Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors

Liu, Chun-Lin; Vaidyanathan, P.P.

doi:10.1016/j.dsp.2016.04.011

Cited by 248 publications

(187 citation statements)

References 91 publications

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“…Fig. 3 illustrates the resolution performance of the three arrays under different ∆θ, as well as the thresholds predicted by (22). The MRA shows best resolution performance of the three arrays, which can be explained by the fact that the MRA has the largest aperture.…”

Section: B Prediction Of Resolvabilitymentioning

confidence: 96%

Coarrays, MUSIC, and the Cramér–Rao Bound

Wang

Nehorai

2017

IEEE Trans. Signal Process.

318

161

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Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability of providing enhanced degrees of freedom. By exploiting the coarray structure, an augmented sample covariance matrix can be constructed and MUSIC (MUtiple SIgnal Classification) can be applied to identify more sources than the number of sensors. While such a MUSIC algorithm works quite well, its performance has not been theoretically analyzed. In this paper, we derive a simplified asymptotic mean square error (MSE) expression for the MUSIC algorithm applied to the coarray model, which is applicable even if the source number exceeds the sensor number. We show that the directly augmented sample covariance matrix and the spatial smoothed sample covariance matrix yield the same asymptotic MSE for MUSIC. We also show that when there are more sources than the number of sensors, the MSE converges to a positive value instead of zero when the signal-to-noise ratio (SNR) goes to infinity. This finding explains the "saturation" behavior of the coarray-based MUSIC algorithms in the high SNR region observed in previous studies. Finally, we derive the Cramér-Rao bound (CRB) for sparse linear arrays, and conduct a numerical study of the statistical efficiency of the coarray-based estimator. Experimental results verify theoretical derivations and reveal the complex efficiency pattern of coarray-based MUSIC algorithms.

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Section: B Prediction Of Resolvabilitymentioning

confidence: 96%

Coarrays, MUSIC, and the Cramér–Rao Bound

Wang

Nehorai

2017

IEEE Trans. Signal Process.

318

161

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“…Hence, sparse sampling has been brought to airborne radar applications, where the effective DoFs are reduced and only limited performance can be achieved. More recently, motivated by attractive advantages including large aperture, low mutual coupling, and increased DoFs in the virtual domain provided by the coprime sampling [114], [115], [116], [117], [118], several STAP algorithms have been developed for clutter suppression using coprime sampling configurations [119], [120]. Two STAP algorithms based on virtual construction and the spatial-temporal smoothing technique for coprime arrays (CPAs) have been proposed in [119], where a much reduced number of array elements and pulses is used while the performance is close to that of a standard array with Nyquist sampling.…”

Section: Introductionmentioning

confidence: 99%

Robust Two-Stage Reduced-Dimension Sparsity-Aware STAP for Airborne Radar With Coprime Arrays

Yang

Huang

Lamare

2020

IEEE Trans. Signal Process.

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Space-time adaptive processing (STAP) algorithms with coprime arrays can provide good clutter suppression potential with low cost in airborne radar systems as compared with their uniform linear arrays counterparts. However, the performance of these algorithms is limited by the training samples support in practical applications. To address this issue, a robust two-stage reduced-dimension (RD) sparsity-aware STAP algorithm is proposed in this work. In the first stage, an RD virtual snapshot is constructed using all spatial channels but only m adjacent Doppler channels around the target Doppler frequency to reduce the slow-time dimension of the signal. In the second stage, an RD sparse measurement modeling is formulated based on the constructed RD virtual snapshot, where the sparsity of clutter and the prior knowledge of the clutter ridge are exploited to formulate an RD overcomplete dictionary. Moreover, an orthogonal matching pursuit (OMP)-like method is proposed to recover the clutter subspace. In order to set the stopping parameter of the OMP-like method, a robust clutter rank estimation approach is developed. Compared with recently developed sparsity-aware STAP algorithms, the size of the proposed sparse representation dictionary is much smaller, resulting in low complexity. Simulation results show that the proposed algorithm is robust to prior knowledge errors and can provide good clutter suppression performance in low sample support.

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“…the inherent presence of RSS measurement features in every wireless device. This means that the utilization of RSS-based localization in practice only requires software upgrades, while offering sufficient precision and 10 fidelity for a wide range of applications.…”

Section: Introductionmentioning

confidence: 99%

Geometric interpretation of theoretical bounds for RSS-based source localization with uncertain anchor positions

Denkovski

Angjelichinoski

Atanasovski

et al. 2017

Digital Signal Processing

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The Received Signal Strength based source localization can encounter severe problems originating from uncertain information about the anchor positions in practice. The anchor positions, although commonly assumed to be precisely known prior to the source localization, are usually obtained using previous estimation algorithm such as GPS. This previous estimation procedure produces anchor positions with limited accuracy that result in degradations of the source localization algorithm and topology uncertainty. We have recently addressed the problem with a joint estimation framework that jointly estimates the unknown source and uncertain anchors positions and derived the theoretical limits of the framework. This paper extends the authors previous work on the theoretical performance bounds of the joint localization framework with appropriate geometric interpretation of the overall problem exploiting the properties of semidefiniteness and symmetry of the Fisher Information Matrix and the Cramèr-Rao Lower Bound and using Information and Error Ellipses, respectively. The numerical results aim to illustrate and discuss the usefulness of the geometric interpretation. They provide in-depth insight into the geometrical properties of the joint localization problem underlining the various possibilities for practical design of efficient localization algorithms. Ellipse 65 For two-dimensional parameter estimation, such as network node localization, the ellipsoids become ellipses. In the case of the FIM, they are referred as Information Ellipses (IEs) and for the CRLB -Error Ellipses (EEs). This paper extends our previous work in [5] and focuses on the geometric interpretation of the joint localization framework and its appropriate theoretical bounds. The 70 geometrical interpretation of the FIM provides insights into the distribution of the information about the unknown positions that is stored in the observation vector by decoupling it into orthogonal spatial dimensions. Equivalently, the geometrical interpretation of the CRLB illustrates the estimation error spread, i.e. the variance of estimation error around the true value of the estimated parame-75ter. These insights are important since they allows deeper understanding of the localization problem. The geometrical interpretation also provides insights into the possibilities for maximizing the location information in terms of problem dimensioning, network topology design, specific node mobility patterns, channel modeling etc., considering specific limitations and conditions. This can assist 80 the definition of algorithmic rules for optimal combining of different information components, resulting in minimization of the estimation error.Considering the benefits that stem from the geometric interpretation of the performance bounds and related metrics, the contributions of this paper are summarized as follows. The paper introduces and discusses the geometric inter-85 pretation of the general problem of parameter estimation, as well as the problem of joint estimation, emphasizing ...

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Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors

Cited by 248 publications

References 91 publications

Coarrays, MUSIC, and the Cramér–Rao Bound

Coarrays, MUSIC, and the Cramér–Rao Bound

Robust Two-Stage Reduced-Dimension Sparsity-Aware STAP for Airborne Radar With Coprime Arrays

Geometric interpretation of theoretical bounds for RSS-based source localization with uncertain anchor positions

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