Capon Method Research Articles

Signal Emitters Localization by Spectral Methods

Methods are considered of generating signals in a radar sensor receiver provided with a colocated antenna system of Multiple Input Multiple Output (MIMO) configuration when synthesizing virtual antenna arrays. Review of the basic spectral methods used in beamforming with digital automobile radars, such as Capon method, MUSIC and ESPRIT was carried out. Spatial spectra obtained by various methods were constructed for a radar signal model, and comparative spectra characteristic by angular resolution is provided. Output heatmaps in the angle-distance coordinate were constructed to represent methods operation according to the real target situation based on data sampling from the front-mounted automobile radar. Advantages of decomposition methods based on MUSIC and ESPRIT algorithms in solving the problem of a signal emitter localization are presented

CLEAN beamforming for the enhanced detection of multiple infrasonic sources

SUMMARY The detection and characterization of signals of interest in the presence of (in)coherent ambient noise is central to the analysis of infrasound array data. Microbaroms have an extended source region and a dynamical character. From the perspective of an infrasound array, these coherent noise sources appear as interfering signals that conventional beamform methods may not correctly resolve. This limits the ability of an infrasound array to dissect the incoming wavefield into individual components. In this paper, this problem will be addressed by proposing a high-resolution beamform technique in combination with the CLEAN algorithm. CLEAN iteratively selects the maximum of the f/k spectrum (i.e. following the Bartlett or the Capon method) and removes a percentage of the corresponding signal from the cross-spectral density matrix. In this procedure, the array response is deconvolved from the f/k spectral density function. The spectral peaks are retained in a ‘clean’ spectrum. A data-driven stopping criterion for CLEAN is proposed, which relies on the framework of Fisher statistics. This allows the construction of an automated algorithm that continuously extracts coherent energy until the point is reached that only incoherent noise is left in the data. CLEAN is tested on a synthetic data set and is applied to data from multiple International Monitoring System infrasound arrays. The results show that the proposed method allows for the identification of multiple microbarom source regions in the Northern Atlantic that would have remained unidentified if conventional methods had been applied.

Experimental evaluation of efficiency of algorithms for direction finding of unmanned aerial vehicles by acoustic radiation

The results of an experimental evaluation of Bartlett, Capon algorithms and cross-correlation function method effectiveness for direction finding of unmanned aerial vehicles are presented. Full-scale studies were carried out using a harmonic signal and acoustic radiation of a prototype of a propeller-driven UAV group indoors and in open space, as well as in real-world conditions of flight modes and UAV hovering. The acoustic emission spectrum of the electric propeller-motor group of modern UAVs includes narrow-band tonal and broadband noise-like components with predominant propeller radiation. The use of algorithms for determining the direction of arrival of acoustic radiation from the spatial spectrum by the methods of Bartlett and Capon involves the use of narrow-band signals. It is shown that to work with UAV acoustic radiation, the MB, MK, and cross-correlation function algorithms require some adaptation (including the use of high-pass filters). The Capon method has a significantly higher resolution than the classic Bartlett method, and a lower level of side lobes. The presence of significant reflections from local objects leads to the appearance of abnormal bearing estimates for the acoustic signal source of the propeller-driven UAV group. The results of determining the bearing of the source of acoustic radiation in a wide frequency band in open space show good agreement with the specified values of the bearing when applying the method of mutual correlation function. To increase the efficiency of the mutual correlation function algorithm when processing UAV acoustic signals, it is necessary to reduce the influence of low-frequency interference caused by anthropogenic and natural acoustic noise.

Joint DOD and DOA Estimation Using Reduced-Capon Method in Bistatic MIMO Array

In order to resolve the problem of joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO array, a dimensional reduced-Capon method based on Taylor series expansion and signal subspace is proposed in this paper. Firstly, the Taylor series expansion of the steering vector is used to reduce the two-dimensional (2D) spectrum peak searching of Capon method to one-dimensional searching. Then, the DOD estimator can be achieved via Lagrange multiplier by one-dimension search. Finally, the steering vector of DOA corresponding to the DOD estimator is achieved and the DOA can be estimated. Hence, the estimated DOD and DOA are obtained automatically paired. And also, the proposed method can avoid the high computational complexity of MIMO Capon method. Simulation results are presented to illustrate the effectiveness of the proposed method.

Aperture‐Synthesis Radar Imaging With Compressive Sensing for Ionospheric Research

AbstractInverse methods involving compressive sensing are tested in the application of two‐dimensional aperture‐synthesis imaging of radar backscatter from field‐aligned plasma density irregularities in the ionosphere. We consider basis pursuit denoising, implemented with the fast iterative shrinkage thresholding algorithm, and orthogonal matching pursuit (OMP) with a wavelet basis in the evaluation. These methods are compared with two more conventional optimization methods rooted in entropy maximization (MaxENT) and adaptive beamforming (linearly constrained minimum variance or often “Capon's Method.”) Synthetic data corresponding to an extended ionospheric radar target are considered. We find that MaxENT outperforms the other methods in terms of its ability to recover imagery of an extended target with broad dynamic range. Fast iterative shrinkage thresholding algorithm performs reasonably well but does not reproduce the full dynamic range of the target. It is also the most computationally expensive of the methods tested. OMP is very fast computationally but prone to a high degree of clutter in this application. We also point out that the formulation of MaxENT used here is very similar to OMP in some respects, the difference being that the former reconstructs the logarithm of the image rather than the image itself from basis vectors extracted from the observation matrix. MaxENT could in that regard be considered a form of compressive sensing.

VHF Radar Observations of Sea Surface in the Northern Taiwan Strait

Abstract A VHF pulsed radar system was set up on the Taoyuan County seashore (24°57′58″N, 121°00′30″E; Taiwan) to observe the sea surface in the northern Taiwan Strait for the first time. The radar used a four-element, vertically polarized Yagi antenna to transmit the 52-MHz radar wave. The receiving linear array consists of four vertical dipole antennas that were located 3 m apart and attached with four independent and identical receivers. With the multichannel echoes, the direction of arrival (DOA) of the radar echoes were determined by using an optimization beamforming approach—the Capon method. Echo intensity was observed to vary principally in semidiurnal oscillation, which matched well the time series of tide gauge measurements and sea level simulations. In addition, the oscillatory characteristics of Doppler/radial velocity of the VHF radar were generally consistent with that of the HF coastal ocean dynamics applications radar (CODAR) nearby. Nevertheless, the contributions of various tidal modes to the parameters of DOA, echo intensity, radial velocity, and spectral width, varied with the range and time period (e.g., neap or spring tides). For example, the semidiurnal tides governed the variation in the echo center only in the range interval between ~15 and ~25 km from the seashore but dominated other parameters throughout the detectable range. Correlations and phase relationships between these parameters were diverse; they varied with time and had dramatic changes at around the distances of 3 and 10 km. Possible causes of these features were discussed, including sea surface wind, nearshore current, sea level height, and bathymetric effect.

Improved Polynomial Rooting of Capon's Algorithm to Estimate the Direction-of-Arrival in Smart Array Antenna

 Direction of arrival algorithms are used, in general, to estimate a number of incident plane waves on the antenna array and their angles of incidence. In this paper, firstly, a new approach representing a more extensive version of the conventional Capon method is proposed. The study employs the root-Capon approach based on cross-correlation matrix in extracting the estimated direction-of-arrival of some number of signals to a given uniform linear array (ULA) antenna system. Secondly, a simple modification on the antenna element's number is employed for the Capon and the proposed approach to obtain more performances. The effectiveness of the proposed algorithm is verified through numerical simulation examples, and it is shown that the root version of Capon method can provide more accurate angle estimation with less computational complexity than conventional Capon algorithm. Similarly, it is found also that the used modification plays a significant role in the performance's improvement of Capon and its variant approaches.

DOA Estimation for Underwater Target by Active Detection on Virtual Time Reversal Using a Uniform Linear Array.

Aiming at addressing the problem caused by multipath effects in direction of arrival (DOA) estimation for underwater targets, a method based on the active detection on virtual time reversal (ADVTR) Capon algorithm is proposed. Unlike the conventional passive target estimation method ignoring the multipath effects but only considering the direct wave, the proposed method is closer to the actual situation in that the multipath signal propagation model is fully taken into account; in addition, active detection (AD) and virtual time reversal (VTR) processes are added, which use active detection to estimate channels, and virtual time reversal to realize focusing in a computer after the source-receive array (SRA) receives the reflected signal of the target. The combination of the two methods can greatly improve the energy of SRA and the precision of target direction estimation. With the popular acoustic field simulation tool Bellhop, the model proposed in this paper is verified. Compared with the conventional Capon method without time reversal, the simulation results show that the ADVTR Capon estimation method is far better, in terms of resolution and suppressing the sidelobes. It is suitable for the target DOA estimation under low signal-to-noise ratio (SNR) conditions. Further, we also show the ADVTR Capon estimation method works well in a real tank experiment.

Noncontact Measurement of the Instantaneous Heart Rate in a Multi-Person Scenario Using <inline-formula> <tex-math notation="LaTeX">${X}$ </tex-math> </inline-formula>-Band Array Radar and Adaptive Array Processing

A noncontact measurement of the heart rate of a specific person using an X -band radar system with a four-element antenna array is presented. The system comprises a 2-D planar wide-beam antenna array with a four-channel network analyzer. The direction of arrival is estimated using the Capon method, and the directionally constrained minimization-of-power algorithm is then applied to the received signals. Signals from the four channels are adaptively combined to enhance the accuracy in estimating the instantaneous heart rate in a multi-person scenario. Measurement results indicate that the proposed system with the adaptive array processing technique is effective for the noncontact measurement of the heart rate of a specific person when there is more than one person in the scene.

Biomedical Signals Analysis Using the Empirical Mode Decomposition and Parametric and non Parametric Time-Frequency Techniques

In this paper, the Empirical mode decomposition (EMD) technique is used, in a first time, to separate the artifact from the biomedical signals. The biomedical signals treated are electroencephalogram (EEG) and Electrocardiogram (ECG) for normal and abnormal patients. Analysis of EEG and ECG signals is a challenging problem due to the fact that the signals are multi-component and very non-stationary. Due to the nature of these signals, the time-frequency analysis is an important tool for representing the evolution of the frequential components of these biomedical signals over time. The time-frequency techniques used are the parametric, Periodogram and Capon methods, and non-parametric Smoothed Pseudo Wigner-Ville method. As a first step of analysis, the EMD technique is applied to eliminate the artifact from these signals after that the parametric and non-parametric time-frequency techniques are processed to the results signals to present the non-stationary multicomponent of these signals in function of time. The results show that the EMD technique associated to the Periodogram method give a good localization of the transient abnormal ECG and the energies of the EEG signals as compared to others time-frequency methods associated to the EMD technique.

High-resolution coherent backscatter interferometric radar images of equatorial spread F using Capon's method

Abstract. We present results of Capon's method for estimation of in-beam images of ionospheric scattering structures observed by a small, low-power coherent backscatter interferometer. The radar interferometer operated in the equatorial site of São Luís, Brazil (2.59° S, 44.21° W, −2.35° dip latitude). We show numerical simulations that evaluate the performance of the Capon method for typical F region measurement conditions. Numerical simulations show that, despite the short baselines of the São Luís radar, the Capon technique is capable of distinguishing localized features with kilometric scale sizes (in the zonal direction) at F region heights. Following the simulations, we applied the Capon algorithm to actual measurements made by the São Luís interferometer during a typical equatorial spread F (ESF) event. As indicated by the simulations, the Capon method produced images that were better resolved than those produced by the Fourier method. The Capon images show narrow (a few kilometers wide) scattering channels associated with ESF plumes and scattering regions spaced by only a few tens of kilometers in the zonal direction. The images are also capable of resolving bifurcations and the C shape of scattering structures.

Ultrawideband Radar Imaging Using Adaptive Array and Doppler Separation

Ultrawideband Doppler radar interferometry is known as an effective method that enables high-resolution imaging when using a simple antenna array. The technique, however, suffers from image artifacts when multiple moving targets with the similar Doppler velocities are present in the same range bin. To resolve this problem, we combine the Doppler interferometry technique with the Capon methods. Through numerical simulations and experiments, we show the remarkable performance improvement achieved by the proposed method.

Adaptive Spectral Estimation Methods in Color Flow Imaging.

Clutter rejection for color flow imaging (CFI) remains a challenge due to either a limited amount of temporal samples available or nonstationary tissue clutter. This is particularly the case for interleaved CFI and B-mode acquisitions. Low velocity blood signal is attenuated along with the clutter due to the long transition band of the available clutter filters, causing regions of biased mean velocity estimates or signal dropouts. This paper investigates how adaptive spectral estimation methods, Capon and blood iterative adaptive approach (BIAA), can be used to estimate the mean velocity in CFI without prior clutter filtering. The approach is based on confining the clutter signal in a narrow spectral region around the zero Doppler frequency while keeping the spectral side lobes below the blood signal level, allowing for the clutter signal to be removed by thresholding in the frequency domain. The proposed methods are evaluated using computer simulations, flow phantom experiments, and in vivo recordings from the common carotid and jugular vein of healthy volunteers. Capon and BIAA methods could estimate low blood velocities, which are normally attenuated by polynomial regression filters, and may potentially give better estimation of mean velocities for CFI at a higher computational cost. The Capon method decreased the bias by 81% in the transition band of the used polynomial regression filter for small packet size ( N=8 ) and low SNR (5 dB). Flow phantom and in vivo results demonstrate that the Capon method can provide color flow images and flow profiles with lower variance and bias especially in the regions close to the artery walls.

Computational complexity reduction techniques for real-time and high-resolution medical ultrasound imaging using the beam-space Capon method

The beam-space (BS) Capon method is an adaptive beamforming technique that reduces computational complexity. However, the complexity is not low enough for real-time imaging. Reducing the number of time-delay and transformation processes from element-space to BS signal processing is required. We propose a technique that replaces the time-delay processes by the multiplication of steering vectors and covariance matrices. In addition, we propose a compensation technique for estimating the intensity accurately. In an experimental study using a 2.0 MHz transmission frequency on a 15 × 10.4 mm2 region of interest, the first side-lobe level, the −6 dB beam width, the intensity’s estimation error, and the calculation time of the conventional method were −15 dB, 0.70 mm, 3.2 dB, and 656 ms. Those of the proposed method were −17 dB, 0.36 mm, 1.6 dB, and 81 ms, respectively. Using our method on three CPUs achieves imaging of 37 frames/s.

Sparse Signal Recovery Based Imaging in the Presence of Mode Conversion With Application to Non-Destructive Testing

We propose a sparse signal representation based method for imaging solid materials in the presence of mode conversion phenomenon using an array of ultrasonic transducers. Traditional imaging techniques, such as MUSIC, Capon, and delay-and-sum (DAS) beamformer, do not take into account mode conversion. Recently, the well-known Capon and MUSIC techniques have been modified such that they can be used in multimodal propagation environments. Referred to as MC-Capon and MC-MUSIC techniques, these methods yield a higher resolution and lower sidelobe levels, as compared to the DAS beamformer. Moreover, unlike the DAS beamformer, they do not suffer from Rayleigh resolution limit, which is independent of the SNR. The MC-MUSIC and MC-Capon methods are capable of taking into account the effect of all different propagation modes, and therefore, find the locations of the reflectors with high precision. These two techniques, however, suffer from all the shortcomings that the MUSIC technique and the Capon method have. To overcome these issues, we propose a sparse signal representation based technique that not only is able to take into account the effect of all modes but also does not suffer from the aforementioned shortcomings. Our method can be implemented using only one snapshot from the array and does not require several snapshots. Its sensitivity to SNR is much less than that of the MC-MUSIC and MC-Capon approaches. Furthermore, unlike the MC-MUSIC method, there is no need to know the number of reflectors in advance. We show, through numerical and experimental examples, that compared to the aforementioned algorithms, our approach offers higher resolution and has lower sidelobe levels.

Application of capon method to direct position determination

Abstract The direct position determination (DPD) approach is a single-step method which uses the Maximum Likelihood estimator to localize sources emitting electromagnetic energy using combined data from all available sensors. The DPD is known to outperform the traditional 2-step methods under low Signal to Noise Ratio (SNR) conditions. We propose an improvement to the DPD approach, using the well known minimum-variance-distortionless-response (MVDR) approach. Unlike Maximum Likelihood, the number of sources need not be known before applying the method. The combination of both the direct approach and MVDR yields unprecedented localization accuracy and resolution for weak sources. We demonstrate this approach on the problem of multistatic radar, but the method can easily be extended to general localization problems.

Assessment of the Impact of Orthogonal Directional Pattern Generating Algorithms on the Accuracy of Wireless Direction Finding by BS-MUSIC and BS-Capon Methods

The paper considers the MUSIC and Capon methods for determination of radio radiation coordinates, possessing a superresolution property, which assumes that two signal sources spaced less than at the Rayleigh limit can be represented as individual peaks on the spatial direction finding relief graph. A computational burden problem arises in such spectrum estimation algorithms; it can be solved by the methods of building so-called orthogonal directional patterns, reducing computational complexity and antenna array dimension. A multibeam array pattern (spatial channel) is formed for this purpose, and then the signals are pre-processed by means of these spatial channels focused in a certain region. The paper gives numerical estimations of accuracy for determination of radio radiation source coordinates by the classical MUSIC and Capon methods, and also after preliminary transformation by orthogonal directional patterns (BS-MUSIC and BS-Capon) versus signal/noise ratio, the number of beams and averaging time of the correlation matrix. A great number of methods of mutually orthogonal spatial channel formation are presented; among them the most well-known discrete Fourier transform, spherical sequences and Taylor series expansion. It is worth noting that to date no comparative studies of the accuracy characteristics of such methods (BS-MUSIC and BS-Capon) has been performed. It is found that the accuracy of the BS-MUSIC and BS-Capon methods increases with the increase in the number of spatial channels from four to five. In this case the accuracy of the method for channel generating by spherical discrete sequences is the highest in the majority of the considered interference cases.

Improvement of Capon DOA estimation by antenna mode switch techniques

In this paper, the antenna mode switch technique is applied to Capon DOA (direction of arrival) estimation of signal sources. The Capon method is a well-known DOA estimation algorithm. However, it often needs a large antenna array to achieve good resolution so that the cost and computation efforts are increased. To achieve good resolution without increasing the number of array elements, our antenna mode switch technique is added to Capon DOA computation. The antenna mode switch technique is a special antenna pattern which reduces the interference from spatial region not being scanned. Such a special antenna pattern can be experimentally implemented. Numerical simulation results show that using our antenna mode switch in Capon DOA computation can significantly improve the resolution. It can be applied to small portable devices of modern wireless communication.

High-contrast and low-computational complexity medical ultrasound imaging using beamspace capon method.

Several adaptive beamforming techniques have been proposed to improve the quality of medical ultrasound images. The beamspace (BS) Capon method is one common method used to depict high-resolution images with low computational complexity. However, the complexity is not low enough for real-time imaging in clinical situations because the conventional BS Capon method employs a time-delay process and a transition process from elementspace signal processing to BS signal processing at all points of interest. Thus, we propose a technique that replaces the time-delay process using a steering vector. In addition, the Capon method employs a spatial averaging (SA) technique to stabilize the estimation in intensity. However, when the averaging size is not adequate, the estimated intensity might be smaller than that given by the delay-and-sum (DAS) method. Because most medical diagnoses are presented based on the estimation of intensity acquired by the DAS beamformer, accurate estimation of intensity is also required. Therefore, we propose a compensation technique that uses both small and large sizes for SA. In an experiment, the -6 dB beam width, sidelobe level, and estimation error in the intensity of the proposed method were 0.17 mm, -27 dB, and 0.92 dB, respectively, where those of the conventional BS Capon method were 0.29 mm, -22 dB, and 8.1 dB. The complexity of the proposed method is one-fourteenth that of the conventional method. Compared with conventional methods, the proposed method succeeded in depicting a higher-contrast image with accurate intensity estimation and lower computational complexity.

Discrete Receive Beamforming

We present a new approach for analog receive beamforming if phase shifters and amplifiers have finite resolution only. Then, the maximization of the signal-to-interference-plus-noise ratio (SINR) is a discrete optimization problem with a nonconcave objective function. The discrete maximization problem is solved exactly by means of a branch-and-bound algorithm. Based on the Capon method, we derive a new and efficient way of computing upper SINR-bounds for the subproblems occurring at the nodes of the branch-and-bound tree. Results of numerical simulations are provided and compared to an earlier approximate approach.