Super Nested Array Research Articles

Sparse channel estimation for underwater acoustic OFDM systems with super-nested pilot design

Sparse channel estimation for underwater acoustic OFDM systems with super-nested pilot design

High-frequency distributed super nested arrays based on Hermitian Toeplitz matrix reconstruction

In array processing, mutual coupling between antenna elements is inevitable, which has an adverse effect on the estimation of parameters. Meanwhile, the expensive computational requirements are also not conducive to the real-time processing. In this paper, a new Hermitian Toeplitz matrix reconstruction algorithm suitable for distributed sparse arrays with contiguous difference co-array is proposed. The computational complexity of the new algorithm is quantitatively analyzed, which is much lower than that of the spatial smoothing algorithm. Then, a new array called distributed super nested arrays (DSNA) is proposed to reduce the mutual coupling between antenna elements. In contrast to super nested arrays (SNA) and nested arrays (NA), the proposed array can further improve the accuracy of direction-of-arrival (DOA) estimation by using the multiscale estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. In high-frequency surface wave radar (HFSWR), the proposed array and algorithm can effectively reduce the mutual coupling in a wide frequency range, improve DOA estimation performance, significantly increase the number of detectable source signals, and reduce computational complexity. Numerical simulations demonstrate the superiority of DSNA using the proposed Hermitian Toeplitz matrix reconstruction algorithm.

Dilated Nested Arrays With More Degrees of Freedom (DOFs) and Less Mutual Coupling—Part I: The Fundamental Geometry

The recent criteria of a preferable linear sparse array for a robust direction of arrival (DOA) estimation are: the closed-form expression for its sensor locations; the large central uniform linear array (ULA) segment in its resulting co-array; and the fewer sensor pairs with small separations in its arrangement. These features, in turn, will lead to a straightforward array design process, more sources being resolved and strong helpful performance for the array within a real-world mutual coupling environment. This paper introduces a new array called the dilated nested array (DNA), which takes into account all these considerations. The sensors of the DNA are arranged in a way that yields an effective difference co-array with a central virtual ULA part larger than that of the co-prime array and equal to that of the nested array, and in an equivalent importance, a physical arrangement with smaller numbers of sensor pairs with small separations than those of the super nested array, so that the array can notably reduce the mutual coupling effects in comparison. A displaced arrangement obtained from the DNA geometry is also introduced to further increase the co-array total number of DOFs and at the same time to decrease the numbers of sensor pairs with small separations. Extensive numerical simulations are included to demonstrate the effectiveness of the proposed DNAs over other sparse arrays.

Distributed Super Nested Arrays: Reduce the Mutual Coupling between Array Antennas

In array, mutual coupling between the antennas is inevitable, which has an adverse effect on the estimation of parameters. To reduce the mutual coupling between the antennas of distributed nested arrays, this paper proposes a new array called the distributed super nested arrays, which have the good characteristics of the distributed nested arrays and can reduce the mutual coupling between the antennas. Then, an improved multiscale estimating signal parameter via rotational invariance techniques (ESPRIT) algorithm is presented for the distributed super nested arrays to improve the accuracy of direction-of-arrival (DOA) estimation. Next, we analyze the limitations of the spatial smoothing algorithm used by the distributed super nested arrays when there are multiple-source signals and the influence of the baseline length of distributed super nested arrays on the accuracy of DOA estimation. The simulation results show that the distributed super nested arrays can effectively reduce the mutual coupling between the array antennas, improve the DOA estimation performance, and significantly increase the number of detectable source signals.

DOA Estimation Using Fourth-Order Cumulants in Nested Arrays with Structured Imperfections.

Recently developed super nested array families have drawn much attention owing to their merits on keeping the benefits of the standard nested arrays while further mitigating coupling in dense subarray portions. In this communication, a new mutual coupling model for nested arrays is constructed. Analyzing the structure of the newly formed mutual coupling matrix, a transformation of the distorted steering vector to separate angular information from the mutual coupling coefficients is revealed. By this property, direction of arrival (DOA) estimates can be determined via a grid search for the minimum of a determinant function of DOA, which is induced by the rank reduction property. We also extend the robust DOA estimation method to accommodate the unknown mutual coupling and gain-phase mismatches in the nested array. Compared with the schemes of super nested array families on reducing the mutual coupling effects, the solutions presented in this paper has two advantages: (a) It is applicable to the standard nested arrays without rearranging the configuration to increase the inter-element spacing, alleviating the cross talk in dense uniform linear arrays (ULAs) as well as gain-phase errors in sparse ULA parts; (b) Perturbations in nested arrays are estimated in colored noise, which is significant but rarely discussed before. Simulations results corroborate the superiority of the proposed methods using fourth-order cumulants.

Extended Coprime Array Configuration Generating Large-Scale Antenna Co-Array in Massive MIMO System

Generally, massive multiple-input multiple-output (MIMO) system incorporates hundreds of antennas at the base station for various attractive merits, whereas severe mutual coupling arises in the dense structure. In this paper, we introduce the sparse array configuration, coprime array, into the massive MIMO system to alleviate mutual coupling, increase the degrees of freedom (DOFs) and enhance the spatial resolution. Specifically, we propose the extended coprime array structures through two systematical schemes. One scheme is to slide one subarray of the typical augmented coprime array to decompose the interleaved subarrays and the resulting sliding extended coprime array (SECA) produces weaker mutual coupling than the traditional dense uniform linear array, especially the newly proposed super nested array and augmented nested array. Meanwhile, SECA can produce an augmented co-array with more antennas than the physical array and resultantly increase the available DOFs as well as the array aperture. The other scheme is to relocate a proper number of antennas in the generalized coprime array composed of two subarrays with a displacement, namely coprime array with displaced subarrays (CADiS), and the resulting relocating extended coprime array can further alleviate mutual coupling and enhance the consecutive co-array. Furthermore, we provide the closed-form expressions of the co-array, sliding factor, the minimum number of relocating sensors, and their corresponding positions.

Robust STAP With Reduced Mutual Coupling and Enhanced DOF Based on Super Nested Sampling Structure

In practical airborne radar, mutual coupling between array elements usually leads to space-time steering vector distortion for space-time adaptive processing (STAP), which seriously degrades radar performance. In this paper, a robust STAP algorithm coupling the second order super nested arrays with pulses (2OSNAP) sampling structure is developed. The proposed method applies difference operation to construct virtual space-time snapshots in the virtual domain. To solve the clutter plus noise covariance matrix (CNCM) corresponding to the virtual space-time snapshots, the space-time smoothing method is used in this paper. Furthermore, the proposed method can directly give a set of virtual and robust STAP weight vector, which is convenient for the subsequent signal processing. Extensive numerical experiments were performed to verify the effectiveness and superiority of the proposed method. The test results also show that our proposed method provides more degrees of freedom (DOF), and eliminates the mutual coupling effect between array elements compared to most existing methods.

Super Nested Arrays: Linear Sparse Arrays With Reduced Mutual Coupling—Part II: High-Order Extensions

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRA) have reduced mutual coupling compared to uniform linear arrays (ULAs). These arrays also have a difference coarray with $O\left({N}^{2}\right)$ virtual elements, where $N$ is the number of physical sensors, and can therefore resolve $O\left({N}^{2}\right)$ uncorrelated source directions. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. In a companion paper, a sparse array configuration called the (second-order) super nested array was introduced, which has many of the advantages of these sparse arrays, while removing most of the disadvantages. Namely, the sensor locations are readily computed for any $N$ (unlike MRAs), and the difference coarray is exactly that of a nested array, and therefore hole-free. At the same time, the mutual coupling is reduced significantly (unlike nested arrays). In this paper, a generalization of super nested arrays is introduced, called the $Q$ th-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for $Q > 2$ . Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.

Super Nested Arrays: Linear Sparse Arrays With Reduced Mutual Coupling—Part I: Fundamentals

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With $N$ denoting the number of sensors, these sparse arrays offer $O({N}^{2})$ freedoms for source estimation because their difference coarrays have $O({N}^{2})$ -long ULA segments. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. This paper introduces a new array called the super nested array, which has all the good properties of the nested array, and at the same time achieves reduced mutual coupling. There is a systematic procedure to determine sensor locations. For fixed $N$ , the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with small separations ( $\lambda /2,2\times \lambda /2$ , etc.) is significantly reduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays. In the companion paper, a further extension called the $Q$ th-order super nested array is developed, which further reduces mutual coupling.