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Aiming at the problem of poor spatial resolution of low-frequency noise sources in a small-aperture spherical microphone array (SMA), this paper proposes a method for localizing and identifying low-frequency noise sources based on virtual-vector open SMA ('p+v' joint processing method of pressure and velocity). Firstly, a virtual open SMA with a larger aperture is obtained using a virtual array extrapolation method. In this method, the virtual SMA and the actual SMA are regarded as a dual-radius SMA, and velocity information is obtained using finite difference elements of the same direction (azimuth and elevation) array of the virtual and actual SMA. At the same time, the sound pressure at the velocity position is obtained using the virtual SMA extrapolation method and the virtual vector array element SMA, whereby both velocity and sound pressure information is obtained. Finally, the vector signal processing technology is introduced into the generalized inverse beamforming algorithm (GIB). After determining the vector transfer function of the 'p+v' joint processing mode, a low-frequency-noise-source localization and identification method based on the vector signal processing GIB is proposed. The simulation and experiment results show that a virtual SMA with a large aperture can be obtained using a virtual array extrapolation method, and the GIB with sound pressure and velocity joint processing has a better spatial resolution. [ABSTRACT FROM AUTHOR]

We present a novel analytical method as an efficient approach to design a geodesic-faceted array (GFA) for achieving a beam performance equivalent to that of a typical spherical array (SA). GFA is a triangle-based quasi-spherical configuration, which is conventionally created using the icosahedron method imitated from the geodesic dome roof construction process. In this conventional approach, the geodesic triangles have nonuniform geometries due to some distortions that occur during the random icosahedron division process. In this study, we took a paradigm shift from this approach and adopt a new technique to design a GFA that is based on uniform triangles. The characteristic equations that relate the geodesic triangle with a spherical platform were first developed as functions of the operating frequency and geometric parameters of the array. Then, the directional factor was derived to calculate the beam pattern associated with the array. A sample design of GFA for a given underwater sonar imaging system was synthesized through an optimization process. The GFA design was compared with that of a typical SA, and a reduction of 16.5% in the number of array elements was recorded in the GFA at a nearly equivalent performance. Both arrays were modeled, simulated, and analyzed using the finite element method (FEM) to validate the theoretical designs. Comparison of the results showed a high degree of compliance between the FEM and the theoretical method for both arrays. The proposed novel approach is faster and requires fewer computer resources than the FEM. Moreover, this approach is more flexible than the traditional icosahedron method in adjusting geometrical parameters in response to desired performance outputs. [ABSTRACT FROM AUTHOR]

5G new radio (NR) provides features such as enhanced mobile broadband (eMBB) services and massive machine-type communications (mMTC). Multiple-input multiple-output (MIMO) transmission is an essential technique to enable these features, using antenna arrays with a sufficient number of elements to generate accurate and high-gain beams to desired user locations. In newer services, various forms of mobile devices are expected to appear in diverse locations, and beamforming need to accommodate such directional diversification. However, utilization of existing array structures has a limitation in transmitting signals to arbitrary receiver positions in the three-dimensional space. Therefore, a new type of array capable of forming accurate beams in isotropic fashion is desired, and the corresponding transmission strategies need to be identified. In this paper, the construction and utilization of the three-dimensional uniform spherical array (USA) are investigated. Beamforming vectors and the basis codebook for such arrays are defined, and characteristics of the generated beams are analyzed via comparison to the beams produced by conventional arrays. Array parameters to minimize the inter-beam interference are determined, and multiuser transmission performance is evaluated using the proper configuration of the array. We also apply the radiation pattern to the antenna elements to present the sum-rate performance in practical settings.

Aiming at the problem of poor spatial resolution of low-frequency noise sources in a small-aperture spherical microphone array (SMA), this paper proposes a method for localizing and identifying low-frequency noise sources based on virtual-vector open SMA (‘p+v’ joint processing method of pressure and velocity). Firstly, a virtual open SMA with a larger aperture is obtained using a virtual array extrapolation method. In this method, the virtual SMA and the actual SMA are regarded as a dual-radius SMA, and velocity information is obtained using finite difference elements of the same direction (azimuth and elevation) array of the virtual and actual SMA. At the same time, the sound pressure at the velocity position is obtained using the virtual SMA extrapolation method and the virtual vector array element SMA, whereby both velocity and sound pressure information is obtained. Finally, the vector signal processing technology is introduced into the generalized inverse beamforming algorithm (GIB). After determining the vector transfer function of the ‘p+v’ joint processing mode, a low-frequency-noise-source localization and identification method based on the vector signal processing GIB is proposed. The simulation and experiment results show that a virtual SMA with a large aperture can be obtained using a virtual array extrapolation method, and the GIB with sound pressure and velocity joint processing has a better spatial resolution.

The article presents the results of numerical simulation of a spherical array synthesized taking into account the polarization properties of the emitters. The formation of a directional diagram of a spherical array with different width of the main lobe and the required levels of the cross-polarization component and side lobes is considered. The article also presents the results of the formation of directional diagrams of a spherical array with the required level of cross-polarization component and a given width of the main lobe at different levels of the side lobes.

Abstract In this paper, we consider the 2-D direction-of-arrival (DOA) tracking problem. The signals are captured by a uniform spherical array and therefore can be analyzed in the spherical harmonics domain. Exploiting the sparsity of source DOAs in the whole angular region, we propose a novel DOA tracking method to estimate the source locations and trace their trajectories by using the variational sparse Bayesian learning (VSBL) embedded with Kalman filter (KF). First, a transition probabilities (TP) model is used to build the state transition process, which assumes that each source moves to its adjacent grids with equal probability. Second, the states are estimated by KF in the variational E-step of the VSBL and the variances of the state noise and measurement noise are learned in the variational M-step of the VSBL. Finally, the proposed method is extended to deal with the off-grid tracking problem. Simulations show that the proposed method has higher accuracy than VSBL and KF methods.

Spherical arrays have been widely used in direction-of-arrival estimation in recent years, and most algorithms in the spherical harmonics domain typically simultaneously obtain the 2-D angles. In this paper, we first use the structured least squares (SLS) to improve the performance of the decoupled spherical harmonics estimation of the signal parameter via rotational invariance technique (D-SHESPRIT) and propose D-SHESPRIT-SLS. Second, we derive the mean square error of the proposed algorithm and compare estimated results with theoretical results. The simulation results demonstrate the satisfactory performance of the proposed method.

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In order to obtain the better direction of arrival (DOA) estimation and reduce the amount of computation for the wideband acoustic source under the condition of low signal-to-noise ratio, the ortho- gonal propagator algorithm is now applied to the spherical harmonic domain. Based on the establishment of a spherical array acoustic field model, two spherical harmonic propagator orientation algorithms are proposed, including the algorithm in which the spherical Fourier transform component is used to obtain the propagator and the algorithm in which the cross spectrum matrix with the spherical Fourier transform component is used to obtain the propagator. The frequency adaptation range of spherical arrays with different radii is analyzed, and the problem of multi-bandwidth acoustic source frequency adaptability is solved. The DOA estimation performances of the two algorithms and the spherical harmonic domain multiple signal classification algorithm under different SNRs are compared and analyzed. Acoustic source orientation experiments were performed, and the DOA estimation time of the three algorithms was test. Experiments show that both algorithms have the characteristics of small computation, less time and accurate orientation. [ABSTRACT FROM AUTHOR]

Reliability is one of the most important aspects for any system onboard a satellite. This paper discusses different failure conditions and a fault-tolerant design of an active spherical phased array antenna (SPAA). This SPAA is having a hemispherical scan coverage for transmission of satellite imagery data at high bit rates to the ground station. Different failure conditions are identified and a criticality rank has been assigned based on their effects on the overall performance of the SPAA. Two entirely different configurations of the array are chosen to select the best one considering the failure effects. Based on these analyses, a rational margin is built such that the array can take care of even the most critical failure condition. This paper provides an insight toward the realization of a reliable phased array and thus useful for a practicing antenna engineer involved in designing antennas for the spacecrafts. [ABSTRACT FROM AUTHOR]

This research proposes an improved narrowband partial adaptive beamformer analysis using a proposed spherical array. Comparison between the fully and the partial adaptive beamformers is given. The study is performed by investigating performance parameters like the beamformer output signal-to-noise ratio and the beamformer output signal-to-interference-plus-noise ratio both in the steady state and along adaptation. Furthermore, computational complexity and convergence speed of the proposed sensor arrangement are also analyzed and examples are given. The results demonstrate that this beamformer considerably reduces the number of complex operations and features faster convergence speed. [ABSTRACT FROM AUTHOR]

Spherical harmonic array processing, also known as phase mode spherical sensor array processing, has been recently studied for different communication purposes. The spherical array arrangement presents desired three-dimensional symmetry, while the phase modes provide frequency-independent spatial processing. This paper proposes two novel sensor arrangements for spherical array which have been compared with the three sensor arrangements most used in spherical array beamforming. It has been proven that these proposed arrays achieve high directivity and more symmetrical beampatterns compared to the other arrangements. The phase mode beamformer with the element space beamformer has also been analyzed in an acoustic field. Furthermore, the phase mode beamformer has been compared when using the proposed sensor arrangements where different simulations show that the phase mode beamformer, at low frequencies, suffers of a huge reduction in array gain compared to that of the element space beamformer. [ABSTRACT FROM AUTHOR]

This paper presents a significant sidelobe reduction if nonuniform elevational spacing of antenna elements on the sphere is used. Antenna elements are progressively phased with a uniform amplitude excitation. The calculation of the required element position is presented. The achieved sidelobe level reduction with unequally spaced arrays could reach even more than 20dB difference with regard to the first significant sidelobe level of equally spaced arrays. By this method, arrays have the ability to produce the desired radiation pattern and could satisfy requirements for many applications.

The paper studies fabrication errors influence on the radiation pattern of a spherical antennas array. The developed Moment Method (MoM) program analyzes a particular influence of an azimuth and elevation position and local angle errors of antenna elements as well as model dimension errors on the radiation pattern. The spectral domain approach to the analysis of the spherical antenna arrays is applied here. Finally, results obtained from the theoretical investigation are verified by comparison with measured results.

This paper deals with the processing of signals measured by a spherical microphone array, focusing on the utilization of near-field information of such an array. The processing, based on the spherical harmonics decomposition, is performed in order to investigate the radial-dependent spherical functions and extract their argument – distance to the source. Using the low-frequency approximation of these functions, the source distance is explicitly expressed. The source distance is also determined from the original equation (using no approximation) by comparing both sides of this equation. The applicability of both methods is first presented in the noise-less data simulation, then validated with data contaminated by the additive white noise of different signal-to-noise ratios. Finally, both methods are tested for real data measured by a rigid spherical microphone array of radius 0.15 m, consisting of 36 microphones for a point source represented by a small speaker. The possibility of determination of the source distance using low-order spherical harmonics is shown. [ABSTRACT FROM AUTHOR]

Spherical arrays have been widely used in direction-of-arrival (DOA) estimation in recent years. In this paper, two unitary transformations for DOA estimation using spherical arrays are developed to transform the complex search vector to a real vector. Furthermore, the covariance matrix is transformed into a real matrix which has real eigenvalues and eigenvectors. Therefore, we can develop a real spherical harmonics multiple signal classification (RSHMUSIC) method to estimate the locations of signals. By exploiting the phase shift characteristic of the real search vector, the computation cost can be further reduced. Compared with the complex spherical harmonics MUSIC, the proposed methods have a lower amount of computations and better performance. Simulation results demonstrate the performance of the real SHMUSIC method. [ABSTRACT FROM AUTHOR]

Spherical arrays have many advantages for direction-of-arrival (DOA) estimation in 3D space. In this paper, a new real-valued method is proposed to estimate DOAs for spherical arrays. It exploits the property of the complex conjugate of spherical harmonics to find a unitary matrix which can transform the complex array steering matrix into a real matrix. Based on the unitary transformation, a new real-valued array model is constructed to keep the same dimension as the complex-valued model. Then variational sparse Bayesian learning (VSBL) is used to model the joint sparsity between the real part and imaginary part of original data. We get the approximate posterior of the sparse components. The real-valued DOA estimation method acquires good estimation performance and simultaneously decreases the computational cost considerably. Simulation results demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: With the three-dimensional symmetry and wide potential application, spherical array signal processing has been a hot research area for years. This paper devotes to the direction-of-arrival (DOA) estimation of the spherical arrays. Based on the orthogonality of the sensors’ location, MUSIC algorithm in spherical space is proposed, named as SH-MUSIC. Similar to beamspace MUSIC, spherical harmonics transformation is operated before MUSIC algorithm and a better performance is gotten because SH-MUSIC utilizes the array configuration’s orthogonality. On account of the transformation matrix’s orthogonality, spherical harmonics transformation is suggested to be operated firstly in other improved MUSIC algorithms without rejection, and it is demonstrated in beamspace MUSIC. In addition, owing to the tiny error between the steering vectors and the spherical harmonics with high order, sphere array data models including open sphere and rigid sphere are constructed. Simulation proves SH-MUSIC to be effective. Moreover, experimental data from a rigid sphere microphone array is dealt with by SH-MUSIC and the DOAs are estimated accurately. [Copyright &y& Elsevier]

The paper studies fabrication errors influence on the radiation pattern of a spherical antennas array. The developed Moment Method (MoM) program analyzes a particular influence of an azimuth and elevation position and local angle errors of antenna elements as well as model dimension errors on the radiation pattern. The spectral domain approach to the analysis of the spherical antenna arrays is applied here. Finally, results obtained from the theoretical investigation are verified by comparison with measured results. [ABSTRACT FROM AUTHOR]

Abstract: Close-talking microphones are required for speech pick-up in high noise environments and are based on the assumption that unwanted noise sources are distant from a desired nearfield source. Common close-talking microphones in use today have to be carefully oriented relative to the desired nearfield source. To address this problem, a new close-talking microphone array is proposed that is orientation-invariant with respect to the attenuation of farfield noise sources. It is shown that by appropriate processing of the close-talking microphone array signals, one can adaptively compensate for the distance and orientation of the microphone for a nearfield source. The proposed close-talking array is based on an spatially orthonormal decomposition of the soundfield for a nearfield source. It consists of four or more pressure microphones that are mounted in the surface of a rigid sphere with a diameter on the order of a centimeter. Finally, it is shown that decomposing the soundfield into spatially orthonormal modes leads to a computationally efficient implementation. [Copyright &y& Elsevier]

The effect of phased accuracy of the driving signals for array transducers on focused ultrasound field was studied. Based on a holed spherical high intensity focused ultrasound (HIFU) array, a phased project of 5-bit quantized accuracy for driving signals was suggested. It solves the problem of discrete adjust and control for driving signals in the phased HIFU treatment system. The simulation results show that this phased project can keep higher sound intensity and initial abilities of restraining the grating lobes of ultrasound field. It provides reliable foundation for the design of the phased HIFU driving system. [ABSTRACT FROM AUTHOR]

• The statistical performance of SH-MUSIC is clarified by investigating the null-spectrum. • The estimation biases of SH-MUSIC for large aperture arrays are inescapable but can be effectively reduced. • A closed threshold inequality to describe the resolution performance of SH-MUSIC is deduced. • SH-MUSIC exhibits better resolution performance than MUSIC for small aperture arrays. In this paper, we present a theoretical analysis of the statistical performance of spherical harmonics multiple signal classification (SH-MUSIC), which is a representative localization algorithm for spherical microphone arrays. What we are concerned about is the influence of spherical harmonics transformation on localization performance, which is mainly manifested in the following aspects: how the spatial aliasing affects the estimation of direction of arrivals (DOAs) in the large aperture case; and how to characterize the resolution capacity of SH-MUSIC in the small aperture case. We advance the research through the detailed examination of the null spectrum of SH-MUSIC. First, by applying the Taylor series expansion of the null spectrum, we give a bias expression to expound the impact of spatial aliasing on DOA estimation. The post-processing for bias reduction is then suggested. Second, utilizing the statistical distribution of the sample covariance matrix and also using the addition theorem of spherical harmonics, we derive an expression for the threshold at which SH-MUSIC can resolve two closely spaced sources to clarify SH-MUSIC's advantages in the small aperture case. Besides, numerical simulations are provided to verify the analytical results. [ABSTRACT FROM AUTHOR]