Gaussian Signal Detection With Product Arrays

Adhikari, Kaushallya; Buck, John R.

doi:10.1109/access.2020.2974985

Cited by 9 publications

(4 citation statements)

References 33 publications

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“…(2) The optimal shading can be obtained for the individual subarrays of these sparse arrays. Then, product or min processing as described in [18]- [25] can be applied to these arrays. The beampatterns for product processing are shown in the bottom panel of Figure 11.…”

Section: Optimal Weights For Standard Sparse Arraysmentioning

confidence: 99%

Array Shading to Maximize Deflection Coefficient for Broadband Signal Detection With Conventional Beamforming

et al. 2021

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This paper develops and applies a numerical optimization procedure to compute broadband noise-adaptive weights for delay and sum beamforming that are conditioned to maximize the deflection coefficient at the output of a square law detector for a given set of underwater pressure measurements. The resulting optimal weights mitigate the effects of noise and interferers and maximize signal detection. Comparison of the optimal weights with minimum variance distortionless response weights show that the presented algorithm provides higher attenuation of interferers. We also use the noise-adaptive algorithm to find the optimal sparse array geometry for a given number of sensors and aperture. Comparison of the resulting optimal array with coprime, nested, and semi-coprime arrays shows that the proposed sparse array suppresses interferers more than the other sparse arrays.

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Section: Optimal Weights For Standard Sparse Arraysmentioning

confidence: 99%

Array Shading to Maximize Deflection Coefficient for Broadband Signal Detection With Conventional Beamforming

et al. 2021

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“…Kullback has called D KL (f z1 ||f z0 ) the mean information per observation from f z1 for discrimination in favor of f z1 against f z0 [52]. In binary hypothesis testing, it is also called the mean discriminating information (MDI) between the alternate and null hypotheses [50], [53]. The KLD serves as a detection performance measure since, according to the Chernoff-Stein lemma, when the probability of missed detection is upper bounded by a small positive number , then [54] lim n→∞, →0 where n is the number of observations or snapshots.…”

Section: B Kullback-leibler Divergencementioning

confidence: 99%

“…Higher values of D KL (f z1 ||f z0 ) indicate faster decay of the probability of false alarm and therefore better asymptotic detection performance. For a CBF detector, evaluating the KLD using its null hypothesis distribution E(σ 2 y,0 ) and alternate hypothesis distribution E(σ 2 y,1 ), gives us [50], [53] log σ 2 y,0…”

Section: B Kullback-leibler Divergencementioning

confidence: 99%

Design and Statistical Analysis of Tapered Coprime and Nested Arrays for the Min Processor

Adhikari

Drozdenko

2019

IEEE Access

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Coprime and nested arrays are sparse sensor arrays that provide O(MN ) degrees of freedom using only O(M + N ) sensors. The signals sampled by these sparse arrays contain the aliasing artifact; the min processor is used to disambiguate this aliasing artifact. The min processor beampattern has the same main lobe width and resolution as the beampattern of a full uniform linear array (ULA) with many more sensors. However, the peak side lobe (PSL) height of the min processor beampattern is higher than the PSL height of a full ULA with the same taper and resolution if the sparse arrays are not extended. Extending the sparse arrays, while keeping the intersensor spacing fixed, can reduce the PSL height to the level of the full ULA. Until now, the analytical expressions of the extension factor required to match the PSL height have not been found for the min processor. Also, the analytical expressions of the probability density function (PDF), mean, and variance of the min processor output for non-uniform tapers have not been derived. In this paper, we derive both of these analytical expressions. We consider the uniform, Hamming, Hann, Blackman-Harris, and Dolph-Chebyshev tapers for both coprime and nested arrays. We use the derived PDF in evaluating detection performance metrics such as receiver operation characteristic, Kullback Leibler divergence, and symmetric Kullback Leibler divergence. Our results show that min processing is superior to conventional beamforming and product processing in Gaussian signal detection for a given extended coprime or nested array.INDEX TERMS Blackman-Harris taper, coprime arrays, Dolph-Chebyshev taper, Hamming taper, Hann taper, min processing, nested arrays, sparse arrays, uniform taper.

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“…Product processing and min processing are the predominant CBF-based methods for coprime and nested arrays [5], [7], [11]- [18]. Various aspects of these two processors are compared in depth in [15], [17], [19], with product processing having the advantage of being less vulnerable to crossterms than min processing [15], [17], [20].…”

Section: Introductionmentioning

confidence: 99%

Product Processing for Tapered Sparse Arrays

Sartori¹,

Adhikari²

2021

Preprint

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The product processor output has recently been introduced as a spatial power spectral density estimate, unifying product arrays such as coprime arrays, nested arrays, and standard uniform line arrays. The expected value and covariance function of this estimate for a white Gaussian process was derived in previous work over these various array configurations. However, this prior work used a uniform taper in all cases. In this paper, we show that when product arrays are windowed with non-uniform tapers, the expected value of the product processor output is the convolution of the true spatial power spectral density with the spatial Fourier transform of the difference coarray. This expected value makes a Fourier transform pair with a spatial autocorrelation estimate obtained by windowing the true autocorrelation function. We also derive the covariance function of the product processor output with non-uniform tapers, and compare these derived statistics for the aforementioned array geometries. Also, in prior work, the moments were provided only for linear arrays; this paper extends the estimation results to multidimensional arrays.

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Gaussian Signal Detection With Product Arrays

Cited by 9 publications

References 33 publications

Array Shading to Maximize Deflection Coefficient for Broadband Signal Detection With Conventional Beamforming

Array Shading to Maximize Deflection Coefficient for Broadband Signal Detection With Conventional Beamforming

Design and Statistical Analysis of Tapered Coprime and Nested Arrays for the Min Processor

Product Processing for Tapered Sparse Arrays

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