Nonuniformly Spaced Arrays Research Articles

A Portable K-Band 3-D MIMO Radar With Nonuniformly Spaced Array for Short-Range Localization

This paper presents a $K$ -band multiple-input-multiple-output (MIMO) radar for short-range localization. This radar features 3-D imaging capability, which can obtain the range, azimuth angle, and zenith angle of a target. The proposed radar system implements the concept of MIMO to synthesize a planar array that realizes 2-D digital beamforming with a small number of transmitter and receiver (T/R) channels. A nonuniformly spaced array configuration is also designed to further reduce the number of T/R channels without sacrificing the beamwidth and sidelobe level. The design principle is detailed in this paper. A prototype with eight transmitter channels and eight receiver channels has been built. A calibration procedure was developed to remove path delays of different MIMO channels. Experiments of the proposed ${K}$ -band MIMO radar prototype reveal its capability in the 3-D localization of multiple targets. This prototype features 7.2° 2-D angular resolution, 90° field of view, −10-dB sidelobe level, and wireless data transfer.

Angular Resolution Enhancement Provided by Nonuniformly-Spaced Linear Hydrophone Arrays in Ocean Acoustic Waveguide Remote Sensing

Uniformly-spaced apertures or subapertures of large, densely-sampled, discrete linear receiver arrays are often used in remote sensing to increase the signal-to-noise ratio (SNR) by coherent beamforming that reduces noise coming from directions outside the signal beam. To avoid spatial aliasing or the presence of grating lobes in real spatial directions, the uniformly-spaced array inter-element spacing d sets a limit on the maximum frequency f max < c / 2 d of signals suitable for beamforming with the array, where c is the medium’s wave propagation speed. Here, we show that a nonuniformly-spaced array, for instance, formed by combining multiple uniformly-spaced subapertures of a nested linear array, can significantly enhance the array angular resolution while simultaneously avoiding dominant grating lobes in real angular space, even for signals with frequencies beyond the maximum that the array is designed for. The array gain, beam width, and maximum grating lobe height are quantified for the Office of Naval Research Five Octave Research Array (ONR-FORA) for various combinations of its uniformly-spaced subapertures, leading to nonuniformly-spaced subarrays. Illustrative examples show angular resolution enhancement provided by the nonuniformly-spaced ONR-FORA subarrays over that of its uniformly-spaced individual subaperture counterparts in both active and passive ocean acoustic waveguide remote sensing, drawn from measurements in the Gulf of Maine 2006 Experiment.

Enhancing angular resolution by coherent beamforming of full non-uniformly spaced linear hydrophone array

Uniformly-spaced apertures or subapertures of discrete linear receiver arrays are often used in remote sensing to increase signal-to-noise ratio (SNR) by coherent beamforming which reduces noise coming from directions outside the signal beam. To avoid grating lobes in real spatial directions, the uniformly-spaced array inter-element spacing d determines the maximum or cut-off frequency f<c/2d of signals suitable for beamforming with the array, where c is the wave speed. Here we show that a non-uniformly spaced array, for instance formed by combining multiple uniformly-spaced subapertures of a nested linear array, can significantly improve the angular resolution while simultaneously avoiding dominant grating lobes in real angular space, even for signals with frequencies beyond the cut-off. The array gain, beamwidth, and maximum grating lobe height are calculated for the ONR Five Octave Research Array (FORA) for various combinations of its uniformly-spaced subapertures, including the full non-uniformly spaced array. Examples are provided of angular resolution enhancement with resulting non-uniformly spaced array or subarray in both active and passive ocean acoustic waveguide remote sensing over that of the uniformly spaced counterpart, including continental-shelf scale imagery of fish populations, and marine mammal vocalization SNR enhancement which improves detection and bearing-time estimation for passive localization.

Synthesis of non-uniformly spaced circular antenna arrays using a data-driven probabilistic model

Synthesis of non-uniformly spaced circular antenna arrays using a data-driven probabilistic model

Near-Chebyshev Pattern for Nonuniformly Spaced Arrays Using Zeros Matching Method

An analytic method is presented to design nonuniformly spaced uniform amplitude antenna arrays (NSUAAs) to have near-Chebyshev radiation pattern. In this method, called zeros matching method (ZMM), the zeros of array factors of NSUAAs are matched with the zeros of the exact-Chebyshev pattern. Some examples are brought to verify the effectiveness of the ZMM approach for both linear and planar NSUAAs.

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

This paper describes a method using Quantum Particle Swarm Optimization to obtain a broadband frequency invariant pattern for synthesis of nonuniformly spaced linear array of isotropic antennas. Two cases related to this work using QPSO have been studied, namely, in the first case, the generated frequency invariant far-field pattern is broadside in the vertical plane and in the second case, the far-field frequency invariant pattern is scanned in a particular direction. An effort is made such that the side lobe level and first null beam widths of the patterns are made similar to their related desired values. The two cases are presented in this paper to show the effectiveness of the proposed method in achieving the desired specifications. Even though, the developed method is utilized here for a linear array of isotropic antennas; it can be extended to other type of arrays.

PEEC-Based Multi-Objective Synthesis of Non-Uniformly Spaced Linear Antenna Arrays

Linear antenna arrays consisting of dipole antennas find wide applications in wireless communication systems. Typically, arrangements with uniform spacing between the array elements are applied to gain highly directive radiation patterns. In the present paper an antenna array arrangement with non-uniformly spacing between the array elements is synthesized in the multi-objective sense. The optimization relies on the firefly algorithm and the PEEC method.

Structured Non-Uniformly Spaced Rectangular Antenna Array Design for FD-MIMO Systems

Full-dimensional multiple-input multiple-output (FD-MIMO) systems, whereby each base station is equipped with a uniformly spaced rectangular antenna array (URA), provides a practical means of realizing massive MIMO systems. However, the spectral efficiency of URA is considerably lower than that of its uniformly spaced linear array counterpart having the same number of antenna elements. In this paper, we first introduce a discrete angular resolution metric for quantifying the low resolution of URA in the antenna-elevation domain. This motivates us to propose a novel antenna device design, referred to as the structured non-uniformly spaced rectangular array (NURA), in which the antenna elements are non-uniformly distributed in the elevation-angle domain. Specifically, we conceive a structured NURA device for which the nonuniform distribution of the elevation-domain antenna elements is controlled by a single parameter. The design of the optimally structured NURA for the given nonlinear antenna-element-positioning function then becomes a single-parameter optimization, namely, that of maximizing the spectral efficiency of the FD-MIMO system, which can be solved efficiently. Our simulation results demonstrate that our structured NURA design significantly outperforms the standard URA in terms of achievable spectral efficiency. Our proposed structured NURA design therefore offers an effective practical framework for enhancing the achievable performance of FD-MIMO systems.

A Novel Nonuniform Fast Fourier Transform Algorithm and Its Application to Aperiodic Arrays

A simple and effective nonuniform fast Fourier transform algorithm is presented. The algorithm is based on the interpolation of the exponential function in the Fourier transform using efficient truncated expansion algorithms for band-limited functions. Examples regarding the far-field evaluation of nonuniformly spaced antenna arrays are provided, and the behavior of the approximation error is analyzed, to confirm the effectiveness of the method.

A Double-Layer Shaped-Beam Traveling-Wave Slot Array Based on SIW

A double-layer shaped-beam traveling-wave slot array based on substrate integrated waveguide (SIW) at $X$ -band is presented. The double-layer SIW longitudinal slot-coupled cavity slot is proposed as the array element, which has an improved bandwidth performance due to the double-resonant feature. By using this kind of slots, a planar nonuniformly spaced shaped-beam traveling-wave array is constructed. To achieve the desired distribution for the shaped-beam pattern, an efficient optimization method, with the mutual coupling effect being considered, is proposed to optimize the array structure parameters. Experimental results show that the array achieves good shaped-beam pattern in a 4.8% frequency band and low-loss characteristic.

Classification and optimization of beam responses synthesized from non-uniformly spaced linear arrays

A probability distribution for the element positions on a linear array is derived so as to match a target beam pattern that approximates a Dolph-Chebychev array. The random beam responses generated from such a configuration exhibit a mean profile in observation angle that is invariant with element size N but the variance decays as 1/N. The beam responses are classified considering the N-1 inter-element distances as features that control the deviation from the mean beam profile and the variance of the class. The inter-element distance constraints are incorporated in a computational model of the firefly algorithm (FA) designed to optimize the location of the array elements that match the target beam pattern. The FA consists of a set of fireflies, representing arrays, which move through the solution space with directed movement based on each fireflies' fitness and random movement to ensure adequate exploration and avoid local minima. The fitness function is a combination of a target beam-width, side-lobe lev...

A sparse recovery technique for the turbulent boundary layer wavenumber-frequency spectrum with non-uniformly spaced array of pressure transducers

Historically, determination of wavenumber-frequency spectra of turbulent wall pressure fluctuations has employed the use of evenly spaced linear arrays of sensors. The reason for this is that even spacing of pressure samples in both the temporal and spatial domains facilitates analysis by direct application of 2-D Fourier transforms. The spacing of pressure measurements directly impacts the resolution of the resulting wavenumber-frequency spectra. This rigid spacing requirements of traditional methods may preclude analysis altogether with even a single sensor failure within the array. Rather than determining sensor locations based on the simplest analysis method, the sparseness of the wavenumber-frequency spectra can be leveraged to allow non-uniform sampling in both temporal and spatial domains. Sparse recovery techniques as an analysis tool for wavenumber-frequency spectra will be demonstrated both theoretically and experimentally for uniformly spaced arrays, uniformly spaced arrays with missing measure...

Synthesis of Nonuniformly Spaced Linear Arrays With Frequency-Invariant Patterns by the Generalized Matrix Pencil Methods

This work extends the matrix pencil method (MPM)-based synthesis technique to the case of nonuniformly spaced linear arrays with wideband frequency-invariant (FI) patterns. A new sampling strategy is proposed to obtain multiple pattern data of different frequencies having the same poles that correspond to the FI element positions. The obtained multiple pattern sequences have the same shape for the FI pattern requirement, but with different lengths. The generalized MPM (GMPM) and its forward-backward version (GFBMPM) are developed to estimate the best common element positions for different frequencies, which can significantly reduce the number of elements required for the specified wideband pattern shape. The element excitations are solved by the regularized least-square (LS) method at each frequency. Then, an efficient method by utilizing the FFT is presented to obtain real-coefficient finite-impulse-response (FIR) filters for implementing the frequency-varying excitations. A set of numerical examples for the FI synthesis of pencil-beams, shaped patterns, scannable patterns, and Taylor patterns with low SLLs are presented to validate the effectiveness and advantages of the proposed methods. The element saving is about 11.2%-49.4% for usual cases.

Synthesis of linearly polarised patterns of conical arrays by the method of least square

Method of least squares is employed for pattern synthesis of non-uniform conical arrays using Euler rotation of coordinate axes. Design specifications involve beam-width of main-lobe, side-lobe and cross-polarisation levels. This method is effective for conformal arrays, because pattern multiplication is not applicable for them. Constructed error function depends on element spacing and current excitations (amplitudes and phases of input currents). Combination of conjugate gradient and genetic algorithms is used for its miniaturisation to determine element spacing and excitations. Recent literature on non-uniform arrays mostly deals with non-uniform excitations with complicated input networks. The non-uniformly spaced arrays will realise any specification obtained by non-uniform excitations. Two examples of non-uniform current excitations are presented. First example leads to reduction of side-lobe level (SLL) from 12 to 20 dB. Second example deals with different upper and lower SLLs. Third example treats non-uniform spacing, which results in the reduction of SLL from 12 to 18 dB. Fourth example synthesises both non-uniform spacing and unequal excitations, which provides the SLL reduction from 12 to 25 dB, besides the reduction of cross-polarisation level from 12 to 25 dB, compared with Qing- Qjang et al. 2011, which decreased SLL by only 8 dB.

Thinned Array Beampattern Synthesis by Iterative Soft-Thresholding-Based Optimization Algorithms

In this paper, we cast thinned array beampattern synthesis as a linear inverse problem (LIP) and apply three iterative soft-thresholding based optimization algorithms to solve it effectively. We combine synthesis algorithms with beampattern error reweighting and beampattern phase adjustment to achieve accurate approximation of the desired reference pattern. The proposed methods can be used to synthesize arbitrarily shaped beam-patterns, including multibeam forming and radiation suppression within several angular regions. These methods offer a number of advantages in regard to array scale, beampattern specifics and computational time compared to existing methods. Since this paper focuses on synthesizing receiver arrays, there are no explicit constraints applied to the excitation weights. Numerical results demonstrate the efficiency of three proposed approaches for designing non-uniformly spaced arrays. In particular, the fast iterative soft-thresholding algorithm can synthesize of up to a few hundred antennas.

Optimization of Linear Dipole Antenna Array for Sidelobe Reduction and Improved Directivity using APSO algorithm

Design of non-uniformly spaced linear array of dipoles is presented. Array synthesis is done by controlling the appropriate excitation amplitudes and element spacing to get the radiation patterns with reduced sidelobe level (SLL) and improved beam width. The objective of this work is to generate synthesized patterns with low sidelobe level and to compensate the coupling effect with a low prefixed dynamic range ratio for non-uniformly spaced array. The excitation amplitude distribution and position of individual array elements are determined. The patterns of dipole elements are compared with those of the isotropic elements. Numerical results show the effectiveness of the algorithm for the design of the linear array.

Pattern Synthesis of Nonuniformly Spaced Arrays Based on Unit Circle Representation and Taguchi Method

Unit circle representation techniques such as Schelkunoff null placement method have been extensively used to synthesize uniformly spaced linear arrays. In this work, it is attempted to extend the unit circle representation approach to synthesize nonuniformly spaced linear arrays with some desired null directions and minimum achievable sidelobe level. The problem is formulated as an optimization task upon which Taguchi method is employed to solve for the set of element positions. Illustrative examples are included to demonstrate the design effectiveness and flexibility for modern wireless communication system applications.

A SHAPED-BEAM SERIES-FED APERTURE-COUPLED STACKED PATCH ARRAY ANTENNA

A shaped-beam series-fed aperture-coupled stacked patch array antenna at X-band is presented. To improve the array bandwidth, two-port aperture-coupled stacked patch antennas, which are suitable for the series-fed array conflguration, are presented as the radiating elements. To ofier the pattern design and optimization progresses more ∞exibility, a uniformly spaced array conflguration is applied in the shaped-beam pattern design, instead of the conventional nonuniformly spaced array conflguration. The experimental results show that, in a 7.6% bandwidth, the main beam shape of the array maintains in good agreement with the design goal, and the side lobe level maintains lower than i18dB.

Nonuniformly Spaced Linear Antenna Array Design Using Firefly Algorithm

A nonuniformly spaced linear antenna array with broadside radiation characteristics is synthesized using firefly algorithm and particle swarm optimization. The objective of the work is to find the optimum spacing between the radiating antenna elements which will create a predefined arbitrary radiation pattern. The excitation amplitudes of all the antenna elements are assumed to be constant. The optimum spacing between the array elements are obtained using firefly algorithm. The minimum allowed distance between the antenna elements is defined in such a way that mutual coupling between the elements can be ignored. Numerical analysis is performed to calculate the far-field radiation characteristics of the array. Two numerical examples are shown to form two different desired predefined radiation patterns. The performance of the firefly algorithm and particle swarm optimization is compared in terms of convergence rate and global best solution achieved. The performances of the optimized nonuniformly spaced arrays are analyzed. Finally, contour plots of the radiated power from the optimized array in the horizontal plane and vertical plane in the far-field region are provided.

Sum, Difference and Shaped Beam Pattern Synthesis by Non-Uniform Spacing and Phase Control

A design procedure for the synthesis of non-uniformly spaced linear arrays is presented, which uses the Poisson sum expansion of the array factor introduced in the literature. By considering the nonzero phase term in the existent formula and using the appropriate line source pattern synthesis methods, a general design procedure is obtained to synthesize any type of pattern, such as sum, difference and shaped beams. This approach converts the nonlinear complex problem of pattern synthesis for non-uniformly spaced linear arrays to a simple problem, which makes it fast and easy to implement. Moreover, an extra optimization process is added to the synthesis procedure to improve final pattern and provide control on computed parameters.