Non-uniform Linear Array Research Articles

Multiple Invariance ESPRIT for Nonuniform Linear Arrays: A Coupled Canonical Polyadic Decomposition Approach

The Canonical Polyadic Decomposition (CPD) of higher-order tensors has proven to be an important tool for array processing. CPD approaches have so far assumed regular array geometries such as uniform linear arrays. However, in the case of sparse arrays such as nonuniform linear arrays (NLAs), the CPD approach is not suitable anymore. Using the coupled CPD we propose in this paper a multiple invariance ESPRIT method for both one- and multi-dimensional NLA processing. We obtain a multiresolution ESPRIT method for sparse arrays with multiple baselines. The coupled CPD framework also yields a new uniqueness condition that is relaxed compared with the CPD approach. It also leads to an eigenvalue decomposition based algorithm that is guaranteed to reduce the multi-source NLA problem into decoupled single-source NLA problems in the noiseless case. Finally, we present a new polynomial rooting procedure for the latter problem, which again is guaranteed to find the solution in the noiseless case. In the presence of noise, the algebraic algorithm provides an inexpensive initialization for optimization-based methods.

Suboptimal aperture radar imaging by combination of pseudo‐polar formatting and gridless sparse recovery method

Imaging radar with a suboptimal aperture length usually has a poor azimuth resolution due to the limited aperture length and sparse non-uniform linear array configuration. To address this problem, an imaging algorithm combining pseudo-polar formatting and gridless sparse recovery method is proposed. After pseudo-polar formatting the echo signal, reweighted atomic norm minimisation is implemented for azimuth imaging to achieve performance with improved resolution and free of off-grid effect. Experiments on ground-based synthetic aperture radar verify the performance of the proposed algorithm.

채널 기반에서 객체 기반의 오디오 콘텐츠로의 변환을 위한 비균등 선형 마이크로폰 어레이 기반의 음원분리 방법

채널 기반에서 객체 기반의 오디오 콘텐츠로의 변환을 위한 비균등 선형 마이크로폰 어레이 기반의 음원분리 방법

Optimum design of non-uniform symmetrical linear antenna arrays using a novel modified invasive weeds optimization

Abstract This paper presents a new modified method for the synthesis of non-uniform linear antenna arrays. Based on the recently developed invasive weeds optimization technique (IWO), the modified invasive weeds optimization method (MIWO) uses the mutation process for the calculation of standard deviation (SD). Since the good choice of SD is particularly important in such algorithm, MIWO uses new values of this parameter to optimize the spacing between the array elements, which can improve the overall efficiency of the classical IWO method in terms of side lobe level (SLL) suppression and nulls control. Numerical examples are presented and compared to the existing array designs found in the literature, such as ant colony optimization (ACO), particle swarm optimization (PSO), and comprehensive learning PSO (CLPSO). Results show that MIWO method can be a good alternative in the design of non-uniform linear antenna array.

An Expanded Trilinear Model-Based Angle Estimation Algorithm for MIMO Radar with Small Number of Transmit/Receive Antennas

In this paper, we address the problem of angle estimation in a bistatic multiple-input multiple-output (MIMO) radar which exploits nonuniform linear array at both the transmitter and the receiver with small number of antennas. It is demonstrated that the conventional trilinear decomposition-based angle estimation algorithm can identify only a comparatively small number of targets under this condition. In order to increase the number of identifiable targets, we derive an expanded trilinear decomposition-based angle estimation algorithm for MIMO radar, which can expand the size of the trilinear model. The proposed algorithm not only has the advantages of not requiring spectral peak searching, nor additional pair matching and being suitable for nonuniform arrays, but also identifies more targets than the conventional trilinear decomposition-based angle estimation algorithm under the same conditions. Moreover, the angle estimation performance of the proposed algorithm is better than that of the conventional trilinear decomposition-based angle estimation algorithm and the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. Simulation results illustrate the effectiveness and improvement of the proposed algorithm.

Iterative GA Optimization Scheme for Synthesis of Radiation Pattern of Linear Array Antenna

This research has proposed the iterative genetic algorithm (GA) optimization scheme to synthesize the radiation pattern of an aperiodic (nonuniform) linear array antenna. The aim of the iterative optimization is to achieve a radiation pattern with a side lobe level (SLL) of ≤−20 dB. In the optimization, the proposed scheme iteratively optimizes the array range (spacing) and the number of array elements, whereby the array element with the lowest absolute complex weight coefficient is first removed and then the second lowest and so on. The removal (the element reduction) is terminated once the SLL is greater than −20 dB (>−20 dB) and the elemental increment mechanism is triggered. The results indicate that the proposed iterative GA optimization scheme is applicable to the nonuniform linear array antenna and also is capable of synthesizing the radiation pattern with SLL ≤ −20 dB.

Peak‐to‐peak search: fast and accurate DOA estimation method for arbitrary non‐uniform linear array

A peak-to-peak (P-to-P) search-based single source direction of arrival estimation is proposed. The P-to-P method aims to search only at each local minima of a least square cost function, thus quickly acquiring the global optimal solution relative to exhaustive grid search. Performance comparisons with existing methods verify that the proposed method achieves high accuracy, possesses low signal-to-noise ratio threshold and computational cost and can be applicable to any non-uniform linear array.

Pattern synthesis of sparse linear array by off‐grid Bayesian compressive sampling

An off-grid (OG) pattern synthesis algorithm for sparse non-uniform linear arrays is presented. It is based on Bayesian compressive sampling (BCS), and the design of maximally sparse linear arrays for the given reference patterns can be obtained. The proposed algorithm novelly introduces the OG model into the pattern synthesis problem, and it makes the synthesis more accurate than the conventional BCS algorithm. Moreover, the proposed algorithm has the advantage of high computational efficiency, since the BCS-based algorithms can be realised by the fast relevance vector machine. Numerical experiments show that the proposed algorithm has improved accuracy in terms of normalised mean square error.

Calibrating Nested Sensor Arrays With Model Errors

We consider the problem of direction of arrival (DOA) estimation based on a nonuniform linear nested array, which is known to provide $O(N^2)$ degrees of freedom (DOFs) using only $N$ sensors. Both subspace-based and sparsity-based algorithms require certain modeling assumptions, e.g., exactly known array geometry, including sensor gain and phase. In practice, however, the actual sensor gain and phase are often perturbed from their nominal values, which disrupts the existing DOA estimation algorithms. In this paper, we investigate the self-calibration problem for perturbed nested arrays, proposing corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares (STLS) is used to deal with the phase error issue. In addition, we provide the Cramer-Rao bound (CRB) to analyze the robustness of the estimation performance of the proposed approaches. Furthermore, we extend the calibration strategies to general nonuniform linear arrays. Numerical examples are provided to verify the effectiveness of the proposed strategies.

Truncated SVD-Based Compressive Sensing for Downward-Looking Three-Dimensional SAR Imaging With Uniform/Nonuniform Linear Array

For downward-looking linear array 3-D synthetic aperture radar, the resolution in cross-track direction is much lower than the ones in range and azimuth. Hence, superresolution reconstruction algorithms are desired. Since the cross-track signal to be reconstructed is sparse in the object domain, compressive sensing algorithm has been used. However, the imaging processing on the 3-D scene brings large computational loads, which renders challenges in both data acquisition and processing. To cover this shortage, truncated singular value decomposition is utilized to reconstruct a reduced-redundancy spatial measurement matrix. The proposed algorithm provides advantages in terms of computational time while maintaining the quality of the scene reconstructions. Moreover, our results on uniform linear array are generally applicable to sparse nonuniform linear array. Superresolution properties and reconstruction accuracies are demonstrated using simulations under the noise and clutter scenarios.

안테나 간격 및 배열에 따른 위상 비교 모노펄스 알고리즘의 성능 분석

모노 펄스 레이더는 단일 송신 신호를 이용해 목표물의 위치를 예측해 내는 레이더이다. 본 논문은 9.41GHz의 X밴드 대역 주파수를 이용하여 해양 환경에서 선박용 레이더에 사용 될 각도 추정 기술로써 위상 비교 모노펄스 알고리즘에 대한 연구를 수행하였다. 또한, 위상 비교 모노펄스 알고리즘을 이용하여 안테나 간격과 타겟의 위치에 따른 평균 제곱근 오차를 계산해 보았다. 이를 이용하여 선형 배열 안테나를 사용할 때와 비선형 배열 안테나를 사용할 때의 위상 비교 모노펄스 알고리즘 성능을 비교 하였다. 마지막으로 본 논문에서 제안한 위상 비교 모노펄스 알고리즘과 MUSIC, BARTLETT 알고리즘의 성능 차이를 분석해 보았다. Monopulse RADAR is the radar which detects the range of the target using a single transmitted signal. In this paper, using 9.41GHz X-band radar, the research for the phase comparison monopulse algorithm used in the marine environment is conducted. In addition, by applying the phase comparison monopulse algorithm, we calculate the RMSE for the various antenna spacings and the positions of the target. Based on that result, we compare the performance of the phase comparison monopulse algorithm in the uniform linear array with that in the non-uniform linear array. Finally, the differences in performance among the MUSIC algorithm, Bartlett method and the proposed phase comparison monopulse algorithm are analyzed.

Study of nonuniform linear differential microphone arrays with the minimum-norm filter

The performance of differential microphone arrays (DMAs) depends on many factors such as the number of sensors and the array geometry. This paper develops an approach that exploits nonuniform linear geometries and the minimum-norm filter to improve the robustness of DMAs against white noise. Unlike the conventional way that forms an Nth-order DMA by subtractively combining the outputs of two DMAs of order N-1, this approach works in the short-time Fourier transform (STFT) domain and applies a complex weight to the output of each sensor and then sum the weighted outputs to form the beamforming output in every STFT subband. The minimum-norm filter is obtained by maximizing the white noise gain of the beamformer subject to the so-called fundamental constraints. The nonuniform linear arrays are created by adjusting the interelement spacing according to some rule. We show that the use of nonuniform linear geometries can significantly improve the robustness of DMAs, particularly at low frequencies. We also show that the diagonal loading technique can help improve the robustness of DMA beamformers, though the improvement is not significant.

MIMO Radar Transmit Beampattern Matching Design

In this paper, a novel transmit beampattern matching design method is proposed for a multiple-input multiple-output (MIMO) radar system. Whereas previous approaches first solve the correlation matrix $R$ and then use $R$ to design the transmit signal $S$ , the proposed one-step method obtains the transmit signal $S$ directly through solving the waveform matrix $P$ . Since MIMO radar transmit beampattern matching design is an inverse problem of the transmit beampattern, in this paper, we first discuss some important properties of the transmit beampattern and standardize the beampattern matching design problem. We then theoretically explain the value of the signal waveform matrix $P$ , followed by an unconstrained optimization problem to solve $P$ . Numerical examples demonstrate the advantages of the proposed one-step method for the MIMO radar transmit beampattern matching design problem, including uniform and non-uniform linear arrays.

Testing spatial co-prime sampling theory

An array of sensors can be used to estimate the direction of arrival of a narrowband signal in the far field with the use of conventional beamforming. In order to avoid spatial aliasing, the distance between the sensors have to be d ≤ λ/2 apart. This is analogous to the Nyquist theorem for sampling in time with fs= 2fo. Co-Prime arrays are non-uniform arrays that can predict what a uniform array with an aperture of L = M×N total sensors can using fewer sensors; they have a total number of sensors L = M + N—1 while maintaining an aperture of M×N sensors in a full uniform line array with λ/2 spacing between elements. Each subarray is uniform linear, equally spaced by Nλ/2 or M λ/2 and then combined to create a non-uniform linear array. The result with the different inter-element spacing between the subarrays is grating lobes in different locations with the exception of the true DOA. Conventional beamforming is done with both subarrays and the outputs are then multiplied together to yield a single beam pattern. The theory to this will be tested using a uniform array of 30 sensors and selecting the data from certain sensors to achieve co-prime sampling.

Fast and efficient DOA estimation method for signals with known waveforms using nonuniform linear arrays

In this paper, a new approach is proposed to estimate the direction of arrival (DOA) of multiple non-coherent source signals with known waveforms but unknown gains based on a nonuniform linear sensor array. Unlike some previous methods, which estimate the DOA using spatial signatures of the signals with known waveforms, the proposed method first uses the known waveforms and mutually independent sensor measurement noises to establish a maximum likelihood estimation problem corresponding to multiple linear regression models, each containing the DOA and the gain information of all the source signals. Then, regression analysis is performed to estimate the coefficients of each linear regression model, and the well-known generalized least squares is used to obtain the estimates of the angles and gains from the estimated regression coefficients. The proposed method does not require a search over a large region of the parameter space, which is normally needed in ML-based DOA estimation methods. The effect of correlated sources on the performance of the parameter estimation is also studied. It is shown that the DOA and gain estimates are asymptotically optimal as the sources tend to be uncorrelated. Finally, simulation results that demonstrate the estimation performance of the proposed method are given.

A Multiple Beamforming Network for Unequally Spaced Linear Array Based on CORPS

This paper proposes an alternative and innovative way to design a simpler beamforming network (BFN) based on balancing alternated power combiners and dividers, to feed a nonuniformly spaced linear array with Gaussian amplitude and coherent (in-phase) signals. Thus, a two-beam design configuration of the feeding network for a nonuniform array with beam steering capability is proposed and analyzed. The nonuniform aperture and the complex inputs of the feeding network are optimized by means of a differential evolution algorithm. In addition, a comparative analysis between a uniform and nonuniform linear array with the proposed feeding network is performed. Simulation results show the advantages and effectiveness of the proposed feeding network exploiting the nonuniformity of the antenna elements, in terms of side lobe level and directivity. Furthermore, research results show an inherent reduction in hardware complexity of the network.

Hybrid PSO – CP technique for the synthesis of non-uniform linear arrays with maximum directivity

A technique to synthesize maximum directivity non-uniform linear layouts subjected to upper bounds on the power pattern is presented. The approach is based on a nested strategy combining an outer particle swarm-based optimization and an inner convex programming solver by taking advantage of the convexity of the synthesis with respect to the excitation coefficients when fixing the array layout. Selected numerical results are discussed to assess the effectiveness, the flexibility, and the limitations of the proposed technique.

Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array

A coprime sensor array (CSA) is a non-uniform linear array obtained by interleaving two uniform linear arrays (ULAs) that are undersampled by coprime factors. A CSA provides the resolution of a fully populated ULA of the same aperture using fewer sensors. However, the peak side lobe level in a CSA is higher than the peak side lobe of the equivalent full ULA with the same resolution. Adding more sensors to a CSA can reduce its peak side lobe level. This paper derives analytical expressions for the number of extra sensors to be added to a CSA to guarantee that the CSA peak side lobe height is less than that of the full ULA with the same aperture. The analytical expressions are derived and compared for the uniform, Hann, Hamming, and Dolph-Chebyshev shadings.

DOA Estimation using Random Linear Arrays via Compressive Sensing

In this article we analyze the performance of nonuniform linear arrays for Direction of Arrival (DOA) estimation. We use different classes of sparse recovery algorithms to estimate the direction of arrival of the signal sources and its information. We focus on three array configurations, a structured or virtual array with prefixed potential locations for the elements, a random array and a random array with a restriction on the minimum distance between elements. We provide simulations of the performance of each configuration under these algorithms for different values of aperture, and number of signal sources.

IMPROVED SPECTRUM SEARCHING GENERALIZED–ESPRIT ALGORITHM FOR JOINT DOD AND DOA ESTIMATION IN MIMO RADAR WITH NON-UNIFORM LINEAR ARRAYS

This paper investigates the problem of angle estimation for bistatic multiple-input multiple-output (MIMO) radar with non-uniform linear arrays, and proposes an improved spectrum searching generalized estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation algorithm in bistatic MIMO radar. The proposed algorithm obtains initial estimation of angles obtained from the signal subspace, and uses the 1D local searchings to achieve the joint estimation of DOD and DOA. Compared to the spectrum searching generalized-ESPRIT algorithm which requires the global searchings and additional pairing, the proposed algorithm just needs the local searchings and obtains automatically paired 2D angle estimation. The angle estimation performance of the proposed algorithm is almost the same as that of the generalized-ESPRIT algorithm, and better than ESPRIT-like algorithm. Furthermore, the proposed algorithm is suitable for irregular array geometry, has much lower complexity than the spectrum searching generalized-ESPRIT algorithm, and imposes less constraint on the transmit/receive sensor spacing, which need not be limited to a half-wavelength strictly. The simulation results verify the effectiveness of the algorithm.