Differential Beamforming Research Articles

Design of differential microphone array beampatterns with sidelobe level constraints

The target beampattern of differential microphone arrays (DMAs) often satisfies design requirements to optimize the performance of the beamformer by maximizing a specific advantage. This paper focuses on designing and implementing the minimum mainlobe width beampattern under the constrained sidelobe level. The main works are as follows. (1) We derive the minimum mainlobe width target beampattern under certain sidelobe level constraints from the Chebyshev-Type pattern that satisfies the sufficient conditions for effective target beampatterns. (2) We design a Jacobi–Anger expansion approximation differential beamforming filter for the Chebyshev-Type target beampattern to ensure that the resulting beampattern is consistent with the Chebyshev-type target beampattern and the beamformer’s robustness can be improved by using more microphones to obtain a minimum-norm solution. Compared with the conventional frequency-independent pattern Jacobi–Anger expansion method, the Chebyshev-Type Jacobi–Anger expansion beamformer we designed can flexibly limit the sidelobe level and obtain the minimum mainlobe beamwidth.

Design of Differential Loudspeaker Line Array for Steerable Frequency-Invariant Beamforming

Differential beamforming has attracted much research since it can utilize an array with a small aperture size to form frequency-invariant beampatterns and achieve high directional gains. It has recently been applied to the loudspeaker line array to produce a broadside frequency-invariant radiation pattern. However, designing steerable frequency-invariant beampatterns for the loudspeaker line array has yet to be explored. This paper proposes a method to design a steerable differential beamformer with a loudspeaker line array. We first determine the target differential beampatterns according to the desired direction, the main lobe width, and the beampattern order. Then, we transform the target beampattern into the modal domain for representation. The Jacobi-Anger expansion is subsequently used to design the beamformer so that the resulting beampattern matches the target differential beampattern. Furthermore, based on the criterion of minimizing the mean square error between the synthesized beampattern and the ideal one, a multi-constraint optimization problem, which compromises between the robustness and the mean square error, is formulated to calculate the optimal desired weighting vector. Simulations and experimental results show that the proposed method can achieve steerable frequency-invariant beamforming from 300 Hz–4 kHz.

Design of Robust Broadband Frequency-Invariant Broadside Beampatterns for the Differential Loudspeaker Array

The directional loudspeaker array has various applications due to its capability to direct sound generation towards the target listener and reduce noise pollution. Differential beamforming has recently been applied to the loudspeaker line array to produce a broadside frequency-invariant radiation pattern. However, the existing methods cannot achieve a compromise between robustness and broadband frequency-invariant beampattern preservation. This paper proposed a robust broadband differential beamforming design to allow the loudspeaker line array to radiate broadside frequency-invariant radiation patterns with robustness. Specifically, we propose a method to determine the ideal broadside differential beampattern by combining multiple criteria, namely null positions, maximizing the directivity factor, and achieving a desired beampattern with equal sidelobes. We derive the above ideal broadside differential beampattern into the target beampattern in the modal domain. We propose a robust modal matching method with Tikhonov regularization to optimize the loudspeaker weights in the modal domain. Simulations and experiments show improved frequency-invariant broadside beamforming over the 250–4k Hz frequency range compared with the existing modal matching and null-constrained methods.

A 5G NR FR2 Beamforming System with Integrated Transceiver Module.

This paper presents a 5G new radio (NR) FR2 beamforming system with an integrated transceiver module. A real-time operating module providing enhanced flexibility and capability has been proposed. The integrated RF beamforming system with an integrated transceiver module can be operated in 8Tx-8Rx mode configuration simultaneously. A series-fed structure 8 × 7 microstrip antenna array for compact size and improved directivity is employed in the RF beamforming module. The RF beamforming module incorporates a custom 28 GHz, eight-channel fully differential beamforming IC (BFIC). An eight-channel BFIC in a phased-array beamforming system offers advantages in terms of increased antenna density and improved beam steering precision. The RF beamforming module is integrated with an RF transceiver module that enables the simultaneous up-conversion and down-conversion of the baseband signal. The RF transmitter module consists of a transmitter, a receiver, a signal generator, a power supply, and a control unit. The RF beamforming system can scan horizontally from -50° to +50° with a step of 10°. To achieve an optimized beam pattern, a calibration was conducted. The transmit and receive conversion gain of around 20 dB is achieved with the transceiver module. To verify the communication performance of the manufactured integrated RF beamforming system, a real-time wireless video transmission/reception test was performed at a frequency of 28 GHz, and the video file was transmitted smoothly in real time without interruption within a range of ±50°.

Design of Fully Steerable Differential Beamformers With Linear Superarrays

Design of Fully Steerable Differential Beamformers With Linear Superarrays

On the Design of Robust Differential Beamformers From the Beampattern Error Perspective

On the Design of Robust Differential Beamformers From the Beampattern Error Perspective

Differential beamforming using Rotman lens for wireless sensor networks

In this article, an optimal beamforming technique using a low cost intelligent Rotman lens antenna is proposed. The proposed technique enjoys full diversity with high coding gain, has a very low encoding and decoding complexity, and does not require channel knowledge at any transmitting or receiving antenna. From our simulation results, the proposed technique outperforms the best known non-coherent multi-antenna techniques. Furthermore, we prove that the BER expressions obtained from the theoretical analysis enjoy full diversity gain and match our conducted simulations.

Research on acoustic fault diagnosis of bearings based on spatial filtering and time-frequency domain filtering

In conventional methods, vibration-based diagnosis (VBD) is commonly used for identifying rolling bearing faults. In contrast, acoustical-based fault diagnosis (ABD) has been extensively studied as an alternative due to its non-contact measurement capabilities, which are superior to VBD. Nonetheless, the accuracy of machine diagnosis may be compromised by multisource aliasing in the recorded acoustic signals. This research integrates spatial domain filtering and time-frequency domain filtering to address the issue of bearing fault diagnosis. By utilizing the second-order cone optimization method, differential power response beamformers have been established to attain a high signal-to-noise ratio of bearing sound while effectively controlling the noise power level. The output of differential beamformers is analyzed using the parametric adaptive MOMEDA approach. The method presented in this paper enables bearing acoustic fault diagnosis and identification of the faulty bearing location. The validity of the proposed ABD method has been demonstrated through experimental and simulation results.

A Multimode 28 GHz CMOS Fully Differential Beamforming IC for Phased Array Transceivers

A 28 GHz fully differential eight-channel beamforming IC (BFIC) with multimode operations is implemented in 65 nm CMOS technology for use in phased array transceivers. The BFIC has an adjustable gain and phase control on each channel to achieve fine beam steering and beam pattern. The BFIC has eight differential beamforming channels each consisting of the two-stage bi-directional amplifier with a precise gain control circuit, a six-bit phase shifter, a three-bit digital step attenuator, and a tuning bit for amplitude and phase variation compensation. The Tx and Rx mode overall gains of the differential eight-channel BFIC are around 11 dB and 9 dB, respectively, at 27.0–29.5 GHz. The return losses of the Tx mode and Rx mode are >10 dB at 27.0–29.5 GHz. The maximum phase of 354° with a phase resolution of 5.6° and the maximum attenuation of 31 dB, including the gain control bits with an attenuation resolution of 1 dB, is achieved at 27.0–29.5 GHz. The root mean square (RMS) phase and amplitude errors are <3.2° and <0.6 dB at 27.0–29.5 GHz, respectively. The chip size is 3.0 × 3.5 mm2, including pads, and Tx mode current consumption is 580 mA at 2.5 V supply voltage.

Eigenbeam-space transformation based steerable differential beamforming for linear arrays

Since linear differential arrays with small apertures can obtain high directivity and frequency-independent spatial response, much attention has been paid to the design of differential beamformers steered to the endfire direction. Although some works focus on the design of steerable differential beamformers with linear arrays, the synthesis of steerable frequency-invariant beampatterns by linear arrays still needs to be investigated. In this paper, an eigenbeam-space transformation based steerable differential beamforming is proposed for linear arrays. The major contributions are as follows. (1) For the beamformer steered away from the endfire direction, an interference suppression constraint might be imposed to ensure a valid beampattern in the situation where the interference from the endfire direction is very strong, which is not considered in the state-of-the-art approaches of the literature. (2) The synthesis of steerable differential beamformers is formulated as an optimization problem in the eigenbeam-space domain and the optimization problem is solved in a closed form. By experimentally determining the best pair of integers mt and N′, the proposed hybrid least-squares-error solution obtained in the eigenbeam-space domain has shown some advantages over the null constrained method and the weighted least-squares method implemented in the element-space domain.

Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level.

The differential microphone array, or differential beamformer, has attracted much attention for its frequency-invariant beampattern, high directivity factor and compact size. In this work, the design of differential beamformers with small inter-element spacing planar microphone arrays is concerned. In order to exactly control the main lobe beamwidth and sidelobe level and obtain minimum main lobe beamwidth with a given sidelobe level, we design the desired beampattern by applying the Chebyshev polynomials at first, via exploiting the structure of the frequency-independent beampattern of a theoretical Nth-order differential beamformer. Next, the so-called null constrained and least square beamformers, which can obtain approximately frequency-invariant beampattern at relatively low frequencies and can be steered to any direction without beampattern distortion, are proposed based on planar microphone arrays to approximate the designed desired beampatterns. Then, for dealing with the white noise amplification at low-frequency bands and beampattern divergence problems at high-frequency bands of the null constrained and least square beamformers, the so-called minimum norm and combined solutions are deduced, which can compromise among the white noise gain, directivity factor and beampattern distortion flexibly. Preliminary simulation results illustrate the properties and advantages of the proposed differential beamformers.

Differential constant-beamwidth beamforming with cube arrays

In this paper, we present an azimuth and elevation constant-beamwidth (CB) differential beamforming approach for cube arrays. We decompose a global cube beamformer into a Kronecker-product (KP) of three sub-beamformers: two constant-beamwidth beamformers along the y and z axes, and a tunable super-directive (SD) beamformer along the x-axis. We propose two design methods to derive cube beamformers whose either white noise gain (WNG) or directivity factor (DF) may be set by design. We show that the CB threshold frequency with respect to the azimuth and elevation angles, and the WNG and DF performance, can be controlled by the number of microphones along each axis. In addition, we focus on the particular case of merely a single microphone along the x-axis, which yields a rectangular azimuth and elevation CB beamformer. We demonstrate that its CB threshold frequencies are controlled by the number of microphones along the y and z axes, and show that the WNG and DF performance measures are maximized when the two axes are equal in size. Finally, we analyze the performance of the proposed beamformers through simulations of speech signals in various reverberant scenarios, including deviations in the desired speech signal’s direction of arrival (DOA). We show that the proposed beamformers outperform previously-presented beamformers and the traditional SD and delay-and-sum (DS) beamformers, particularly in terms of the intelligibility of their corresponding time-domain enhanced signals.

An event-based magnetoencephalography study of simulated driving: Establishing a novel paradigm to probe the dynamic interplay of executive and motor function.

Magnetoencephalography (MEG) is particularly well-suited to the study of human motor cortex oscillatory rhythms and motor control. However, the motor tasks studied to date are largely overly simplistic. This study describes a new approach: a novel event-based simulated drive made operational via MEG compatible driving simulator hardware, paired with differential beamformer methods to characterize the neural correlates of realistic, complex motor activity. We scanned 23 healthy individuals aged 16-23 years (mean age=19.5, SD=2.5; 18 males and 5 females, all right-handed) who completed a custom-built repeated trials driving scenario. MEG data were recorded with a 275-channel CTF, and a volumetric magnetic resonance imaging scan was used for MEG source localization. To validate this paradigm, we hypothesized that pedal-use would elicit expected modulation of primary motor responses beta-event-related desynchronization (B-ERD) and movement-related gamma synchrony (MRGS). To confirm the added utility of this paradigm, we hypothesized that the driving task could also probe frontal cognitive control responses (specifically, frontal midline theta [FMT]). Three of 23 participants were removed due to excess head motion (>1.5cm/trial), confirming feasibility. Nonparametric group analysis revealed significant regions of pedal-use related B-ERD activity (at left precentral foot area, as well as bilateral superior parietal lobe: p <.01 corrected), MRGS (at medial precentral gyrus: p <.01 corrected), and FMT band activity sustained around planned braking (at bilateral superior frontal gyrus: p <.01 corrected). This paradigm overcomes the limits of previous efforts by allowing for characterization of the neural correlates of realistic, complex motor activity in terms of brain regions, frequency bands and their dynamic temporal interplay.

Differential Beamforming From a Geometric Perspective

Differential Beamforming From a Geometric Perspective

Design of 2D and 3D Differential Microphone Arrays With a Multistage Framework

Differential microphone arrays (DMAs) have demonstrated a great potential for high-fidelity acoustic and speech signal acquisition in a wide range of applications since such arrays are able to achieve frequency-invariant beampatterns with high directivity. Consequently, a great number of efforts have been devoted to the design of DMAs and the associated beamformers in the literature. However, most of the methods only work for arrays with particular topologies, e.g., linear, circular, concentric circular, and spherical ones. How to design general two-dimensional (2D) and three-dimensional (3D) DMAs that can measure the desired differential sound field and form the desired spatial response in the 3D space remains an unsolved problem. This paper investigates this problem and presents a multistage design approach. The major contributions of this work are as follows. First, we reexamine the differentials of the acoustic pressure field in the 3D space and derive the general expression of the directivity patterns resulting from the spatial differential operation, which serves as the foundation for differential beamforming with 2D or 3D microphone arrays. Second, we present a multistage approach to the design of 2D and 3D DMAs, and deduce the relationship between the global beamformer and the beamformers at different stages as well as the relationship between their beampatterns. Third, several algorithms are presented for the design of differential as well as robust differential beamformers in this multistage framework. Simulation results validate the proposed approach and justifies its properties.

A Perspective on Fully Steerable Differential Beamformers for Circular Arrays

Both the null-constrained method and the Jacobi-Anger expansion method are commonly adopted to design the fully steerable circular differential microphone arrays (CDMAs). So far, these two methods have been independently studied, and it is unclear why they exhibit pronounced performance difference and whether they have a potential connection. In this letter, we develop a unified framework for the design of the fully steerable CDMA, which jointly utilizes the null constraints and the Jacobi-Anger expansion. We show that the existing two methods can be treated as special cases of the proposed approach and they can indeed be connected. We then reveal that the null-constrained CDMA can be viewed as the regularized Jacobi-Anger expansion-based CDMA, which theoretically explains why the former can alleviate the deep nulls problem in white noise gain in certain cases and why it still suffers from the severe deep nulls in other cases. We further explain why the magnitude of the synthesized beampattern of the Jacobi-Anger expansion-based method in nulls' direction can be much larger than that of the null-constrained method. Simulations support the theoretical results well.

A Novel Method to Design Steerable Differential Beamformer Using Linear Acoustics Vector Sensor Array

A Novel Method to Design Steerable Differential Beamformer Using Linear Acoustics Vector Sensor Array

Design of Steerable Linear Differential Microphone Arrays With Omnidirectional and Bidirectional Sensors

This paper is dedicated to the design of fully steerable linear differential microphone arrays (LDMAs). We analyze the steerable ideal spatial responses and explain why conventional LDMAs consisting of only omnidirectional microphones have limited steering ability. In order to circumvent this limitation, we suggest to use both omnidirectional and bidirectional (with a dipole shaped directivity pattern) microphones. We discuss the minimum numbers of omnidirectional and bidirectional sensors required for achieving steerable spatial responses and present a method to design fully steerable differential beamformers with LDMAs through the Jacobi-Anger series expansion. Simulations validate the presented technique and the steering flexibility of the designed LDMAs.

Multistage approach for steerable differential beamforming with rectangular arrays

This paper presents a multistage rectangular approach for steerable differential beamforming. As a first step, we propose employing a two-dimensional (2-D) differentiation scheme that operates independently on the columns and rows of a uniform rectangular array (URA). This yields a differentials matrix controlled by two parameters, Pc and Pr, which indicate the number of differential stages for the URA columns and rows. Then, as a second step, we design a rectangular differential beamformer and apply it to the vector form of the differentials matrix. We show that the proposed differentiation scheme may significantly improve the directivity of the resulted beamformer at the expense of white noise amplification. This improvement is heavily tied to selecting the (Pc,Pr) configuration per the desired signal incident angle. Next, we propose four rectangular differential beamformers and analyze their performances in terms of the white noise gain (WNG) and directivity factor (DF) measures. In addition, we address reverberant scenarios with three distinct incident angles of the desired signal. We examine the performances of each beamformer in terms of four reduction factors calculated from the noisy and enhanced signals and investigate their quality and intelligibility. We demonstrate that the proposed rectangular differential beamformers outperform common linear and differential beamformers in these measures, mainly when the incident angle is far from the endfire direction. Finally, we compare the proposed approach to two existing rectangular differential beamforming approaches from the literature. We show the proposed method to be preferable, considering both the quality and intelligibility of the enhanced signals.

Fundamental Approaches to Robust Differential Beamforming With High Directivity Factors

Differential beamforming, which measures the spatial derivatives of the acoustic pressure field, can be used in a wide range of small devices that require high-fidelity sound and speech acquisition as it can achieve frequency-invariant spatial responses with high directivity factors (DFs). Since a differential process is inherently sensitive to sensors' self noise and other array imperfections, the most challenging problem in the design of any differential beamformer is how to achieve the maximum possible DF while maintaining a proper level of robustness for practical usage. While significant efforts have been made on this topic, the problem remains unsolved and further study is indispensable. This paper is devoted to dealing with this challenging problem. It presents a study on theory and methods to achieve the optimal and fundamental compromise between the white noise gain (WNG), which quantifies how robust is the beamformer, and the DF in differential beamforming. The major contributions of this work are as follows. 1) We show and prove that any null constrained fixed beamformer can be decomposed as the sum of two orthogonal filters, i.e., the maximum WNG (MWNG) beamformer and a reduced-rank one. Based on this decomposition, we develop three kinds of differential beamformers from the WNG perspective, which can achieve a flexible and optimal compromise between DF and WNG. 2) We show that a transformed null constrained beamformer can also be decomposed as the sum of two orthogonal filters, i.e., the transformed maximum DF (MDF) beamformer and another reduced-rank one. Based on this decomposition, we also develop three kinds of differential beamformers, which can obtain the desired level of DF while using the rest of the degrees of freedom to maximize the WNG. Simulations are performed to validate the theoretical analysis and developed differential beamformers.