Direction of Arrival Estimation by Matching Pursuit Algorithm With Subspace Information

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.

FOMP algorithm for Direction of Arrival estimation

The orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

For the millimeter wave (mmWave) time-varying system, beamforming poses a formidable challenge for huge power overhead. In this paper, an adaptive step-size prediction joint orthogonal matching pursuit (OMP) algorithm (ASP-OMP), is proposed for beam tracking. With the direction of arrival (DOA) information obtained by OMP algorithm, kalman filter is used to predict the beamforming vector during N time slots to avoid huge sampling loss. In addition, we propose to determine the prediction step-size with outlier identification and eliminate the beam tracking error through data fusion based on Bayesian estimation. The simulation results demonstrate that the proposed algorithm can converge quickly and have a good performance for mmWave beam tracking.

Acoustic emission(AE) dynamic monitoring of HRB400 welding specimens during tension process will collect a large number of mixed noise data, increasing the storage space and transmission time of data. And the sparsity of the signal changes with the change of ambient noise, which affects the reconstruction performance of the orthogonal matching pursuit (OMP) algorithm under fixed sparse degree. An adaptive threshold piecewise weak orthogonal matching pursuit (SWOMP) algorithm is proposed to reconstruct the signal, which is solved the problem of data quantity and guarantees the quality of real-time monitoring and reconstruction. The simulation results show that the reconstruction error of SWOMP and OMP algorithm decreases with the increase of measurement value, and the reconstruction performance of SWOMP algorithm is obviously better than that of OMP algorithm. The reconstructed quality of OMP algorithm fluctuates greatly when reconstructing multi-segment signals, while the reconstructed error of SWOMP algorithm is stable at about 0.05, which can reconstruct signals effectively and has high adaptability.

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

For two-dimensional (2D) direction of arrival (DOA) estimation in a uniform rectangular array (URA), the conventional method converts the 2D problem into a one-dimensional (1D) problem; however, the computational complexity is high, and the accuracy is limited by the grid interval. To address this issue, based on sparse representation theory and a separable observation model (SPM), this paper presents a novel off-grid-framework-based 2D DOA estimation approach by designing a modified 2D off-grid model and a solution for the multisnapshot case in the SPM. The proposed algorithm can be divided into two stages. In the first stage, we use a matching pursuit and focal underdetermined system solver (MFOCUSS) algorithm to quickly identify the candidate or potential areas where the true sources may exist. In the second stage, the candidate areas obtained in the first stage are regarded as the initialization. Then, for a specific source, we regard other sources as interference. By using an alternating descent method, we can obtain accurate DOAs. Moreover, based on the equivalence of time delay and spatial spacing, a 2D off-grid method for multisnapshot cases is proposed in this paper. Numerical simulations demonstrate the effectiveness and efficiency of the proposed algorithm.

This article introduces an algorithm-hardware codesign optimized for low-latency and resource-efficient direction-of-arrival (DOA) estimation, employing a refined orthogonal matching pursuit (OMP) algorithm adept at handling the complexities of multisource detection, particularly in scenarios with closely spaced signal sources. At the algorithmic level, this approach incorporates a secondary correction mechanism (SCM) into the traditional OMP algorithm, significantly improving estimation accuracy and robustness. On the hardware front, a bespoke OMP accelerator has been developed, featuring a reconfigurable generic processing element (PE) array that supports various computational modes and leverages multilevel spectral peak search strategy and pipelining techniques to enhance computational efficiency. Experimental evaluations reveal that the proposed system achieves a root mean square error (RMSE) for DOA estimation of less than 0.3° in multisource conditions with a signal-to-noise ratio (SNR) of 20 dB. In addition, the deployment of the OMP accelerator on a Zynq XC7Z020 development board utilizes modest logic resources: 5.49k LUTs, 3.28k FFs, 11.5 BRAMs, and 32 DSPs. Furthermore, the design achieves a computational latency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.83~\mu \text { s}$ </tex-math></inline-formula> for single-source estimation with eight antennas. This achievement reflects a reduction of approximately 17.8% in LUTs, 56.3% in FFs, and 5.7% in DSPs compared to current leading-edge technologies after normalization all while maintaining competitive estimation accuracy and favorable estimation rates.

Power-line noise is mainly comes from power systems and has become one of the most common noises during the acquisition of magnetotelluric (MT) signal, its components including a fundamental frequency signal and a lot of odd harmonics. There are trap circuits designed in most of the acquisition instruments to separate these noise, however, the fundamental frequency of the power line noise will fluctuate with the changing of load current, but the center frequency of the trap circuits are fixed, hence the MT data are still seriously disturbed by the power line noise. To mitigate the disturbance of power line noise, a novel denoising method was proposed based on orthogonal matching pursuit (OMP) algorithm. Semisynthetic experiments and real data obtained from Lu-Zong ore-concentration district illustrate that the proposed method can effectively suppress the power line noise while remain the useful MT signal, the apparent resistivity and phase curves are greatly improved over previous.

A methodology for automatic incipient broken rotor bar detection in induction motors (IMs) is presented. Sparse representations of signals are applied as a diagnosis technique. The novelty of this technique is that it can analyze the frequency spectra from vibration signals even when the differences among signals are small. This representation allows decomposing or reconstructing signals through a trained dictionary that has learned the features of one specific group/class. The main feature of this paper is the use of over-complete dictionaries trained from sets of signals with faults to be detected. In this way, trained dictionaries perform the decomposition of signals using the orthogonal matching pursuit (OMP) algorithm. The decomposition is evaluated and classified by error-based criteria and a majority decision classifier, allowing the detection of early damage, ranging from 1 mm to one broken bar. The detection is performed by the decomposition of vibration signals from three axes (x, y, and z) of IMs under three load conditions (unloaded, half loaded, and three-fourths loaded) and different levels of damage (healthy or 0 mm, 1-9 mm, and one broken bar). These signals are processed by the Fourier transform and the spectrum obtained is evaluated by the OMP algorithm. Finally, the retrieved information is evaluated and the diagnosis is given. All algorithms are developed in MATLAB software and the detection accuracy is higher than 90% for damages as small as 1 mm.

Aiming at the problem of anomaly detection of hyperspectral imagery sub-pixel targets, this paper proposes a novel algorithm of kernel sparse representation. The key idea is that background pixels can be sparsely represented by their neighborhoods, whereas anomalous pixels cannot, and the algorithm can be solved by orthogonal matching pursuit algorithm. The algorithm introduced the kernel method to map the original data to high-dimensional space, and derived the kernel orthogonal matching pursuit(KOMP) algorithm to solve the pixel non-linear mixed problem. Through the introduction of sum to one constraint, the detection value of anomalous pixels and background pixels is increased, which is more conducive to detection. The regularization model is added to make the solution of kernel orthogonal matching pursuit algorithm more stable. Finally, this algorithm is compared with other algorithms on the actual hyperspectral data set, and achieved good results.

Direction of Arrival (DOA) estimation is one of the most fundamental problems in array signal processing, and it is widely used in many fields such as radar, sonar, and communications. This paper uses Compressed Sensing (CS) technology to focus on DOA estimation. Aiming at the problems caused by fewer snapshots in the practical application of DOA estimation, a Nonuniform Overcomplete Dictionary (NUOD) combining initialization space is proposed. In addition, the new DOA estimation algorithm of Orthogonal Match Pursuit (OMP) is improved by a Genetic Algorithm (GA). Furthermore, in order to improve the performance of DOA estimation of CS technology, the following three improvements are proposed. (1) Make full use of the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) to determine the initialization point and then determine the scope of the initialization space according to the Crame’r–Rao bound (CRB). (2) Aiming at a large amount of calculation, the algorithm can realize the nonuniform over-complete dictionary design of the popular array matrix according to the sparse representation of the partition of the initialization space. (3) To further improve the algorithm’s performance, the nonuniform over-complete dictionary design is combined with the processing flow of the GA improved OMP algorithm. The simulation results prove that the method in this paper has the advantages of less computing time, low estimation error, and wide application range.

This brief presents a new variant of the orthogonal matching pursuit (OMP) algorithm for reducing the computational complexity of the digital predistortion (DPD) behavioral model in the forward path. The proposed spectral weighting OMP (SW-OMP) algorithm focuses on selecting the most relevant basis functions to compensate for the out-of-band residual distortion which may eventually be masked by the dominant in-band residual error. This basis selection is carried out in an off-line process that does not affect the computational complexity of the real-time closed-loop DPD but, on the contrary, reduces its complexity while enhancing the robustness. Experimental results show that by selecting the DPD coefficients with the SW-OMP, the inherent ACLR and NMSE degradation suffered when reducing the number of coefficients is mitigated under strong nonlinear operation, when compared to using the basis functions selected by the classical OMP 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.