Two-Dimensional Sparse Array Design of Three-Dimensional MIMO Radar Imaging System

In this paper we present the recent advances on the design of sparse arrays using log-periodic antennas for the SKA AA-Mid instrument. The SKA AA-Mid instrument will explore the southern hemisphere sky from ∼400 MHz up to 1.4 GHz with unprecedented sensitivity and survey speed. Large collecting area, low system noise and great survey speed are key to achieve the demanding requirements of the SKA. The University of Cambridge proposes designing this instrument as a collection of stations, each of them being a random sparse array of ultra wideband log-periodic antennas. The advantage of this approach, amongst others, is the increasing collecting area with wavelength (as a square of the wavelength) that sparse arrays offer over dense arrays, and which facilitates the realization of the SKA science goals. We have now advanced our developments to study the system implications of this decision and have started the design of a 16-element prototype array that will be located at the MRAO Observatory at Lords Bridge, Cambridge, UK. This array will help us progress our developments.

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.

Reducing the number of antenna elements within a fixed aperture while maintaining low sidelobe levels is a key challenge in sparse array design. Although various sidelobe suppression techniques exist, most are tailored for large-scale arrays and are not directly applicable to small-scale sparse arrays. This paper addresses a critical gap in array design for small sparse arrays with low sidelobes using mechanical rotation and time-averaging techniques. By continuously rotating the array and time-averaging radiation patterns, the mainlobe remains coherent and stable, while the rapidly varying sidelobes are effectively averaged out and suppressed. An analytical model is developed to determine the required integration time, optimize element placement, mitigate Doppler effects, and enhance time-selective radiation pattern strategies. Experimental validation using a four-element circularly polarized array with 0.74λ spacing demonstrates a PSLL reduction of 11.5 dB compared to a conventional non-rotated array, and can be further reduced by 4.7 dB through time-selected pattern optimization. The proposed method has many potential applications, such as passive remote sensing using rotating UAV swarm arrays, making it a flexible and low-cost solution for precision agriculture and environmental monitoring applications.

This paper presents our study on a sparse antenna array for 0.22 THz imaging. Based on the effective aperture concept for the design of sparse antenna array, two schemes for high performance THz imaging of a target at distance of 1 m have been achieved in simulation. Then, different schemes of larger array element spacing and mechanical scanning spacing have been investigated to build the relationship between their configurations and imaging performance. Based on the study, it is predicted theoretically and from the reconstructed images that only 16 transmitting and 16 receiving antennas will be sufficient to scan a 2.0 m * 0.8 m target. And the spatial resolution of 4.44 mm at 5 m is potentially achieved. Therefore, this study will provide a valuable guideline for the following sparse array design in a high performance THz imaging system.

Sparse arrays are of great interest since they can identify O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) uncorrelated sources with N physical sensors. This stems from their large difference coarray, defined as the differences between sensor locations. In a recent study, desired array properties such as closed-form expression for sensor locations, symmetry and large hole-free difference coarray were considered and it was shown that most existing sparse arrays do not exhibit these characteristics simultaneously. Standard Cantor arrays were shown to satisfy all the criteria above, however, their difference coarrays are of size O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">log2 3</sup> ) which is smaller than that obtained with minimum redundancy arrays and nested arrays. In this paper, we introduce a fractal array design where a generator array is extended in a simple recursive fashion. In contrast to previous work, the generator is assumed to be a sparse array with a hole-free difference coarray. We study the resulting arrays and prove they inherit their properties from the generator. Thus, this approach can be used to extend any known sparse configuration to an arbitrarily large array. A small-scale array, which meets all design criteria, can be created and then expanded to generate a symmetric fractal array with a difference coarray of size O(N2), unlike Cantor arrays.

We present novel generalized non-redundant sparse array design strategies that achieve the highest possible number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation. These array designs offer difference co-arrays that do not contain any lag redundancies except the unavoidable redundancies at lag zero. We first develop a co-array-based zero-redundancy design rule which serves as a baseline for constructing these non-redundant arrays, and a large-aperture naïve structured non-redundant sparse array is presented. We then develop a systematized design framework based on disjunctive programming to obtain non-redundant sparse array structures with a minimum array aperture, resulting in minimum hole arrays. The disjunctive programming framework is then extended to an equivalent mixed-integer linear programming problem. As a result, given the same number of physical sensors, the design framework provides a difference co-array with the maximum number of correlation lags and resolves more sources than existing sparse array structures. The non-redundant sparse array design is further generalized in two new directions, respectively achieving an arbitrary array aperture and reducing mutual coupling effects. Among the several new sparse array designs obtained from such generalizations, the hybrid non-redundant sparse array design simultaneously achieves the highest number of DOFs, meets a desired array aperture requirement, and reduces mutual coupling effects. Structured matrix completion methods are employed to interpolate the missing lags in the resulting difference co-arrays, thereby enabling high-resolution gridless DOA estimation with improved performance. Simulation results demonstrate the superiority of the generalized non-redundant sparse array design strategies over existing sparse array structures

To address the issue of traditional Particle Swarm Optimization (PSO) being prone to local optima and insufficient global search capability in sparse phased array optimization, a hybrid optimization algorithm integrating PSO with a Genetic Algorithm (GA) is proposed. Within the PSO framework, the proposed algorithm incorporates the adaptive crossover and mutation operations of the GA to enhance population diversity. It combines an adaptive weighting factor and a constriction factor to balance global exploration and local exploitation capabilities. Furthermore, a density-weighted method is employed to generate a high-quality initial population, thereby accelerating convergence. The proposed algorithm is applied to an 8 × 8 planar sparse array. On the E-plane (φ = 0°) and H-plane (φ = 90°), simulation results indicate that the achieved normalized maximum sidelobe level is −23.14 dB, which is significantly superior to those obtained by standalone PSO and GA. Based on these simulation results, microstrip patch antennas are introduced for array constitution and analysis. Full-wave electromagnetic simulation proves that the proposed sparse array has the ability of wide-angle scanning and low sidelobe. Our work demonstrates that the PSO-GA hybrid algorithm effectively enhances search capability and convergence performance, providing a reliable solution for sparse array design.

Irregular microphone array design for broadband beamforming

The design of sparse antenna arrays is realized by a novel and effective method based on convex programming in this paper. By the use of synthesis model in terms of thinned arrays, a novel binary quadratic optimization problem is established for design of sparse array, where the required antenna element number satisfying user-defined constraints (peak sidelobes and directivity) is fully minimized. To reduce computational cost, an effective optimization approach combining the reweighted <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{1}$</tex> -norm minimization with the element location expansion and contraction is proposed. By comparing to fully populated half-wavelength arrays, a numerical example is presented to assess the advantages of the described approach.

An effective sparse array synthesis approach based on recently introduced compressed sensing theory has been proposed and applied to the design of pencil beams with the minimum number of sensors.

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.

Sparse arrays are popular in sonar, ultrasonic imaging and other acoustic equipment. For inter-element spacing larger than one wave length, there will be grate lobes for ordinary sparse array and may course ghost image for acoustic imaging and severe interference for underwater object detection. For some other applications of sparse array in which the reverberation suppression is crucial, the lower the side lobes of the array directivity pattern, the better the equipment performance, and then the low side lobe for the array directivity pattern is one of the main objects to be achieved for this kind of acoustic equipment. Using genetic algorithm to optimize the design of sparse array with randomly spaced elements to suppress the grate lobes/side lobes is introduced in this paper. Fitness function design and variable choosing method for genetic algorithms used in these kinds of application are presented.

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

This paper presents an improved snake optimization (ISO) algorithm for the beamforming design of sparse conformal arrays. To reduce the array element number and achieve the best sparse array configuration, the ISO algorithm employs the Sobol sequences for population initialization, resulting in enhanced uniformity and comprehensive coverage of the solution space as compared with the conventional random initialization method. Besides, the ISO algorithm employs the Cauchy mutation operator to escape local optimization and suppress the sidelobe levels of the conformal array. To increase array sparseness and optimize the radiation patterns, the ISO algorithm is further equipped with a nonlinear time-varying factor inspired by the whale algorithm and a modified flag control function, which improve its capacity for global exploration and local development. Simulation verification of a sparse cylindrically conformal array has demonstrated the superior performance of the proposed ISO algorithm over conventional optimization algorithms. It achieves a 50% array sparsity, and lower sidelobe levels as compared with the genetic algorithm (GA), particle swarm optimizer and traditional snake optimizer (SO). Moreover, it features notably faster convergence rates, outpacing the SO by 10% and GA by 46%, respectively. In addition, the sparse conformal array exhibits good radiation characteristics over a relatively wide beam scanning range of 54° in the azimuthal plane and 90° in the elevation plane, respectively.

The design of a sparse conformal phased array with elements located on a truncated cone shape is addressed. The antenna, supposed to be a fully-digital receiver of an air traffic control system, has to simultaneously generate multiple receiving beams along the elevation plane in order to cover a desired angular region. The synthesis problem is carried out by means of the Multi-Task Bayesian Compressive Sensing (MT-BCS) in order to define the positions of the array elements and the set of complex excitations for each individual beam. A preliminary numerical result is reported to validate the effectiveness of the proposed method.