49269122
DOA Estimation of Noncircular Signals for Unfolded Coprime Linear Array: Identifiability, DOF and Algorithm (May 2018)
An ambiguity-free direction of arrival (DOA) estimation method is presented for unfolded coprime linear array (UCLA) in this paper to resolve noncircular signals. Unlike the existing methods which process the two subarrays of coprime linear array separately, we stack the received signals of the two subarrays and derive the total subspace to produce the MUSIC spectrum. Specifically, we demonstrate that the ambiguity problem can be suppressed owing to the coprime property and the true DOA estimates can be obtained immediately. As the self-information and mutual information are jointly employed, the proposed method can achieve the full degrees of freedom (DOFs) and improved DOA estimation performance. Meanwhile, the extended aperture of UCLA can be feasibly exploited, which endows the proposed method with an enhanced identifiability. In addition, the non-circularity is utilized to double the available DOF and further improve the estimation accuracy of the proposed method. Simulation results verify the effectiveness and superiority of the proposed method.
31251598
Multiple emitter location and signal Parameter estimation
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.
206465293
Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT
The UCA-ESPRIT is a closed-form algorithm developed for use in conjunction with a uniform circular array (UCA) that provides automatically paired source azimuth and elevation angle estimates. The 2-D unitary ESPRIT is presented as an algorithm providing the same capabilities for a uniform rectangular array (URA). In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two major array axes. The 2-D unitary ESPRIT offers a number of advantages over other proposed ESPRIT based closed-form 2-D angle estimation techniques. First, except for the final eigenvalue decomposition of a dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to efficient beamspace implementations that are presented. Third, it is applicable to array configurations that do not exhibit identical subarrays, e.g., two orthogonal linear arrays. Finally, the 2-D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common. Simulation results are presented verifying the efficacy of the method.
8420104
Sparse Sensing With Co-Prime Samplers and Arrays
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 xc(NTn) and xc(MTn) in the time domain can be arbitrarily sparse - in fact from the sparse set of samples xc(NTn) and xc(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.
9809941
Direction of Arrival Estimation of Quasi-Stationary Signals Using Unfolded Coprime Array
Direction of arrival (DOA) estimation of quasi-stationary signals (QSS) is discussed in this paper, and an algorithm using unfolded coprime array is proposed. Coprime array consists of two uniform linear subarrays with coprime relationship, and the two subarrays of the unfolded coprime array in this paper are arranged along the positive axis and negative axis, respectively. Through the vectorization of the low dimensional cross-covariance matrix and the further exploiture of the non-circularity within the second-order statistics of QSS, 2MN-1 degrees of freedom can be achieved with M+N physical elements. The uniqueness of the DOA estimation based on the non-continuous virtual elements generated from the unfolded coprime array is proved, and unitary polynomial root finding technique is employed to estimate the DOA. The proposed algorithm has low complexity, and it can obtain better DOA estimation performance and handle more sources than Khatri–rao subspace approach and original coprime array-based method. Simulation results verify the effectiveness of the proposed approach.
14363545
DECOM: DOA estimation with combined MUSIC for coprime array
In this paper, we propose a direction-of-arrival (DOA) estimation method by combining multiple signal classification (MUSIC) of two decomposed linear arrays for the corresponding coprime array signal processing. The title “DECOM” means that, first, the nonlinear coprime array needs to be DECOMposed into two linear arrays, and second, Doa Estimation is obtained by COmbining the MUSIC results of the linear arrays, where the existence and uniqueness of the solution are proved. To reduce the computational complexity of DECOM, we design a two-phase adaptive spectrum search scheme, which includes a coarse spectrum search phase and then a fine spectrum search phase. Extensive simulations have been conducted and the results show that the DECOM can achieve accurate DOA estimation under different SNR conditions.
35144192
Two-Dimensional Direction-of-Arrival Estimation for Co-Prime Planar Arrays: A Partial Spectral Search Approach
In this paper, we investigate the issue of 2-D direction-of-arrival (DOA) estimation of multiple signals in co-prime planar arrays, where phase ambiguity problem arises due to the large distance between adjacent elements for each subarray. According to the co-prime characteristic, the ambiguity problem can be eliminated by searching for the common peaks of the spatial spectrum of each subarray, where the spectrum search involves a tremendous computation burden. In this paper, we exploit the property that all the ambiguous peaks for each DOA are uniformly distributed in a new transformed domain. Relying on the linear relations, we propose a partial spectral search (PSS)-based estimation method, where it involves a limited search over only a small sector. Therefore, the proposed PSS method is very computationally efficient. Numerical results are provided to verify the effectiveness of the proposed method over the state-of-the-art methods, in terms of both computational complexity and estimation accuracy.
3355223
DOA Estimation Based on Real-Valued Cross Correlation Matrix of Coprime Arrays
A fast direction of arrival (DOA) estimation method using a real-valued cross-correlation matrix (CCM) of coprime subarrays is proposed. Firstly, real-valued CCM with extended aperture is constructed to obtain the signal subspaces corresponding to the two subarrays. By analysing the relationship between the two subspaces, DOA estimations from the two subarrays are simultaneously obtained with automatic pairing. Finally, unique DOA is determined based on the common results from the two subarrays. Compared to partial spectral search (PSS) method and estimation of signal parameter via rotational invariance (ESPRIT) based method for coprime arrays, the proposed algorithm has lower complexity but achieves better DOA estimation performance and handles more sources. Simulation results verify the effectiveness of the approach.
111167956
Azimuth and elevation estimation for noncircular signals
A novel 2D direction-finding algorithm for noncircular signals using two parallel linear arrays, called the extended rank reduction (ERARE) algorithm, is presented. The method needs only 1D search for joint azimuth and elevation estimation. The azimuth and elevation angles estimated by ERARE are paired automatically.
8808972
Performance analysis of ESPRIT-type algorithms for non-circular sources
High-resolution parameter estimation algorithms designed to benefit from the presence of non-circular (NC) source signals allow for an increased identifiability and a lower estimation error. In this paper, we present a 1-D first-order performance analysis of the NC standard ESPRIT and NC Unitary ESPRIT estimation schemes for strictly second-order (SO) non-circular sources, where NC Unitary ESPRIT has a lower complexity and a better performance in the low signal-to-noise ratio (SNR) regime. Our derived expressions are asymptotic in the effective SNR and explicit in the noise realizations, i.e., no assumptions about the noise statistics are necessary. As a main result, we show that the asymptotic performance of both NC ESPRIT-type algorithms is identical in the effective SNR and that NC Unitary ESPRIT is even applicable to array geometries without a centro-symmetric structure as required for Unitary ESPRIT.
14340437
MUSIC-like estimation of direction of arrival for noncircular sources
This paper examines the asymptotic performance of MUSIC-like algorithms for estimating directions of arrival (DOA) of narrowband complex noncircular sources. Using closed-form expressions of the covariance of the asymptotic distribution of different projection matrices, it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace-based algorithms valid for Gaussian or non-Gaussian and complex circular or noncircular sources. We also derive different robustness properties from the asymptotic covariance of the estimated DOA given by such algorithms. These results are successively applied to four algorithms: to two attractive MUSIC-like algorithms previously introduced in the literature, to an extension of these algorithms, and to an optimally weighted MUSIC algorithm proposed in this paper. Numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance (AMV) algorithms introduced as benchmarks
15135582
DOA Estimation of Temporally and Spatially Correlated Narrowband Noncircular Sources in Spatially Correlated White Noise
The main contribution of our work consists in developing for the first time a method of estimating the direction of arrival (DOA) parameters assuming noncircular and temporally and spatially correlated signals. This new approach, based on a significant enhancement of the two-sided instrumental variable signal subspace fitting (IV-SSF) method, outperforms its classical version in terms of lower bias and error variance. Moreover, it will be shown that our new method is statistically more efficient than the MODE method especially in the case of partly and fully coherent signals where only the extended and the classical two-sided IV-SSF methods are applicable. We also derive an explicit expression for the stochastic Cramér-Rao bound (CRB) of the DOA estimates from temporally and spatially correlated signals generated from noncircular sources. The new CRB is compared to those of circular temporally correlated and noncircular independent and identically distributed signals to show that the CRB obtained assuming both noncircular sources and temporally correlated signals is lower than the CRBs derived considering only one of these two assumptions. This illustrates the potential gain that both noncircularity and temporal correlation provide when considered together. It will also be proven that the difference between the three CRBs increases with the number of snapshots. However, as the signal-to-noise ratio (SNR) increases, the CRBs merge together and decrease linearly. Moreover, at low SNR values it will be shown that temporal correlation is more informative about the unknown DOA parameters than noncircularity. Finally, the CRB derived assuming noncircular and temporally correlated signals depends on the noncircularity rate, the circularity phase separation, and the DOA separation.
29531015
A non-circular sources direction finding method using polynomial rooting
In this paper, we present a new direction finding algorithm for non-circular sources based on the polynomial rooting technique. Due to the non-circularity characteristics of the impinging sources, the proposed method is able to handle more sources than sensors. Using polynomial rooting instead of a searching technique limits the method to linear uniformly spaced arrays. Polynomial rooting, however, reduces computation cost and enhances resolution power significantly. Computer simulations are used to show the performance of the algorithm.
35723351
The propagator method for source bearing estimation
Abstract This paper investigates the propagator method as a possible alternative to the MUSIC method for source bearing estimation with arrays consisting of a large number of sensors. Indeed, the propagator method (PM) is a subspace-based method which does not require the eigendecomposition of the cross-spectral matrix (CSM) of the received signals. The propagator is a linear operator which only depends on the steering vectors and which can be easily extracted from the data. We here propose a new version of the propagator method referred to as the orthonormal propagator method (OPM). The performance of the PM and the OPM is theoretically analysed in terms of the mean squared error on the source bearing estimates and in terms of computational complexity. The performance results are then compared to those of MUSIC. We find that at high and medium signal-to-noise ratio, the OPM performs quite like MUSIC with a complexity reduced by the ratio of the number of sources to the number of sensors. Simulations are presented to strengthen the theoretical results. At low signal-to-noise ratio, the OPM can also perform like MUSIC when the assumed number of sources is slightly overestimated.
126376983
DOA Estimation of Noncircular Signals with Combined ESPRIT for Coprime Linear Array
Direction of arrival (DOA) estimation of noncircular signals for coprime linear array is investigated, and a combined estimation of signal parameters via rotational invariance technique (ESPRIT) based algorithm is proposed. The coprime linear array can be de-composed into two uniform linear arrays, so ESPRIT is firstly used to obtain ambiguous DOA estimations, then unique DOA estimation is achieved by finding the coincide results from the two decomposed subarrays based on the coprimeness. The proposed algorithm increase the degree of freedom, enhance the performance of angle estimation, and identifies more targets than conventional methods. Numerical simulations are conducted to demonstrate the improvement of the proposed algorithm.
4934175
Direction of Departure (DOD) and Direction of Arrival (DOA) Estimation in MIMO Radar with Reduced-Dimension MUSIC
This letter discusses the problem of direction of departure (DOD) and direction of arrival (DOA) estimation for multi-input multi-output (MIMO) radar, and derives a reduced-dimension multiple signal classification (MUSIC) algorithm therein. The proposed algorithm, which only requires one-dimension search, can avoid the high computational cost within two-dimension MUSIC (2D-MUSIC) algorithm. We illustrate that the algorithm has better performance ESPRIT algorithm, and has very close performance to 2D-MUSIC algorithm. Further our algorithm requires no pair matching. Simulation results verify the usefulness of our algorithm.
40026813
Source number estimators using transformed Gerschgorin radii
We introduce effective uses of Gerschgorin radii of the unitary transformed covariance matrix for source number estimation. There are two approaches, likelihood and heuristic, used for developing the detection criteria. The likelihood approach combines the Gerschgorin radii to the well-known source number detectors and improves their detection performances for Gaussian and white noise processes. It is verified that the Gerschgorin likelihood estimators (GLE) are consistent. The Gerschgorin AIC yields a consistent estimate and the Gerschgorin MDL criterion does not tend to underestimate for small or moderate data samples. The heuristic approach applying the Gerschgorin disk estimator (GDE) developed from the projection concept, overcomes the problem in cases of small data samples, an unknown noise model, and data dependency. Furthermore, the detection performances of both approaches through the suggested rotations and averaging can be further improved. Finally, the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data. >
3815178
DOA Estimation for Coprime Linear Arrays: An Ambiguity-Free Method Involving Full DOFs
In this letter, an ambiguity-free direction of arrival (DOA) estimation method for coprime linear array (CLA), which generally consists of two uniform linear subarrays, is proposed. By stacking the received data of two subarrays, the proposed method can suppress the ambiguity problem and obtain the unique DOA estimates based on coprime property. In addition, full degrees of freedom can be attained due to a joint utilization of self-information and mutual information. Moreover, unlike the general CLA with two subarrays interleaved, a coprime array with adjoined subarrays (CAAdS) is devised to enlarge the array aperture by adjoining the two subarrays, with which the methods for DOA estimation can achieve more accurate DOA estimates and enhanced resolution. Furthermore, Cramer-Rao bound of CAAdS is provided as a benchmark for the lower bound of unbiased DOA estimates. Simulations are given to validate the effectiveness and superiority of the proposed ambiguity-free method for both CAAdS and the general CLA.
8440648
Noncircular-PARAFAC for 2D-DOA estimation of noncircular signals in arbitrarily spaced acoustic vector-sensor array subjected to unknown locations
AbstractsIn this paper, we propose a noncircular-parallel factor (NC-PARAFAC) algorithm for two-dimensional direction of arrival (DOA) estimation of noncircular signals for acoustic vector-sensor array. The proposed algorithm enhances the angle estimation performance via utilizing the noncircularity of the signals, and it can be suitable for arbitrary array subjected to unknown locations and achieve automatically paired two-dimensional angle estimation. The proposed algorithm has better angle estimation performance than estimation of signal parameters via rotational invariance technique, PARAFAC algorithm, and propagator method. Furthermore, the proposed algorithm has a lower computational complexity than the PARAFAC algorithm. We also derive the Crámer-Rao bound of DOA estimation of noncircular signal in acoustic vector-sensor array. The simulation results verify the effectiveness of the algorithm.
9826861
Performance study of conditional and unconditional direction-of-arrival estimation
A numerical and analytical study of conditional and unconditional direction-of-arrival (DOA) estimation is presented. Explicit expressions for the unconditional Cramer-Rao bounds on the DOA estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given. It is shown that many DOA estimation methods have the same asymptotic statistical properties under conditional and unconditional models. The situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed. >
16184867
Deterministic Cramér-Rao Bound for Strictly Non-Circular Sources and Analytical Analysis of the Achievable Gains
Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. As a benchmark for these NC methods, we derive the closed-form deterministic R-D NC Cramér-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources in this paper. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved under the deterministic data assumption in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain. Our analysis is supported by extensive simulation results.
630008
Low-Complexity DOA Estimation Based on Compressed MUSIC and Its Performance Analysis
This paper presents a new computationally efficient method for direction-of-arrival (DOA) estimation with arbitrary arrays. The total angular field-of-view is first divided into several small sectors and the original noise subspace exploited by the multiple signal classification (MUSIC) algorithm is mapped from one sector to the other sectors by a Hadarmard product transformation. This transformation gives a new noise-like subspace cluster (NLSC), whose intersection is found to be simultaneously orthogonal to the steering vectors associated with the true DOAs and several virtual DOAs. Based on such a multiple orthogonality, a novel compressed MUSIC (C-MUSIC) spatial spectrum at hand is derived. Unlike MUSIC with tremendous spectral search, C-MUSIC involves a limited search over only one sector, and hence it is computationally very attractive. To obtain the intersection of NLSC for more than two sectors, a low-complexity method is also proposed in the present work, which shows advantages over the existing alternative projection method (APM) and singular value decomposition (SVD) techniques. Furthermore, the mean square errors (MSEs) of the proposed estimator is derived. Simulation results illustrate that C-MUSIC trades-off MSEs by complexity and resolution as compared to the standard MUSIC efficiently.