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Target Detection via Cognitive Radars Using Change-Point Detection, Learning, and Adaptation

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Abstract

Many radar detection algorithms that assume a stationary environment (clutter) have been proposed and analyzed over the years. However, in practice, changes in the nonstationary environment can perturb the parameters of the clutter distribution, or even alter the clutter distribution family, which can greatly deteriorate the target detection capability. To avoid such potential performance degradation, cognitive radar systems are envisioned which are required to rapidly realize the nonstationarity, accurately learn the new characteristics of the environments, and adaptively update the detector. In this paper, aiming to develop a fully cognitive radar for target detection in nonstationary environments, we propose a unifying framework that integrates (i) change-point detection of clutter distributions by using a data-driven cumulative sum (CUSUM) algorithm and its extended version, (ii) learning/identification of clutter distribution by applying sparse theory and kernel density estimation methods, and (iii) adaptive target detection by automatically modifying the likelihood-ratio test and corresponding detection threshold. Further, with extensive numerical examples, we demonstrate the achieved improvements in detection performance due to the proposed framework in comparison with a nonadaptive case, an adaptive matched filter method, and the clairvoyant case. We also use Wilcoxon rank-sum tests to evaluate the statistical significance of the performance improvements.

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Acknowledgements

The work was supported by AFOSR under Grant No. FA9550-16-1-0386. The work of Sen was performed at the Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy, under Contract DE-AC05-00OR22725. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

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Authors and Affiliations

  1. Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Yijian Xiang & Arye Nehorai

  2. Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA, 15213, USA

    Murat Akcakaya

  3. Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Satyabrata Sen

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  1. Yijian Xiang
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  2. Murat Akcakaya
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  4. Arye Nehorai
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Correspondence to Arye Nehorai.

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Appendices

Appendices

1.1 Proof of \(\hat{t}_{\text {AMF}}\sim F(2, 2LN)\) under the null hypothesis

First, under the null hypothesis,

$$\begin{aligned} LN\frac{\hat{\sigma }^2}{\sigma ^2/2}\sim \chi ^2_{2LN}. \end{aligned}$$
(32)

Further, because \(\varvec{y}_0^{(k)H}\varvec{1}\sim \mathcal {CN}(0, N\sigma ^2)\), we have

$$\begin{aligned} \frac{|\varvec{y}_0^{(k)H}\varvec{1}|^2}{N\sigma ^2/2}\sim \chi ^2_2. \end{aligned}$$
(33)

Note that \(\varvec{1}^H\varvec{1}=N\), thus, we have

$$\begin{aligned} \hat{t}_{\text {AMF}}\sim \frac{\chi ^2_2/2}{\chi ^2_{2LN}/2LN}, \end{aligned}$$
(34)

where the right-hand side coincides with definition of an F-distribution, because these two \(\chi ^2\)-distributions are independent due to the independence of the data in the CUT and the secondary data.

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Xiang, Y., Akcakaya, M., Sen, S. et al. Target Detection via Cognitive Radars Using Change-Point Detection, Learning, and Adaptation. Circuits Syst Signal Process 40, 233–261 (2021). https://doi.org/10.1007/s00034-020-01465-z

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