Two-level Nested Array Research Articles

Direction estimation using a two-level nested array with gain–phase error calibration

Direction estimation using a two-level nested array with gain–phase error calibration

DOA Estimation of a Novel Generalized Nested MIMO Radar with High Degrees of Freedom and Hole-Free Difference Coarray

A novel generalized nested multiple-input multiple-output (MIMO) radar for direction of arrival (DOA) estimation is proposed in this paper. The proposed structure utilizes the extended two-level nested array (ENA) as transmitter and receiver and adjusts the interelement spacing of the receiver with an expanding factor. By optimizing the array element configuration, we can obtain the best number of elements of the transmitter and receiver and the attainable degrees of freedom (DOF). Compared with the existing nested MIMO radar, the proposed MIMO array configuration not only has closed-form expressions for sensors’ positions and the number of maximum DOF, but also significantly improves the array aperture. It is verified that the sum-difference coarray (SDCA) of the proposed nested MIMO radar can get higher DOF without holes. MUSIC algorithm based on Toeplitz matrix reconstruction is employed to prove the rationality and superiority of the proposed MIMO structure.

Near-Field Source Localization With Two-Level Nested Arrays

The concept of the nested array has been used widely for underdetermined far-field source localization. In this case, the enhanced degrees-of-freedom (DOFs) is often achieved by using spatial smoothing because the difference co-array of a two-level nested array behaves like a uniformly-spaced linear array (ULA). This ingenious operation cannot be used for near-field localization because the ULA behavior of the co-array is violated by the near-field's curved wavefronts and range-dependent attenuation. Thus, the application of nested arrays for near-field localization becomes challenging. In this letter, we propose to concatenate the vectorization of multiple fourth-order cumulant matrices to increase the DOFs offered by the nested arrays. We also show that when the sources are in the near-field, the maximum DOFs provided by a two-level nested array with L physical sensors can mathematically be up to exactly L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The well-posed identification conditions are discussed as well. Numerical examples are conducted to verify our analysis. Comparisons with existing ULA-based methods are also provided.

A new nested array for direction-of-arrival estimation

In this paper, the problem of direction-of-arrival (DOA) estimation with a new nested array is addressed. It is known that the original two-level nested array is composed of two uniform linear arrays (ULAs), and there exist some redundant elements in their difference co-array. In order to reduce the redundancy, a new array configuration which consists of a ULA and a non-uniform linear array, rather than two ULAs, is proposed. On one hand, the proposed array can effectively increase degrees of freedom as well as virtual array aperture. On the other hand, it has a group of continuous lags in the virtual array. Thanks to the advantages of the proposed array configuration, higher resolution and better estimation performance of DOA estimation can be achieved. Simulation results show the superiority of the proposed array structure.

A Novel Two-Level Nested STAP Strategy for Clutter Suppression in Airborne Radar

Nested arrays have been studied recently in array signal processing field because of their closed-form expressions for the sensor locations and achievable degrees of freedom (DOFs). In this paper, the concept of nesting is further extended to space-time adaptive processing (STAP). Different from the traditional uniform-STAP method that calculates the clutter plus noise covariance matrix (CNCM) and performs the STAP filter direct using the data snapshots collected from the uniform linear array (ULA) and the transmitting pulses with uniform pulse repetition interval (PRI), we present a new optimum two-level nested STAP (O2LN-STAP) strategy which employs an optimum two-level nested array (O2LNA) and an optimum two-level nested PRI (O2LN-PRI) to exploit the enhanced DOFs embedded in the space-time O2LN structure. Similar to the difference coarray perspective, we first construct a virtual space-time snapshot from the direct covariance matrix of the received signals. Then, a new CNCM estimation corresponding to the virtual space-time snapshot can be computed by the spatial-temporal smoothing technique for STAP filter. Furthermore, the comparative simulations and analyses with the traditional uniform-STAP and the recently reported coprime-STAP are carried out to verify the effectiveness of the O2LN-STAP approach.

DOA Estimation Exploiting Moving Dilated Nested Arrays

A novel dilated nested array is presented to obtain an enhanced fully filled difference coarray exploiting array motions. The proposed sparse array is suitable for the cases when the sensing environment can be assumed stationary over an array motion of half wavelength or shorter. Closed-form expressions of the number of degrees of freedom in the difference coarray of the combined array before and after the translation motion are presented for direction-of-arrival (DOA) estimation. It is shown that the maximum number of consecutive lags for this case is three times that of the corresponding conventional two-level nested array. Numerical results of DOA estimation using the proposed array are provided for performance comparison and to validate array analyses.

An improved expanding and shift scheme for the construction of fourth-order difference co-arrays

Abstract An improved expanding and shift (IEAS) scheme for efficient fourth-order difference co-array construction is proposed. Similar to the previously proposed expanding and shift (EAS) scheme, it consists of two sparse sub-arrays, but one of them is modified and shifted according to a new rule. Examples are provided with the second sub-array being a two-level nested array (IEAS-NA), as such a choice can generate more fourth-order difference lags (FODLs), although with the same number of consecutive lags. Furthermore, the array aperture of IEAS-NA is always greater than the corresponding EAS structure, which helps improving the DOA estimation result. Simulations results are provided to show the improved performance by the proposed new scheme.

A New Nested Array Configuration With Increased Degrees of Freedom

In this paper, a new linear array configuration based on the concept of two-level nested array is proposed. Specifically, the proposed array configuration consists of two uniform linear arrays (ULAs) plus a separate sensor with appropriate spacing apart. Compared with the original two-level nested array, the degrees of freedom of our proposed array configuration can be increased by $2L-6$ for an array with $L$ physical sensors. Moreover, the virtual array aperture can be enlarged by nearly $({L^{2}}/{2}-L-2)d_{1}$ , where $d_{1}$ is the inter-element spacing of the first ULA. Owing to these advantages, our proposed array configuration has enhanced resolution and achieves better performance in parameter estimation, such as direction-of-arrival (DOA) estimation. Numerical simulations of DOA estimation exhibit the effectiveness and superiority of this array configuration.

An Expanding and Shift Scheme for Constructing Fourth-Order Difference Coarrays

An expanding and shift (EAS) scheme for efficient fourth-order difference co-array construction is proposed. It consists of two sparse sub-arrays, where one of them is modified and shifted according to the analysis provided. The number of consecutive lags of the proposed structure at the fourth order is consistently larger than two previously proposed methods. Two effective construction examples are provided with the second sparse sub-array chosen to be a two-level nested array, as such a choice can increase the number of consecutive lags further. Simulations are performed to show the improved performance by the proposed method in comparison with existing structures.

Sparse Extension Array Geometry for DOA Estimation With Nested MIMO Radar

The two-level nested array geometry, which systematically nests two uniform linear subarrays, is proved to offer $O(N^{2})$ degrees of freedom (DOFs) with only $N$ sensors. In this paper, a novel sparse extension array geometry for nested multiple-input multiple-output radar is proposed to provide $O(N^{4})$ DOFs with $N$ sensors. In the proposed geometry, both the transmitter and receiver are equipped with the two-level nested arrays, where we particularly extend the inter-element spacing of the transmitter with a sparse extension factor, leading to a great increase of DOF. Furthermore, we derive the closed-form expressions for the sensor locations and the available DOFs. Spatial smoothing-based MUSIC algorithm is employed to validate the effectiveness and superiority of the proposed sparse extension array for direction of arrival estimation.

Improved nested array with hole‐free DCA and more degrees of freedom

A new linear sparse array based on the nested array is proposed, which enjoys all the good properties of the two-level nested array, and can provide more degrees of freedom (DOF). The new array is constructed by two uniform linear arrays (ULAs) and an additional sensor. The sensor locations, the array aperture, and the achievable DOF from its difference co-array (DCA) are all benefited for closed-form expressions. Furthermore, the resulting DCA is kept as a hole-free ULA. The optimal numbers of sensors in the two ULAs provided the total number of physical sensors are derived. This new array can resolve more sources and achieve better angle estimation performance than the two-level nested array. Simulation results validate these conclusions.

Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review

Direction of arrival (DOA) estimation from the perspective of sparse signal representation has attracted tremendous attention in past years, where the underlying spatial sparsity reconstruction problem is linked to the compressive sensing (CS) framework. Although this is an area with ongoing intensive research and new methods and results are reported regularly, it is time to have a review about the basic approaches and methods for CS-based DOA estimation, in particular for the underdetermined case. We start from the basic time-domain CS-based formulation for narrowband arrays and then move to the case for recently developed methods for sparse arrays based on the co-array concept. After introducing two specifically designed structures (the two-level nested array and the co-prime array) for optimizing the virtual sensors corresponding to the difference co-array, this CS-based DOA estimation approach is extended to the wideband case by employing the group sparsity concept, where a much larger physical aperture can be achieved by allowing a larger unit inter-element spacing and therefore leading to further improved performance. Finally, a specifically designed uniform linear array structure with associated CS-based underdetermined DOA estimation is presented to exploit the difference co-array concept in the spatio-spectral domain, leading to a significant increase in degrees of freedom. Representative simulation results for typical narrowband and wideband scenarios are provided to demonstrate their performance.