy and angular resolution. In this paper, all new proposed SAA configurations are modelled and also examined, numerically. In this paper, two well-known DOA estimation algorithms, multiple signal classification (MUSIC) and minimum variance distortionless response (MVDR), are used to evaluate the effectiveness of proposed arrays using total root mean square error (RMSE) criterion. In addition, two new scenarios are proposed which divide angular search to two parts, directions close to array endfires as well as middle angles. For middle angles, which belong to (−70∘≤𝜃≤70∘), ULA is considered, and for endfire angles, the angles which belong to (−90∘≤𝜃≤−70∘) and (70∘≤𝜃≤90∘), SAA is considered. Simulation results of new proposed scenarios for DOA estimation of narrowband signals show the better performance with lower computational load.

An improved algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO radar based on fourth order cumulants is presented. Firstly, the data of receiver is reset and divided to acquire the rotational invariance property of transmitter and receiver, respectively. The fourth order cumulants matrixes in twain are constructed which are based on the basic definition of the cumulant. Then we use the propagator method (PM), which only requires linear operation but does not involve any eigendecomposition of the cumulant matrix, to estimate the DODs and DOAs, respectively. Finally, the maximum likelihood method is used to solve the pairing problem. The proposed method is effective in prohibiting the Gaussian colored noise and improves the performance of the angle estimation slightly. It does not need two-dimensional spectrum peak searching and eigenvalue decomposition on the cumulant matrix, thus the computation complexity is reduced. At the same time, it has no exceptive claim on the number of receive arrays or receive arrays. Simulation results verify the effectiveness and feasibility of the proposed method.

We investigate the problem of direction of arrival (DOA) estimation with 1-b measurements in massive MIMO systems, as 1-b quantization offers low cost and low complexity in the implementation. We first establish the connection between 1-b DOA estimation and linear classification based on the sparsity of the incident signals. Then, we present an iterative refinement procedure based on Taylor expansion to obtain DOA estimation off the grid. This refinement procedure can be easily extended to other 1-b DOA estimation algorithms with minor changes. Finally, simulations are conducted for validation and the results illustrate the high performance of the proposed algorithm in spite of the extreme 1-b quantization.

This paper presented a study of direction of arrival estimation using multiple signal classification algorithm on two frequency bands (UHF-band and C-band). The used algorithm in the paper is one of the superresolution direction of arrival estimation algorithms and it was simulated to analyze the effects of various parameters on the direction of arrival accuracy and resolution. Then, the measuring workplace was established to verify the results of the simulation. In the practical measurement, two 4-element uniform linear arrays were used to estimate the direction of arrival of the noncoherent signal sources for the different frequency bands. The measured signals were processed in the Matlab using multiple signal classification algorithm for direction of arrival estimation. The measurement system estimated the direction of arrival of the signal in the UHF-band with accuracy around 4° and resolution around 10°. In the C-band, the accuracy and resolution of direction of arrival estimation were around 3° and 10° respectively. In comparison, the measurement results were a bit different from the simulation due to environment condition of measuring workplace.

Direction of arrival (DOA) estimation has become a major factor in the performance of smart antenna systems. Through DOA estimation techniques, it is possible to determine the angular position of signal sources and interferers in the cell environment. Nevertheless, in a multipath fading channel, electromagnetic waves interact with the environment in a very complex way, thus significantly degrading the performance of DOA estimation algorithms. This paper provides insight into how Root MUSIC enhances resolution on DOA estimation and has better performance than spectral MUSIC in the context of a linear equispaced array in a multipath macrocell environment. This improvement and its better precision result in a higher channel capacity, given that it allows to spatially separate closely spaced sources.

The acoustic vector sensor (AVS) array is a powerful tool for direction of arrival (DOA) estimation of underwater targets. However, traditional DOA estimation algorithms generally suffer from low signal-to-noise ratio (SNR) as well as snapshot deficiency. A novel signal self-nulling based DOA estimation method is proposed. Firstly, achieve the crude estimation of the desired DOA using the traditional algorithms. Secondly, set the observation angular interval around the crudely estimated DOA. Thirdly, make the observation direction vary in the observation angular interval, and for each imaginary DOA, calculate the amplitude response of the minimum variance distortionless response (MVDR) beamformer. Finally, the pseudo spatial spectrum is achieved. Computer simulations verify that the proposed method is efficient in DOA estimation, especially in low SNR and insufficient snapshot data scenarios.

A novel algorithm for the direction of arrival (DOA) estimation based on the fractional Fourier transform (FRFT) is proposed. Firstly, using the properties of FRFT and mask processing, Multi-component LFM sig-nals are filtered and demodulated into a number of stationary single frequency signals. Then the one-dimensional (1-D) direction estimation of LFM signals can be achieved by combining with the tradi-tional spectrum search method in the fractional Fourier (FRF) domain. As for the multi-component LFM signals, there is no cross-term interference, the mean square error (MSE) and Cramer-Rao bound (CRB) are also analyzed which perfects the method theoretically, simulation results are provided to show the validity of our method. The proposed algorithm is also extended to the uniform circular array (UCA), which realizes the two-dimensional (2-D) estimation. Using the characteristics of time-frequency rotation and demodulation of FRFT, the observed LFM signals are demodulated into a series of single frequency ones; secondly, operate the beam-space mapping to the single frequency signals in FRF domain, which UCA in array space is changed into the virtual uniform circular array (ULA) in mode space; finally, the DOA estimation can be realized by the traditional spectral estimation method. Compared with other method, the complex time-frequency cluster and the parameter matching computation are avoided; meanwhile enhances the esti-mation precision by a certain extent. The proposed algorithm can also be used in the multi-path and Doppler frequency shift complex channel, which expands its application scope. In a word, a demodulated DOA esti-mation algorithm is proposed and is applied to 1-D and 2-D angle estimation by dint of ULA and UCA re-spectively. The detailed theoretical analysis and adequate simulations are given to support our proposed al-gorithm, which enriches the theory of the FRFT.