Figure 2 - uploaded by Wei Liu
Content may be subject to copyright.
Source publication
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...
Contexts in source publication
Context 1
... physical layout of these two schemes is shown in Fig. 2, and the way of constructing the IEAS scheme is summarised in Tab. 1. The steps of constructing the EAS scheme is a little different, which only uses the steps 1, 2, 5, 6 and 7. The EAS scheme can remove one co-located sensor of the two sub-arrays by the shifting, while the IEAS scheme can generate more FODLs using the consecutiveness ...
Context 2
... physical layout of these two schemes is shown in Fig. 2, and the way of constructing the IEAS scheme is summarised in Tab. 1. The steps of constructing the EAS scheme is a little different, which only uses the steps 1, 2, 5, 6 and 7. The EAS scheme can remove one co-located sensor of the two sub-arrays by the shifting, while the IEAS scheme can generate more FODLs using the consecutiveness of the second ...
Similar publications
This paper experimentally investigates a direction of arrival (DOA)-based wave source location estimation method for spectrum sharing in millimeter-wave band local and private fifth-generation (5G) mobile communication systems. In the DOA-based wave source location estimation, it is important to extract a line-of-sight (LOS) component from the rece...
In this paper, we investigate the problem of sparse array design for the direction of the arrival (DOA) of non-Gaussian signals and exploit the unfolded coprime linear array with three subarrays (UCLATS) to obtain physical sensors location. With the motivation from the large consecutive degree of freedom (DOF), we optimize the process of obtaining...
p>The performance of direction-of-arrival (DOA) estimation is severely affected by noise and clutter, and conventional methods fail to simultaneously cope with different situations because of the difficulties to predict noise and clutter. In order to solve this problem, a generalized robust framework for noise reconstruction in the received data do...
Abstract This letter proposes a direction of arrival (DOA) and time of delay (TOA) joint estimation algorithm with deep transfer learning. Recently deep learning technique has been applied to solve the joint estimation problem by using the pretrained network and perform well. But in real applications, different scenarios require to cost much time t...
Frequency–wavenumber (f–k) analysis can estimate the direction of arrival (DOA) of broadband signals received on a vertical array. When the vertical array configuration is sparse, it results in an aliasing error due to spatial sampling; thus, several striation patterns can emerge in the f–k domain. This paper extends the f–k analysis to a sparse re...
Citations
... Recently, scholars have been attracted by coprime arrays due to their high degrees of freedom (DOF) and high estimation resolution [6,7]. In order to further increase DOF, one subarray of the coprime array is modified and shifted in [8,9], while some scholars used displaced multistage cascade subarrays to form a novel sparse array with high DOF in [10]. In [11], the authors proposed a search-free method to reduce the computational complexity. ...
A novel direction of arrival (DOA) estimating method is proposed based on the coprime array, which can work without a priori information of the source number. The fourth-order statistics is adopted to construct a virtual array with a large aperture, which can also suppress Gaussian noise leading to a higher estimation accuracy and more importantly allowing the propagator construction. A propagator combining source number estimation and DOA estimation is presented firstly. Then considering the risk brought by the source number estimator, an improved propagator is constructed without the priori or estimated source number. The performance of the proposed method has been verified through some simulations.
... Two representative sparse array structures are the co-prime arrays [21]- [23] and nested arrays [24], [25]. Many methods have been proposed for DOA estimation based on such arrays, which can estimate more sources than the number of physical sensors by exploiting the difference coarrays [21], [22], [26]- [32]. At the same time, the CRB especially applied to sparse arrays has also been derived [3]- [6], and the existence conditions of these CRBs imply that more sources than the number of physical sensors can be identified by using sparse arrays. ...
... where h d is a column vector whose pth element is given by [h d ] p = δ [1 d ]p,0 , ∀p ∈ l d , with δ [1 d ]p,0 denoting the Kronecker function. Using (19), (20), (32), and (33), we can rewrite G e and Q e as ...
The Cramer-Rao bound (CRB) offers insights into the inherent performance benchmark of any unbiased estimator developed for a specific parametric model, which is an important tool to evaluate the performance of direction-of-arrival (DOA) estimation algorithms. In this paper, a closed-form stochastic CRB for a mixture of circular and noncircular uncorrelated Gaussian signals is derived. As a general one, it can be transformed into some existing representative results. The existence condition of the CRB is also analysed based on sparse arrays, which allows the number of signals to be more than the number of physical sensors. Finally, numerical comparisons are conducted in various scenarios to demonstrate the validity of the derived CRB.
... where C φ , D φ , and F φ are shown in (49), (50), and (51), respectively. Result 16: Consider the case where the sources are known a priori to be spatially uncorrelated. ...
The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case.
... For a fair comparison, we consider these two geometries utilizing the entire array as both transmit and receive arrays. On the other hand, we also compare passive array geometries using 4-DC, which are referred to as SAFE-CPA [101], IEAS [126] and E-FL-NA [104]. It can be seen that the consecutive DOFs of CPA using 2-DC are limited to 69 while those of I-NA are 309 due to its increased inter-element spacing. ...
Sparse array and sparse sensing attract increasing attention due to their capability to increase the DOFs. The DOA or the frequency of signals can be estimated with few antenna sensors or few collected sub-Nyquist samples. In this dissertation, we focus on one of the most recognized sparse structures, coprime configuration, to estimate the DOA or the frequency of signals.We first investigate the coprime sampling for frequency estimation and come across with a diagonal property loss phenomenon for which the estimation totally fails. To address this problem, we propose a random delay based mechanism to ensure the effectiveness of coprime sampling based methods. Then we also develop a multi-rate coprime sampling scheme to fully utilize the information brought by the coprime sampling.Apart from the frequency estimation, we also work on the DOA estimation with coprime array. We rearrange the coprime array structure to further increase the DOFs without introducing additional hardware cost. Then we introduce fourth order cumulants in active DOA estimation with coprime MIMO radar. The DOFs of MIMO radar can be enhanced by adopting the fourth order cumulants. Finally, we optimize the MIMO radar geometry using fourth order cumulants and the DOFs can be significantly increased.
... To further increase the consecutive DOFs in the coarray, the inter-element spacing of the newly added subarray is expanded according to the number of virtual sensors in the 2-DC [8]. In [9], [10], two sub-arrays, which can be of a nested array or coprime array, are rearranged such that the first subarray maintains its original structure while the second sub-The authors are with the Institut d'Électronique et des Technologies du numéRique, Université de Nantes, France (e-mail: zhe fu@foxmail.com, pascal.charge@univ-nantes.fr, yide.wang@univ-nantes.fr) ...
... array is expanded and shifted to the end of the first sub-array. The total DOFs are increased in [10] while the same length of consecutive DOFs as in [9] is maintained. ...
... For a fair comparison, we consider these two geometries utilizing the entire array as both transmit and receive arrays. On the other hand, we also compare passive array geometries using 4-DC, which are referred to as SAFE-CPA with three sub-arrays [5], IEAS with two sub-arrays [10] and E-FL-NA with four subarrays [8]. It can be seen that the consecutive DOFs of CPA using 2-DC are limited to 69 while those of I-NA are 309 due to its increased inter-element spacing. ...
In active direction of arrivals (DOA) sensing, the multiple-input multiple-output (MIMO) radar can lead to more degrees of freedom (DOFs). The DOFs can be further increased when the fourth order cumulants are used in MIMO. However, most array geometries are not designed for fourth order cumulants based MIMO and this array geometry optimization problem is still an open issue. To have a simple guideline for this optimization problem, we reformulate it into two separate problems, which are a fourth order sum coarray optimization problem and a second order difference coarray problem. The fourth order sum coarray optimization is realized by solving a postage stamp problem and a virtual nested array can be obtained. The number of elements in this virtual nested array can be significantly increased with only a few physical sensors. The corresponding inter-element spacing of virtual nested array is expanded simultaneously. Then the second order difference coarray is adopted to the virtual nested array to further increase the DOFs. Numerical results validate the high DOFs achieved by our proposition.
... Recently fourth-order statistics based fourth-order difference coarrays received much attention because of its increased sparsity compared with the second-order statistics based co-arrays [22][23][24], such as the extension of co-prime arrays based on fourth-order difference co-array concept [22], fourth-order cumulant-based nested array design [23], improved expanding and shift scheme for the construction of fourth-order difference co-arrays [24]. ...
... Recently fourth-order statistics based fourth-order difference coarrays received much attention because of its increased sparsity compared with the second-order statistics based co-arrays [22][23][24], such as the extension of co-prime arrays based on fourth-order difference co-array concept [22], fourth-order cumulant-based nested array design [23], improved expanding and shift scheme for the construction of fourth-order difference co-arrays [24]. ...
A detailed analysis of the degrees of freedom (DOFs) (and therefore the maximum number of signals to be estimated) of the fourth-order sum and difference co-arrays for direction of arrival (DOA) estimation in the presence of circular, strictly noncircular and nonstrictly noncircular signals is presented. There are different ways in combining noncircularity, fourth-order cumulants and sparse arrays to increase the DOFs of the system for DOA estimation. However, there are some confusions or a lack of clarity in the combination. In this work, we aim to fill the gap and clarify some relevant issues by providing a detailed analysis for the fourth-order co-array for a mixture of circular, strictly noncircular and nonstrictly noncircular signals based on a general signal model, including consideration of the noncircular phases of signals in DOA estimation, the fourth-order co-array aperture by considering all the fourth-order cumulants, the difference in the number of signals to be resolved for the strictly and nonstrictly noncircular signals, and the general analysis of DOFs for a mixture of circular, strictly noncircular and nonstrictly noncircular signals based on either uniform or sparse arrays. Furthermore, the expansion and shift scheme with one sub-array being a nested array and another one being a stamp array is proposed, which provides the most DOFs among considered sparse array construction schemes.
The expanding and shift scheme with two nested arrays (EAS-NA-NA) is easy to construct and effective for achieving large number of degrees of freedom (DOFs), which is one of the representative sparse arrays exploiting the fourth-order difference co-array (FODC). In this letter, it is found that by suitably enlarging the sensor spacing of the expanded nested array in the original EAS-NA-NA, EAS-NA-NA with larger spacing (EAS-NA-NALS) can be built and the DOFs available for direction of arrival (DOA) estimation can be remarkably increased. The proposed EAS-NA-NALS can achieve the longest consecutive virtual array among the well-known FODC-based sparse arrays when the number of physical sensors is large. Simulation experiments are conducted to verify the DOA estimation performance of EAS-NA-NALS and several representative sparse arrays are taken for comparison. Experimental results show that EAS-NA-NALS can achieve more DOFs than other sparse arrays, thus acquiring the improved performance for DOA estimation.
