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Abstract
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.
... In practical applications of DOA estimation, if the source frequency is too high, the distance between adjacent antennas can not reach half the wavelength due to the actual antenna diameter. In [30] a sparse array design method is proposed to overcome this problem [31]. presents a scheme of expansion and displacement with two nested arrays that make it possible to achieve high degrees of freedom (DOFs) in the fourth-order difference co-array (FODC). ...
In this paper A different approach based on the reconstruction of the data covariance matrix is presented. In the presented approach, by vectorization of the reconstructed matrix, the covariance matrix is reconstructed in two steps. Hence an extensive network of virtual sensors is created, which is introduced as a second-order difference co-array. Then, by using the well-known spatial smoothing technique full-rank covariance matrix is obtained for DOA estimation algorithms. Therefore the MN sources can be detected using a physical array with M + N sensors. The degrees of freedom (DOF) of the second-order difference co-array are significantly increased as opposed to the physical array which provides only N − 1 degrees of freedom. As a result, for a certain number of array elements, in addition to the resolution improvement, the number of detectable targets is sharply increased. Simulation results verify the effectiveness of the proposed method and MUSIC-based or ESPRIT-based DOA estimators could be designed to perform DOA estimation.
... Introduction: The direction of arrival (DOA) is widely estimated using the antenna array in fields such as radar and wireless communications [1][2][3]. Various methods, including spectrum methods and compressive sensing methods [4], have been proposed to deal with the DOA estimation issue in the traditional antenna array architecture. However, with the development of millimeter-wave communications, the traditional antenna array architecture has become obsolete. ...
Abstract The application of the emerging hybrid analog–digital architecture for future millimeter‐wave communications has attracted significant attention. Although this architecture can reduce the hardware cost and power consumption considerably, the high‐resolution direction of arrival (DOA) estimation in the architecture based on switches is still a challenge. As a solution, an alternating switches algorithm (ASA) is proposed in this paper. By appropriately adjusting the switch connected to each antenna, the real‐valued spatial covariance matrix (SCM) is reconstructed with low‐dimensional vector‐to‐vector multiplication. Subsequently, the DOA angle of each signal is estimated based on a split subspace extracted from the real‐valued SCM. Finally, a set of simulation experiments are performed to verify the performance of the proposed algorithm. The results indicate that the ASA can reconstruct the real‐valued SCM and realize high‐resolution DOA estimation with a substantially low computational cost.
... Shu et al. 9 extended the nested array to the near-field source localization and the full co-array aperture of parallel nested array in 2D direction finding was illustrated. The extensions of nested array to DOA estimation with high-order cumulants are considered in [10][11][12] . ...
As an emerging technology, the hybrid analog-digital structure has been considered for use in future millimeter-wave communications. Although this structure can reduce the hardware cost and power consumption considerably, the spatial covariance matrix (SCM), as the core of subspace-based direction of arrival (DOA) estimation, cannot be obtained directly. Previously, the beam sweeping algorithm (BSA) has been found effective for reconstructing the spatial covariance matrix and realizing DOA estimation by forming the beams to difference directions. However, it is computationally intractable owing to the high-dimensional matrix operation. To address this problem and improve the DOA estimation performance, this paper applies the nested array to the hybrid analog-digital structure and proposes the enhanced BSA (EBSA) for DOA estimation. By deleting a large number of redundant elements exist in the SCM to be reconstructed, the computational cost can be considerably reduced. Also, the nested array can offer high degrees of freedom. Finally, simulation experiments are conducted to verify the performance of EBSA. The results indicate that the proposed EBSA is better than the state-of-the-art method in terms of estimation accuracy and computational cost.
In sparse linear array (SLA) design, mutual coupling (MC) is a non-negligible metric, while both MC effects and lower degrees of freedom (DOFs) can reduce the accuracy of direction of arrival (DOA) estimation. To mitigate the MC effect and achieve more unique DOFs, we propose two novel enhanced dilated nested array (EDNA) configurations, named EDNA-I and EDNA-II, respectively. In contrast to most advanced SLA configurations, the proposed EDNA-I and EDNA-II have fewer sensor pairs at smaller separations and thus have better robustness to MC effects. In addition, their sensor locations and DOFs can be derived as simple explicit expressions. Theoretical proofs and numerical simulations show that the proposed EDNA-I and EDNA-II have superior performance in terms of DOFs and weight function and also effectively suppress the MC effect, which in turn exhibits better DOA estimation performance in the presence of MC.
Linear sparse arrays with fourth-order cumulant processing can resolve
$\mathcal{O}(N^4)$
directions-of-arrival (DOAs) using
$N$
physical sensors, provided that the fourth-order difference co-array
$\Delta_4$
contains a contiguous segment of size
$\mathcal{O}(N^4)$
. Furthermore, if
$\Delta_4$
has no holes, then the received data can be fully exploited in subspace-based DOA estimators. However, few existing arrays attain large hole-free
$\Delta_4$
. Many existing arrays designed for
$\Delta_4$
are constructed from two smaller arrays, called the basis arrays. Nevertheless, such arrays either restrict the basis arrays to certain types or have no guarantee of hole-free
$\Delta_4$
. This paper proposes the half-inverted (HI) arrays, parameterized by two basis arrays
$\mathbb{S}^{(1)}$
and
$\mathbb{S}^{(2)}$
, the shifting parameter
$M$
, and the scaling parameter
$\sigma$
. An HI array consists of
$\mathbb{S}^{(1)}$
and an inverted, scaled, and shifted version of
$\mathbb{S}^{(2)}$
. HI arrays are guaranteed with hole-free
$\Delta_4$
over a range of
$(M,\sigma)$
pairs. This property unifies several existing arrays with hole-free
$\Delta_4$
and admits an optimization problem over
$(M,\sigma)$
. The half-inverted general hole-free (HIGH) scheme is defined as the HI array with a closed-form and optimized
$(M,\sigma)$
pair determined by the second-order co-arrays of the basis arrays. The HIGH scheme enjoys a large hole-free
$\Delta_4$
. The shift-scale representation (SSR) is presented to study
$\Delta_4$
of HI arrays visually. From these results, the half-inverted array based on second-order optimization and extended shift (HI-SOES) is proposed. For a fixed
$N$
, HI-SOES synthesizes a hole-free
$\Delta_4$
larger than an existing array. Numerical examples demonstrate the DOA estimation performance of HI arrays and existing arrays.
A generalized sum-difference expansion scheme is proposed to construct sparse arrays based on the fourth-order difference co-array with increased degrees of freedom (DOFs). Different from existing structures, both the second-order sum and difference co-arrays are exploited in array construction under this scheme, leading to a large consecutive fourth-order difference co-array with its number of uniform DOFs (uDOFs) derived. To optimize the provided uDOFs, required design properties of the initial prototype arrays are discussed. Three examples are then provided to demonstrate its superior performance over existing structures in both resolution capacity and estimation accuracy.
In the field of array signal processing research, there has been considerable attention to sparse arrays for the ability to provide larger array apertures and more degrees of freedom (DOFs) under the constraint of fixing the number of physical sensors to save the use of resources. Aiming at this, a novel relocating improved nested array (RINA) configuration with increasing DOFs and hole-free co-array is proposed and simple closed-form expressions for its array geometry and DOFs are given. Compared with most existing sparse array configurations, the proposed RINA can achieve more consecutive DOFs and larger effective array apertures. Based on the mentioned good properties of the proposed RINA, a cross-correlation domain (C-CD) algorithm is proposed for direction of arrival (DOA) estimation. The algorithm is based on the virtual co-array of RINA to build the cross-correlation domain, followed by the generalized eigenvalue method and the least squares method for noise compensation and optimization, respectively. The results of theoretical analysis and simulations demonstrate the superior performance of the proposed RINA. The simulation results show that the proposed C-CD algorithm has better DOA estimation performance compared with those of existing algorithms, and the advantage of its spatial spectrum without pseudo peaks can achieve fast estimation for source directions. The experimental results demonstrate the feasibility of the proposed RINA and C-CD algorithm applied to underwater DOA estimation.
The use of the emerging hybrid analog-digital structure for future millimeter-wave communications has attracted much attention. Although this structure can reduce the power consumption considerably, the spatial covariance matrix (SCM), as the core of subspace-based direction of arrival (DOA) estimation algorithms, cannot be obtained directly. The beam sweeping algorithm (BSA) was proposed for SCM reconstruction from compressed measurements. However, the BSA is computationally intensive owing to the high-dimensional matrix-to-matrix multiplication and matrix inversion. To address this issue, a BSA algorithm with high accuracy and low computational-cost using the submatrix multiplication (BSASM) is proposed in this paper. By appropriately adjusting the weight, which consists of a switch and a phase shifter, connected to each antenna, the SCM can be accurately reconstructed with low-dimensional matrix-to-vector multiplication and 2-dimensional matrix inversion, thus reducing the computational-cost significantly. After SCM reconstruction, various DOA estimation algorithms can be exploited to obtain the DOA information. Simulation experiments are conducted to verify the performance of the proposed algorithm. The results indicate that using a substantially lower computational-cost, BSASM can reconstruct SCM more accurately than BSA.
The spatial covariance matrix, as the core of subspace direction of arrival (DOA) estimation, is unavailable in the hybrid analog-digital structure, which is widely used in large-scale transceivers to reduce the number of radio frequency chains. In previous studies, the beam sweeping algorithm (BSA) has been used for effectively reconstructing the spatial covariance matrix. However, the BSA is not practical owning to the intractable computational cost due to the high-dimensional matrix operations. To address this problem, a high-efficiency BSA (HeBSA) is proposed. The main motivation behind the HeBSA is to avoid the high-dimensional matrix multiplication and inversion. By appropriately adjusting weights connected to antennas, the real-valued spatial covariance matrix can be reconstructed according to low-dimensional matrix multiplication. Then the classical U-root multiple signal classification can be adopted to estimate the DOA angle of each signal. Finally, simulation experiments are conducted to verify the performance of the HeBSA. The results indicate that the HeBSA can achieve DOA estimation performance comparable with that of BSA even at considerably lower computational cost.
In this paper, a more generalized dilated nested array (DNA) named multi-level dilated nested array (multi-level DNA), which further extends the original DNA to the general situation and improves the direction of arrival (DOA) estimation performance, is proposed. The original DNA, which consists of a nested array and a time-shifted array, possesses the capabilities of handling more sources and achieving improved estimation accuracy compared with the nested array. However, only one time-shifted array is employed in DNA and the performance improvement is quite limited. Here, a new multi-level DNA, which utilizes multiple time-shifted nested arrays, is proposed. The multi-level DNA can provide more degrees of freedom (DoFs), meanwhile its difference co-array is still hole-free. The closed form expression of uniform DoFs in multi-level DNA is derived. The corresponding DOA Cramér-Rao bound, which gives the low bound on the variance of estimated DOA, is deduced in detail and some properties related to it are concluded. In total, for the DOA estimation, multi-level DNA can detect more sources and achieve more accurate estimation performance compared with the original DNA. Numerical simulations are performed to verify the superiority of the proposed multi-level DNA.
Based on the high order difference co-array concept, an enhanced four level nested array (E-FL-NA) is first proposed, which optimizes the consecutive lags at the fourth order difference co-array stage. To simplify the formulations for sensor locations for comprehensive illustration and also convenient structure construction, a simplified and enhanced four level nested array (SE-FL-NA) is then proposed, whose performance is compromised but still better than the four level nested array (FL-NA). This simplified structure is further extended to the higher order case with multiple sub-arrays, referred to as simplified and enhanced multiple level nested arrays (SE-ML-NAs), where significantly increased degrees of freedom (DOFs) can be provided and exploited for underdetermined DOA estimation. Simulation results are provided to verify the superior performance of the proposed E-FL-NA, while a higher number of detectable sources is achieved by the SE-ML-NA with a limited number of physical sensors.
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.
In this paper, we propose a novel sparse array design for direction-of-arrival estimation based on the fourth-order statistics of the received signals. The utilization of fourth-order statistics provides a higher number of degrees of freedom and flexibility as compared to the commonly used covariance-based methods. The proposed sparse array design scheme yields the fourth-order difference co-array which offers a significant increment in the number of consecutive lags as compared to the existing sparse array structures used by fourth-order cumulant-based direction-of-arrival estimation methods. Moreover, the proposed array is designed in such a way that the resulting difference co-array does not contain any holes. Simulation results verify the effectiveness of the proposed array structure.
A coprime array uses two uniform linear subarrays to construct an effective difference coarray with certain desirable characteristics, such as a high number of degrees-of-freedom for direction-of-arrival (DOA) estimation. In this paper, we generalize the coprime array concept with two operations. The first operation is through the compression of the inter-element spacing of one subarray and the resulting structure treats the existing variations of coprime array configurations as well as the nested array structure as its special cases. The second operation exploits two displaced subarrays, and the resulting coprime array structure allows the minimum inter-element spacing to be much larger than the typical half-wavelength requirement, making them useful in applications where a small interelement spacing is infeasible. The performance of the generalized coarray structures is evaluated using their difference coarray equivalence. In particular, we derive the analytical expressions for the coarray aperture, the achievable number of unique lags, and the maximum number of consecutive lags for quantitative evaluation, comparison, and design of coprime arrays. The usefulness of these results is demonstrated using examples applied for DOA estimations utilizing both subspace-based and sparse signal reconstruction techniques.
The conventional coprime array consists of two uniform linear subarrays to construct an effective difference coarray with desirable characteristics. Such linear coprime arrays only provide one-dimensional (1-D) direction-of-arrival (DOA) estimation. In this paper, we propose a novel coprime array configuration with parallel subarrays, along with an effective method for two-dimensional (2-D) DOA estimation. The 2-D DOA estimation problem is cast as two separate 1-D problems for reduced complexity and is solved using one of the two mechanisms based on the number of sensors and that of sources. When there are less sources than the number of sensors, subspace-based and rank-reduction estimation (RARE) techniques are sequentially applied to the physical array output. On the other hand, when the number of sources is equal to or larger than that of sensors, a virtual difference coarray is formed and group sparse reconstruction and least squares operations are then applied. In both scenarios, the proposed methods automatically pair the corresponding azimuth and elevation angles. The proposed methods resolve up to MN sources using 2M+N−1 sensors, which are the same as in the 1-D DOA estimation using conventional coprime arrays. Simulations results are presented delineating both the accuracy and resolution capability of the proposed method.
In this paper, we provide an approach to perform direction of arrival (DOA) estimation with the hole-free part of difference coarray, including the physical sparse uniform linear array (ULA) itself. The sparse two-level nested linear array (NLA), whose inter-element spacings are all enlarged by the identical rate compared with the conventional two-level NLA, is selected as the example to present our work due to the typicalness, under-determinedness and the relatively obvious mutual coupling effect. The difference coarray of the sparse two-level NLA is a sparse ULA and the existing methods can not be exploited for it. We derive the sparse uniform linear array discrete Fourier transform (SULA-DFT) algorithm based on the original DFT method to extend its application from only conventional ULA to sparse ULA to solve this problem. With the SULA-DFT, reliable estimation for positive angle within a limited range under a constraint condition between angle and sparsity of array is able to be obtained directly without any ambiguous angle. Compared with the conventional two-level NLA and many other state of the art configurations, the sparse two-level NLA is able to get least mutual coupling effect and largest array aperture and the SULA-DFT often obtain better estimation accuracy with the sparse two-level NLA. On the whole, sparse two-level NLA with more sparsity gets better estimation accuracy. The numerical simulations verify the superiority of the SULA-DFT with the sparse two-level NLA.
We consider transmit design and direction-of-arrival (DOA) estimation for a wideband multiple-input multiple-output (MIMO) system equipped with a colocated nested array for both transmit and receive. We present a new transmit scheme which separates the transmitted waveforms in the frequency domain, and allows us to form a sum coarray in the wideband case. Based on the proposed scheme, two coherent DOA estimation methods which construct focusing matrices from the difference coarray of the MIMO virtual array are presented to take full advantage of the degrees of freedom (DOF) and improve the accuracy of DOA estimation. Simulation results illustrate that the proposed system exhibits better performance than several competing configurations.
Traditional MUSIC-like methods for direction-of-arrival (DOA) estimation require the number of sources a priori and suffer from the heavy computational burden caused by complex-valued operations and exhaustive spectral search. In this paper, we propose two novel real-valued estimation methods without knowing the number of sources to overcome these weaknesses. Specifically, we first transform the complex-valued second-order statistics (covariance matrix) into real-valued one by unitary transformation and taking its real (or imaginary) part, respectively. We then formulate a real-valued low rank recovery problem to reveal the relation between the real-valued covariance matrices and source number. Finally, we propose a computationally efficient approach to solve the optimization problem via reweighted nuclear norm minimization. Simulation results show that without knowing the number of sources, the proposed methods exhibit superior estimation performance and can substantially reduce the complexity, as compared to the state-of-the-art techniques.
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.
To reach a higher number of degrees of freedom by exploiting the fourth-order difference co-array concept, an effective structure extension based on two-level nested arrays is proposed. It increases the number of consecutive lags in the fourth-order difference coarray, and a virtual uniform linear array (ULA) with more sensors and a larger aperture is then generated from the proposed structure, leading to a much higher number of distinguishable sources with a higher accuracy. Compressive sensing based approach is applied for direction-of-arrival (DOA) estimation by vectorizing the fourthorder cumulant matrix of the array, assuming non-Gaussian impinging signals.
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 closedform 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 (λ/2,2 x λ/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 Qth-order super nested array is developed, which further reduces mutual coupling.
Recently, direction-of-arrival estimation (DOA) algorithms based on arbitrary even-order $(2q)$ cumulants of the received data have been proposed, giving rise to new DOA estimation algorithms, namely the $2q$ MUSIC algorithm. In particular, it has been shown that the $2q$ MUSIC algorithm can identify $O(N^{q})$ statistically independent non-Gaussian sources. However, in this paper, it is demonstrated that the processing power of the $2q$th-order cumulant based methods can potentially be even larger. It will be shown that the $2q$th-order cumulant matrix of the data is directly related to the concept of a $2q$th-order difference co-array which can potentially have $O(N^{2q})$ virtual sensors, leading to identification of $O(N^{2q})$ statistically independent non-Gaussian sources using $2q$ th-order cumulants. However, the number of actually realizable virtual elements in the $2q$ th-order difference co-array depends on the geometry of the physical array. In order to ensure that the co-array indeed has the desired degrees of freedom, a new generic class of linear (one dimensional) nonuniform arrays, namely the $2q$th-order nested array, is proposed, whose $2q$ th-order difference co-array is proved to contain a uniform linear array with $O(N^{2q})$ sensors. In order to exploit these increased degrees of freedom of the co-array, a new algorithm for DOA estimation is also developed, which acts on the same $2q$ th-order cumulant matrix as the earlier methods and can yet identify $O(N^{2q})$ sources. It is proved that the proposed method can identify the maximum number of sources among all methods that use $2q$ th-order cumulants.
The classical higher order MUSIC-like methods based on a simultaneous search for all directions of arrival (DOA's) show: i) a capacity for processing underdetermined mixtures of sources; ii) a high robustness with respect to both a Gaussian noise with unknown spatial coherence and modeling errors; and iii) a better resolution than algorithms based on second order statistics. However, these methods have some limits: for a finite number of samples, they show poor performance for sources exhibiting quasi-colinear DOA's. In order to overcome this drawback, two new sequential MUSIC-like algorithms are proposed in this paper, namely the 2q -D-MUSIC and the 2q -RAP-MUSIC (q ≥ 2) algorithms. These methods are based on a sequential optimization of proposed generalized noise and signal 2q -MUSIC metrics, respectively. That allows us to learn and then to take into account the level of correlation between sources. A comparative study, both in terms of performance and numerical complexity, is performed showing the interest of the proposed techniques when some sources are angularly close. Eventually, an upper bound of the maximum number of sources which can be processed by the 2q -MUSIC-like techniques is given for all q . This improves recent work on the 2q th-order virtual arrays.
A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O ( N <sup>2</sup>) degrees of freedom using only N physical sensors when the second-order statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimum-input-minimum-output (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested co-array, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations.
This paper considers the sampling of temporal or spatial wide sense stationary (WSS) signals using a co-prime pair of sparse samplers. Several properties and applications of co-prime samplers are developed. First, for uniform spatial sampling with M and N sensors where M and N are co-prime with appropriate interelement spacings, the difference co-array has O(MN) freedoms which can be exploited in beamforming and in direction of arrival estimation. An M-point DFT filter bank and an N-point DFT filter bank can be used at the outputs of the two sensor arrays and their outputs combined in such a way that there are effectively MN bands (i.e., MN narrow beams with beamwidths proportional to 1/MN), a result following from co-primality. The ideas are applicable to both active and passive sensing, though the details and tradeoffs are different. Time domain sparse co-prime samplers also generate a time domain co-array with O(MN) freedoms, which can be used to estimate the autocorrelation at much finer lags than the sample spacings. This allows estimation of power spectrum of an arbitrary signal with a frequency resolution proportional to 2π/(MNT) even though the pairs of sampled sequences x_c(NTn) and x_c(MTn) in the time domain can be arbitrarily sparse - in fact from the sparse set of samples x_c(NTn) and x_c(MTn) one can estimate O(MN) frequencies in the range |ω| < π/T. It will be shown that the co-array based method for estimating sinusoids in noise offers many advantages over methods based on the use of Chinese remainder theorem and its extensions. Examples are presented throughout to illustrate the various concepts.
From the beginning of the 1980s, many second-order (SO) high-resolution direction-finding methods, such as the MUSIC method (or 2-MUSIC), have been developed mainly to process efficiently the multisource environments. Despite of their great interests, these methods suffer from serious drawbacks such as a weak robustness to both modeling errors and the presence of a strong colored background noise whose spatial coherence is unknown, poor performance in the presence of several poorly angularly separated sources from a limited duration observation and a maximum of N-1 sources to be processed from an array of N sensors. Mainly to overcome these limitations and in particular to increase both the resolution and the number of sources to be processed from an array of N sensors, fourth-order (FO) high-resolution direction-finding methods have been developed, from the end of the 1980s, to process non-Gaussian sources, omnipresent in radio communications, among which the 4-MUSIC method is the most popular. To increase even more the resolution, the robustness to modeling errors, and the number of sources to be processed from a given array of sensors, and thus to minimize the number of sensors in operational contexts, we propose in this paper an extension of the MUSIC method to an arbitrary even order 2q (qges1), giving rise to the 2q-MUSIC methods. The performance analysis of these new methods show off new important results for direction-finding applications and in particular the best performances, with respect to 2-MUSIC and 4-MUSIC, of 2q-MUSIC methods with q>2, despite their higher variance, when some resolution is required
For about two decades, many fourth order (FO) array processing methods have been developed for both direction finding and blind identification of non-Gaussian signals. One of the main interests in using FO cumulants only instead of second-order (SO) ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array, which eventually introduces the FO Virtual Array concept presented elsewhere and allows, in particular, a better resolution and the processing of more sources than sensors. To still increase the resolution and the number of sources to be processed from a given array of sensors, new families of blind identification, source separation, and direction finding methods, at an order m=2q (q≥2) only, have been developed recently. In this context, the purpose of this paper is to provide some important insights into the mechanisms and, more particularly, to both the resolution and the maximal processing capacity, of numerous 2qth order array processing methods, whose previous methods are part of, by extending the Virtual Array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space, angular and/or polarization diversity.
An approach to the general problem of signal parameter estimation
is described. The algorithm differs from its predecessor in that a total
least-squares rather than a standard least-squares criterion is used.
Although discussed in the context of direction-of-arrival estimation,
ESPRIT can be applied to a wide variety of problems including accurate
detection and estimation of sinusoids in noise. It exploits an
underlying rotational invariance among signal subspaces induced by an
array of sensors with a translational invariance structure. The
technique, when applicable, manifests significant performance and
computational advantages over previous algorithms such as MEM, Capon's
MLM, and MUSIC
Processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions. The general problem considers sensors with arbitrary locations and arbitrary directional characteristics (gain/phase/polarization) in a noise/interference environment of arbitrary covariance matrix. This report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution. A description is given of the multiple signal classification (MUSIC) algorithm, which provides asymptotically unbiased estimates of 1) number of incident wavefronts present; 2) directions of arrival (DOA) (or emitter locations); 3) strengths and cross correlations among the incident waveforms; 4) noise/interference strength. Examples and comparisons with methods based on maximum likelihood (ML) and maximum entropy (ME), as well as conventional beamforming are included. An example of its use as a multiple frequency estimator operating on time series is included.