Design of Ultrasonic Synthetic Aperture Imaging Systems Based on a Non-Grid 2D Sparse Array

This work provides a guide to design ultrasonic synthetic aperture systems for non-grid two-dimensional sparse arrays such as spirals or annular segmented arrays. It presents an algorithm that identifies which elements have a more significant impact on the beampattern characteristics and uses this information to reduce the number of signals, the number of emitters and the number of parallel receiver channels involved in the beamforming process. Consequently, we can optimise the 3D synthetic aperture ultrasonic imaging system for a specific sparse array, reducing the computational cost, the hardware requirements and the system complexity. Simulations using a Fermat spiral array and experimental data based on an annular segmented array with 64 elements are used to assess this algorithm.

Low Discrepancy Sparse Phased Array Antennas

Sparse arrays have grating lobes in the far field pattern due to the large spacing of elements residing in a rectangular or triangular grid. Random element spacing removes the grating lobes but produces large variations in element density across the aperture. In fact, some areas are so dense that the elements overlap. This paper introduces a low discrepancy sequence (LDS) for generating the element locations in sparse planar arrays without grating lobes. This nonrandom alternative finds an element layout that reduces the grating lobes while keeping the elements far enough apart for practical construction. Our studies consider uniform sparse LDS arrays with 86% less elements than a fully populated array, and numerical results are presented that show these sampling techniques are capable of completely removing the grating lobes of sparse arrays. We present the mathematical formulation for implementing an LDS generated element lattice for sparse planar arrays, and present numerical results on their performance. Multiple array configurations are studied, and we show that these LDS techniques are not impacted by the type/shape of the planar array. Moreover, in comparison between the LDS techniques, we show that the Poisson disk sampling technique outperforms all other approaches and is the recommended LDS technique for sparse arrays.

Compilation of sparse array programming models

This paper shows how to compile sparse array programming languages. A sparse array programming language is an array programming language that supports element-wise application, reduction, and broadcasting of arbitrary functions over dense and sparse arrays with any fill value. Such a language has great expressive power and can express sparse and dense linear and tensor algebra, functions over images, exclusion and inclusion filters, and even graph algorithms. Our compiler strategy generalizes prior work in the literature on sparse tensor algebra compilation to support any function applied to sparse arrays, instead of only addition and multiplication. To achieve this, we generalize the notion of sparse iteration spaces beyond intersections and unions. These iteration spaces are automatically derived by considering how algebraic properties annotated onto functions interact with the fill values of the arrays. We then show how to compile these iteration spaces to efficient code. When compared with two widely-used Python sparse array packages, our evaluation shows that we generate built-in sparse array library features with a performance of 1.4× to 53.7× when measured against PyData/Sparse for user-defined functions and between 0.98× and 5.53× when measured against SciPy/Sparse for sparse array slicing. Our technique outperforms PyData/Sparse by 6.58× to 70.3×, and (where applicable) performs between 0.96× and 28.9× that of a dense NumPy implementation, on end-to-end sparse array applications. We also implement graph linear algebra kernels in our system with a performance of between 0.56× and 3.50× compared to that of the hand-optimized SuiteSparse:GraphBLAS library.

DOA Estimation of an Enhanced Generalized Nested Array with Increased Degrees of Freedom and Reduced Mutual Coupling

Aiming at low degrees of freedom (DOF) and high mutual coupling (MC) of the existing sparse arrays, an enhanced generalized nested array (EGNA) is proposed in this paper. Specifically, the proposed array adds a single antenna on the basis of generalized nested array (GNA), and the difference of coprime factors is employed as the spacing between the second subarray and the additional antenna. Then, the values of the coprime factors are analyzed in detail, which indicates that Yang-NA can be explained as a special case. Compared with the majority of the existing sparse arrays, EGNA not only has the closed-form expressions of the physical antenna locations, consecutive lags, and unique lags, but also significantly increases DOF and reduces MC. In view of the above advantages, EGNA can obtain superior performance in direction of arrival (DOA) estimation. Numerical simulation results verify the rationality and superiority of the proposed nested array.

Minimal Redundancy Linear Array and Uniform Linear Arrays Beamforming Applications in 5G Smart Devices

Minimum Redundancy Linear Arrays (MRLAs) and Uniform Linear Arrays (ULAs) investigation conducted with the possibility of using them in future 5G smart devices. MRLAs are designed to minimize the number of sensor pairs with the same spatially correlated delay. It eliminates selected antennas from the entire composite antenna array and preserves all possible antenna spacing. MRLAs have attractive features for linear sparse arrays, even if the built-in surface is deformed, it works without problems. To our knowledge, MRLAs have not been applied to smart devices so far. In this work, a 7-element ULAs and 4-element MRLAs (same aperture) were used for the simulation. The Half Power Beamwidth (HPBW) is 0.666 and the Null-to-Null Beamwidth ( ) is 1.385 in ψ-space. In comparison, the standard 4-element arrays are 1.429 and 3.1416, while the standard 7-element linear arrays are 0.801 and 1.795 respectively. Experimental results show that 4-element MLRAs have a narrower mean beam, much higher sidelobes and shallow nulls. Therefore, in terms of main lobe features, 4- elements MRLAs have an improvement over the standard 7-element ULAs. Doi: 10.28991/esj-2021-SP1-05 Full Text: PDF

The Analysis of Using Spatial Smoothing for DOA Estimation of Coherent Signals in Sparse Arrays

When there is coexistence of uncorrelated and coherent signals in sparse arrays, the conventional algorithms for direction-of-arrival (DOA) estimation using difference coarray fail. In order to solve the problems, this paper analyzes the feasibility of using spatial smoothing in sparse arrays. Firstly, we summarize the two types of sparse arrays, one consisting of identical sparse subarrays and the other consisting of several uniform linear subarrays. Then, we give the feasibility analysis and the processes of applying spatial smoothing. At last, we discuss the performance of the number of detectable coherent signals in different sparse arrays. Numerical experiments prove the conclusions proposed by the paper.