Grating Lobe Level Research Articles

Large-Pitch Synthetic Transmit Aperture Imaging: A Feasibility Study.

A 3-D or large-aperture 2-D synthetic transmit aperture (STA) ultrasound imaging system with a fully sampled array usually leads to high hardware complexity and cost since each element in the array is individually controlled. To reduce the hardware complexity, we propose a large-pitch method for STA (LPSTA) imaging integrated with a spatial response function (SRF) in the image reconstruction to improve image quality. To achieve this, we decreased the total number of measurement channels M (the product of the number of transmissions IT and the number of the receive channels in each transmission IR ). We combined L adjacent elements in transmission and K adjacent elements in receive into subapertures (SAPs), where L and K were coprime (no common factors) integers to suppress the grating lobes. We denoted it as an ( N/L, N /K ) system, where N is the number of transducer elements. In this article, first, we derived the beam pattern of the LPSTA using a far-field approximation. We demonstrated that the coprime selection and SRF can significantly reduce the grating lobes level (GLL) by using a beam pattern analysis. We also found that the LPSTA can have a similar beam pattern as that of a full array when the target is located along the steering direction. Second, the imaging performance of LPSTA was evaluated and validated with Field II simulations and experiments. The simulation results demonstrated that the proposed LPSTA with ( N /3, N /5) can achieve on average ~25% improvement in lateral resolution, ~24.6% and ~42.3% improvement in contrast-to-noise ratio (CNR) and contrast ratio (CR), respectively, over B-mode with a large-pitch receiver with ( N , N /5). LPSTA achieved comparable image contrast to the standard STA with the full array ( N , N ) at the cost of a reduced field of view. The experiment results were consistent with the simulation results. Finally, in addition to reducing the system (hardware) complexity, the LPSTA was more computationally efficient than the standard STA with a full array. The proposed method may help in realizing clinical applications of real-time 2-D or 3-D ultrasound imaging using large arrays.

Sparse Rectangular and Spiral Array Designs for 3D Medical Ultrasound Imaging.

In three-dimensional (3D) medical ultrasound imaging with two-dimensional (2D) arrays, sparse 2D arrays have been studied to reduce the number of active channels. Among them, sparse 2D arrays with regular or uniform arrangements of elements have advantages of low side lobe energy and uniform field responses over the entire field of view. This paper presents two uniform sparse array models: sparse rectangular arrays (SRAs) on a rectangular grid and sparse spiral arrays (SSAs) on a sunflower grid. Both arrays can be easily implemented on the commercially available or the custom-made arrays. To suppress the overall grating lobe levels, the transmit (Tx) and receive (Rx) array pairs of both the array models are designed not to have grating lobes at the same locations in the Tx/Rx beam patterns, for which the theoretical design rules are also proposed. Computer simulation results indicate that the proposed array pairs for both the SRAs and the SSAs achieve peak grating lobe levels below –40 dB using about a quarter of the number of elements in the dense rectangular array while maintaining similar beam widths to that of the dense array pair.

Efficient focused energy delivery with grating lobe mitigation for precision electronic warfare

Focused energy delivery, which can precisely transmit energy to the target area, is the key technology in precision electronic warfare (PREW). In practical applications, focused energy delivery technology is generally designed for ultra-sparse arrays. However, high computational complexity and severe grating lobe effect are still two main challenges in this field, especially when focused energy delivery is applied for complicated environments and multiple moving platforms. In this paper, we aim at designing highly efficient focused energy delivery technique with low grating lobe levels for ultra-sparse sensor arrays. Unlike existing methods that build models via estimating the covariance matrix of the transmitted signal, we directly establish array signal estimation models and consider the grating lobe effect in the objective function by proposing two metrics. To solve proposed models, we develop three efficient algorithms under the framework of majorization-minimization (MM) and alternating direction method of multiplier (ADMM). These algorithms all have low computational complexity and can achieve tighter upperbounds. Numerical simulations show that, the proposed algorithms are computationally more efficient and can alleviate the grating lobe effect compared to state-of-art algorithms.

Wideband Dual-Polarized Two-Beam Antenna Array With Low Sidelobe and Grating-Lobe Levels for Base-Station Applications

This paper presents a wideband dual-polarized $4\,\times \,6$ antenna array with two beams for base-station applications. It consists of three $4 \times 2$ subarrays. For obtaining ± 45° dual-polarized radiation, a wideband crossed dipole is employed as a basic element. For each $4 \times 2$ subarray, the lower and upper $4 \times 1$ subarrays are misaligned in the horizontal plane. By using this innovative scheme, the $4\,\times \,2$ subarray is equivalent to an $8 \times 1$ subarray with a half adjacent-element spacing, resulting in good grating-lobe suppression. For achieving stable two-beam radiation with low sidelobe over a wide frequency band, specific wideband beam-forming networks with little magnitude and phase imbalances are designed. Moreover, the adjacent-element spacing is optimized to obtain stable 10 dB beamwidth around 120°, thus satisfying the coverage requirement of 120° in the horizontal plane for base-station applications. For demonstration, the proposed $4 \times 6$ antenna array is designed, fabricated, and measured. The array exhibits two beams with stable 10 dB beamwidth around 120° in the horizontal plane and around −10 dB cross level between two beams. The impedance bandwidth is measured to be 56.1% (1.64–2.92 GHz) for VSWR < 1.5 and horizontally, sidelobe and grating-lobe levels of the two beams are measured to be better than 18 dB. Moreover, the proposed method can easily be extended to multibeam base-station antenna array designs.

Contrast and Volume Rate Enhancement of 3-D Ultrasound Imaging Using Aperiodic Plane Wave Angles: A Simulation Study.

Three-dimensional plane wave imaging (PWI) with a 2-D array has been studied for ultrafast volumetric imaging in medical ultrasound. Compared to 2-D PWI, 3-D PWI requires the transmission of an increased number of plane waves (PWs) to scan a volume of interest and achieve transmit dynamic focusing in both the lateral and elevational directions. To reduce the number of PW angles for a given 2-D angular range by mitigating the grating lobe level, we propose two aperiodic patterns of PW angles: concentric rings with a uniform radial interval and the well-known sunflower pattern. Both patterns are validated to provide uniform angle distributions without regular periodicity, and thereby reduce the grating lobe level compared to a periodic angle distribution with the same number of PW angles. Simulation studies show that the aperiodic patterns enhance the contrast of B-mode images by approximately 3-6 dB over all depths. This enhancement implies that the aperiodic angle sets can increase the volume rate by approximately 2-6 times compared to the periodic angle set at the same contrast and spatial resolution.

Bayesian Compress Sensing Based Countermeasure Scheme Against the Interrupted Sampling Repeater Jamming.

The interrupted sampling repeater jamming (ISRJ) is considered an efficient deception method of jamming for coherent radar detection. However, current countermeasure methods against ISRJ interference may fail in detecting weak echoes, particularly when the transmitting power of the jammer is relatively high. In this paper, we propose a novel countermeasure scheme against ISRJ based on Bayesian compress sensing (BCS), where stable target signal can be reconstructed over a relatively large range of signal-to-noise ratio (SNR) for both single target and multi-target scenarios. By deriving the ISRJ jamming strategy, only the unjammed discontinuous time segments are extracted to build a sparse target model for the reconstruction algorithm. An efficient alternate iteration is applied to optimize and solve the maximum a posteriori estimate (MAP) of the sparse targets model. Simulation results demonstrate the robustness of the proposed scheme with low SNR or large jammer ratio. Moreover, when compared with traditional FFT or greedy sparsity adaptive matching pursuit algorithm (SAMP), the proposed algorithm significantly improves on the aspects of both the grating lobe level and target detection/false detection probability.

Gap-filling method for suppressing grating lobes in ultrasound imaging: Theory and simulation results.

Sparse array (SA) is an approach to reduce the number of system channels. However, SA suffers from grating lobe (GL) artefacts due to the sparsity of array aperture resulting in degradation of the ultrasound image quality. Based on a given or known data sets of radio frequency (RF) echo acquired from active elements of an array, RF echo data in unknown and/or inactive elements of array can be created virtually and used to suppress the GL artefact in SA. This letter presents gap-filling (GF) approaches to generate channel data, which are not physically acquired. It is demonstrated that the proposed GF technique can reduce the artefacts of SA by filling the gaps in the array aperture. Simulation results show that the GF technique can suppress the GL level of SA by up to 16 dB. Also, the GF technique can improve the image quality of fully sampled arrays with small number of active elements.

Ultrasound Baseband Delay-Multiply-and-Sum (BB-DMAS) nonlinear beamforming

Compared to conventional Delay-and-Sum (DAS) beamforming, Delay-Multiply-and-Sum (DMAS) imaging uses multiplicative coupling of channel pairs for spatial coherence of receiving aperture to improve image resolution and contrast. However, present DMAS imaging is based on the radio-frequency (RF) channel signals (RF-DMAS) and thus requires large oversampling to avoid aliasing and switching of band-pass filtering to isolate the corresponding spectral components for imaging. Baseband DMAS (BB-DMAS) beamforming in this study is based on the demodulated channel signals to provide similar results but with simplified signal processing. The BB-DMAS beamforming scales the magnitude of time-delayed channel signal by p-th root while maintaining the phase. After channel sum, the output dimensionality is restored by p-th power. The multiplicative coupling in BB-DMAS always renders baseband signal and thus the need for oversampling is eliminated. Besides, the BB-DMAS can use any rational p values to provide flexible image quality and an explicit relation between BB-DMAS beamforming and channel-domain phase coherence exists. Our results show that the image characteristics between BB-DMAS and RF-DMAS are similar. The suppression of lateral side lobe level, grating lobe level and uncorrelated random noises gradually increases with the rational p value in BB-DMAS beamforming. The image contrast improves from −24.8 dB in DAS to −34.3 dB, −43.0 dB and −51.4 dB in BB-DMAS, respectively with p value of 1.5, 2.0 and 2.5. In conclusion, BB-DMAS beamforming provides flexible manipulation of image quality by introducing baseband spatial coherence in the ultrasonic imaging.

Planar Sub-Millimeter-Wave Array Antenna With Enhanced Gain and Reduced Sidelobes for 5G Broadcast Applications

In this paper, a compact, broadband, planar array antenna with omnidirectional radiation in horizontal plane is proposed for the 26 GHz fifth-generation (5G) broadcast applications. The antenna element is composed of two dipoles and a substrate integrated cavity (SIC) as the power splitter. The two dipoles are placed side-by-side at both sides of the SIC, and they are compensated with each other to form an omnidirectional pattern in horizontal plane. By properly combing the resonant frequencies of the dipoles and the SIC, a wide impedance bandwidth from 24 to 29.5 GHz is achieved. To realize a large array while reducing the complexity, loss, and size of the feeding network, a novel dual-port structure combined with radiation and power splitting functions is proposed for the first time. The amplitude and phase on each element of the array can be tuned, and therefore, the grating lobes level can be significantly reduced. Based on the dual-port structure, an eight-element array with an enhanced gain of over 12 dBi is designed and prototyped. The proposed antenna also features low profile, low weight, and low cost, which is desirable for 5G commercial applications. Measured results agree well with the simulations, showing that the proposed high-gain array antenna has a broad bandwidth, omnidirectional pattern in horizontal plane, and low side-lobes.

Low Grating Lobe Array Antenna With Electrically Large Property Based on TM50 Mode

In this paper, a low grating lobe array antenna with electrically large property is proposed based on TM 50 mode square patch antenna elements. By introducing transverse slots on the square radiating patch, four side lobes of the TM 50 mode element antenna can be reduced effectively. However, undesired grating lobes are created in the array pattern. That's because the antenna element distance is more than one wavelength on high modes. In order to solve this issue, a new method is proposed by making the grating lobes of the array factor pattern coincide with the null/(zero) ranges of element pattern. It can effectively suppress grating lobes caused by large element spacing. The method introduced here was supported by analytical 1×2 and 1×4 uniform liner arrays. Meanwhile, in order to further reduce transmission line loss and side lobes, substrate integration coaxial line structure and unequal amplitude feeding method are introduced. Finally, a 1×8 liner array is fabricated and measured for verification. When the element spacing is 1.4λ 0 , the grating lobes level at 22.3GHz is only -22dB.

High Gain and Low Grating Lobe Electrically Large Array Antenna by Using Fabry-Perot Cavity

In this paper, a high gain and low grating lobe electrically large array antenna is proposed by using Fabry-Perot cavity (FPC). The feeding array antenna is composed by elements with electrically large property (ELP) based on TM30 mode. The FPC between a ground plane and a single-layer partially reflecting surface (PRS) made by substrate with arrays of square metal patches printed on both the top and bottom surfaces is used here to narrow the beamwidth of element patterns, thus the large grating lobes of array caused by large element spacing can be avoided. By analyzing the parameters of PRS unit cell, suitable cell spacing is determined. Finally, a 2 × 2 array was fabricated and measured to validate its effectiveness. Measurements demonstrate that the gain of the array can reach up 20.9dBi at the center working frequency. When the element spacing is 1.47λ0, the maximum grating lobe level at 21GHz is only -15.5dB.

High-resolution ultrasound camera with sparse array for machine diagnosis

Fault detection plays a crucial role in maintenance of mechanical systems. Ultrasound is known to be a prevalent feature of incipient fault. Industrial ultrasound detectors are widely used to find out initial malfunction of machinery. Especially, ultrasound camera can shows the fault by overlapping beamforming power distribution with optical camera image. One can easily observe where the faults are. Ultrasound transducer usually has larger size than the wavelength of its resonance frequency for highly sensitive measurement. It must be a useful approach to design sparse array that gets over the spatial aliasing problem. The aliased beamforming distribution contains high grating-lobe level due to rough spatial sampling beyond half wavenumber spacing. The sparse array is optimized to minimize maximum side-lobe level by genetic algorithm under given constraints. Being with the constraints of size and number of elements, a limitation on spatial resolution is inevitable. Functional beamforming is simple but effective to dramatically increase spatial resolution as well as reduce side-lobes. A high resolution imaging scheme based on functional beamforming with an optimal sparse array is introduced.

Multi-beam steering with low grating lobes using optimized unequally spaced phased array

We propose a multi-beam steering technique with low grating lobes using unequally spaced phased array. The multi-beam steering is achieved using Array Division Multiplexing (ADM) technique. The unequal spacing distribution in ADM is optimized by the algorithm of particle swarm optimization (PSO) to minimize the grating lobes levels. The results show that the grating lobe level can be effectively reduced from 37.96% to 4.99% of the main lobe power using the proposed technique within the whole scanning range of the two steered beams.

Exploiting platform motion for passive source localization with a co-prime sampled large aperture array.

Co-prime array geometries have received a great deal of attention due to their ability to discriminate O(MN) sources with only O(M + N) sensors. This has been demonstrated both theoretically and in simulation. However, there are many practical limitations that make it difficult to realize the enhanced degrees of freedom when applying co-prime geometries to real acoustic data taken on a horizontal line array. For instance, co-prime sampling leads to grating lobes that can obscure lower signal-to-noise-ratio acoustic signals making them difficult to detect. In this work, a synthetic aperture (SA) method is presented for filling in holes and increasing redundancy in the difference co-array by exploiting array motion. The SA method is applied to acoustic data collected off the Southeastern shore of Florida on a fixed large aperture horizontal array. Array motion is simulated by taking a co-prime sampled subarray and virtually moving it along the horizontal aperture of the fixed array. It is demonstrated that SA processing on real acoustic data results in reduced side-lobe and grating lobe levels compared to that of the physical co-prime aperture.

High-Volume-Rate 3-D Ultrasound Imaging Based on Synthetic Aperture Sequential Beamforming With Chirp-Coded Excitation.

Three-dimensional (3-D) ultrasound imaging is a promising modality for many medical applications. Unfortunately, it generates voluminous data in the front end, making it unattractive for high-volume-rate portable medical applications. We apply synthetic aperture sequential beamforming (SASB) to greatly compress the front-end receive data. Baseline 3-D SASB has a low volume rate, because subapertures fire one by one. In this paper, we propose to increase the volume rate of 3-D SASB without degrading imaging quality through: 1) transmitting and receiving simultaneously with four subapertures and 2) using linear chirps as the excitation waveform to reduce interference. We design four linear chirps that operate on two overlapped frequency bands with chirp pairs in each band having opposite chirp rates. Direct implementation of this firing scheme results in grating lobes. Therefore, we design a sparse array that mitigates the grating lobe levels through optimizing the locations of transducer elements in the bin-based random array. Compared with the baseline 3-D SASB, the proposed method increases the volume rate from 8.56 to 34.2 volumes/s without increasing the front-end computation requirement. Field-II-based cyst simulations show that the proposed method achieves imaging quality comparable with baseline 3-D SASB in both shallow and deep regions.

Micro-beamforming with Error Compensation.

One of the main issues in the development of 2D arrays is the high system complexity due to the requirement for a large number of elements. 2D array systems suffer from high system complexity. Micro-beamforming (MBF) method has been proposed to reduce the system complexity; however, distortions of MBF approach such as focusing errors of post-beamforming process results in broadening the main lobe and increasing the side-lobe and grating-lobe levels, which together degrade the image quality. As the pre-steered radio-frequency (RF) data can be estimated from MBF data at the digital back end, better post-beamforming can be performed and higher image quality can be achieved. In this study, a compensation approach is proposed to estimate the pre-steered RF data from MBF data by utilizing additional headers and compensation factors. The compensation factors and headers are estimated at the probe front end and then applied to the back-end digital system to reconstruct the required pre-steered RF data. As the absolute values of the MBF errors are modeled as a single-sided Gaussian distribution, the theoretical mean square error (MSE) with the proposed method is approximately 2.75 times lower than that of its counterpart without compensation; this implies better reconstruction of pre-steered RF data can be achieved with the proposed method. The simulation results showed that the main lobe is improved, and the side-lobe and grating-lobe levels in both the lateral and elevation directions were improved by 11.73 dB and 19.12 dB, respectively, while the peak signal-to-noise ratios improved by 6-9 dB with the proposed method. The contrast-to-noise ratios also are enhanced by 0.5 dB when using the proposed method. Analog circuits are presented to demonstrate that this novel compensation method can be realized in practice. The reduction of cables and analog-to-digital converters (ADCs) are about 7-fold compared to fully-sampled 2D array systems as 4 by 4 channels are grouped for the proposed method as well.

Sidelobe Level and Aperture Efficiency Optimization for Tiled Aperiodic Array Antennas

Array antennas with aperiodic element placement provide a way to mitigate grating lobe level when the array element spacing is larger than one half wavelength. Design techniques for aperiodic arrays include thinning, numerical optimization, and other methods, but even with modern tools, designing electrically large aperiodic arrays remain computationally challenging. To reduce the complexity of the large aperiodic array design problem, we study the use of discrete rotated tiles with element positions and tile orientations optimized to minimize peak sidelobe level (PSLL). The directivity, frequency sensitivity of PSLL, and optimization complexity for uniform arrays, aperiodic arrays, and tiled arrays are compared. Based on many numerical examples, an approximate relationship between PSLL and array element number and density for aperiodic and tiled arrays is proposed as a convergence estimator for the design optimization process.

Dual stage beamforming in the absence of front-end receive focusing

Ultrasound front-end receive designs for miniature, wireless, and/or matrix transducers can be simplified considerably by direct-element summation in receive. In this paper we develop a dual-stage beamforming technique that is able to produce a high-quality image from scanlines that are produced with focused transmit, and simple summation in receive (no delays). We call this non-delayed sequential beamforming (NDSB). In the first stage, low-resolution RF scanlines are formed by simple summation of element signals from a running sub-aperture. In the second stage, delay-and-sum beamforming is performed in which the delays are calculated considering the transmit focal points as virtual sources emitting spherical waves, and the sub-apertures as large unfocused receive elements. The NDSB method is validated with simulations in Field II. For experimental validation, RF channel data were acquired with a commercial research scanner using a 5 MHz linear array, and were subsequently processed offline. For NDSB, good average lateral resolution (0.99 mm) and low grating lobe levels (<−40 dB) were achieved by choosing the transmit as 0.75 and the transmit focus at 15 mm. NDSB was compared with conventional dynamic receive focusing (DRF) and synthetic aperture sequential beamforming (SASB) with their own respective optimal settings. The full width at half maximum of the NDSB point spread function was on average 20% smaller than that of DRF except for at depths <30 mm and 10% larger than SASB considering all the depths. NDSB showed only a minor degradation in contrast-to-noise ratio and contrast ratio compared to DRF and SASB when measured on an anechoic cyst embedded in a tissue-mimicking phantom. In conclusion, using simple receive electronics front-end, NDSB can attain an image quality better than DRF and slightly inferior to SASB.

Numerical evaluation of the effect of electronically steering a phased array transducer: axially post-focal shifting

Purpose: HIFU has been emerging as an effective and safe modality for the treatment of solid tumours and cancers. The focus shifting range of phased array HIFU transducer is an important safety concern because of the presence of grating lobe in the pre-focal region. However, previous studies were only based on linear acoustic wave model.Materials and methods: The nonlinear wave propagation from a 256-element phased array through multiple layered media was simulated using the angular spectrum approach (ASA) in marching fractional steps with the consideration of diffraction, attenuation and non-linearity effects by a second-order operator splitting scheme. The distribution of acoustic intensities, temperature elevations, lesion sizes and grating lobe levels were calculated at various axially post-focal shifting distances and driving frequencies.Results: Axially shifting HIFU focus leads to significant increase of the acoustic intensity at the grating lobe, but decrease at the main lobe. The influences on the acoustic field, thermal field and lesion sizes are determined by the shifting distance and driving frequency, and variations can be fit monotonically and linearly. Prediction accuracies by simple regression models are satisfactory. Irreversible tissue coagulation could be generated by the grating lobe at certain conditions.Conclusions: The established nonlinear wave propagation algorithm allows the accurate description of HIFU field and consequently the evaluation of grating lobe and steerability of focus. The influence of focus shifting may be predicted simply. The treatment planning of phased array HIFU ablation could be optimised by setting the appropriate exposure and focus scanning schemes.

Antipodal Vivaldi Antenna for Sum and Difference Radiation Patterns With Reduced Grating Lobes

A new design of an E -plane double-element Vivaldi antenna with sum and difference radiation patterns is presented in this letter. The antenna operates in the frequency range of 2.3–15 GHz (ratio of 6.5:1) with the highest grating lobe level of $-$ 10 dB at 15 GHz and competitive gain performance from 6.8 dBi at 2.3 GHz up to 14.7 dBi at 15 GHz. The grating lobes are reduced effectively by decreasing the distance between the two input ports to one wavelength at the highest operating frequency. The active S -parameters of the antenna are improved using modifications of the geometry, including a new method consisting of an increased length of the internal flares, as well as combinations of known methods such as elliptical corrugations on the outer edges, and optimal shaping of inner edges of the antenna. The gain is also improved by the addition of a dielectric lens, which also provides extra space for lengthening the internal flares. The proposed double-element antenna satisfactorily provides the sum and difference radiation patterns when fed by a wide band rat-race coupler. To warrant a near-ideal beam symmetry, the antenna is designed so that the directive radiation pattern occurs when the antenna elements are fed by out-of-phase signals, i.e., when the difference ( $\Delta$ ) port of the coupler is excited.