Adaptive detection of distributed targets in noise and interference which is partially related with targets
Introduction
Adaptive radar detection of distributed targets in structured interference and Gaussian noise is a long-standing topic of interest in the field of signal processing [1], [2], [3], [4], [5], [6], [7], [8], [9]. Examples of distributed targets are: a target observed by a high resolution radar is resolved into a set of dominant scattering centers; a target of large size (such as large ships) occupies several range cells; a cluster of point-targets share the same velocity, direction of arrival, or distance, etc. Hence, a distributed target (if present) usually occupies a number of cells under test (CUTs). The signal in a CUT is formulated as a known steering vector scaled by an unknown amplitude factor. Since the steering vector is possible to change from cell to cell, the detection system response for a distributed target can be described as a steering matrix; the signal of a distributed target lies in the subspace spanned by the columns of this steering matrix. The structured interference denotes the coherent pulsed jammers impinging on the sensors of a detection system; this structured means that the directions of arrival (DOAs) of those jammers can be roughly estimated by using an Electronic Support Measure system [7]; therefore, those jammers are supposed to lie in an interference subspace which covers all possible DOAs and uncertainties tied to this estimate. The noise represents a wide sense of uninterested random components, such as thermal noise and clutter, etc. The noise covariance matrix (NCM) of the primary data in the CUTs is unknown in practice, a set of homogeneous noise-only (secondary) data, which are sampled from the cells adjacent to the CUTs, are usually available to estimate this NCM.
For distributed target detection in structured interference, the signal and interference subspaces are assumed to be known a priori and linearly independent [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]; this denotes the situations where the signal and interference are dividable in spatial, temporal and/or frequency domains. For instance, the targets and interference sources have different Doppler spectra without overlap; they have dividable DOAs, etc. A large number of detectors have been designed under the aforementioned assumption. Instructive works have been done by L.L. Scharf et al. from the perspective of oblique projection [10], [11], by using the generalized likelihood ratio test (GLRT). J. Liu et al. [12] extend the work in [10], [11] by introducing multiple primary data, and propose two distributed matched subspace detectors for known and unknown noise power, respectively. As the NCM is proportional to a unit matrix in [10], [11], [12], its estimate involves the primary data alone; while the secondary data are necessary if the noise with respect to (w.r.t.) different channels/sensors are related, such as the cases in [13], [14], [15], [16], [17], [18], [19], [20], [21]. F. Bandiera et al. [13] derive the one-step (1S)1 GLRT and two-step (2S)2 GLRT in both homogeneous environment (HE)3 and partially HE (PHE)4; the false alarm rate of the 1S GLRT in HE is addressed in [14]; the statistical performance of the 1S GLRT and 2S GLRT in HE, and the 1S GLRT in PHE is discussed in [15] for the case of one primary data. The detection problem in [13] is also studied by using the Rao test in [16] and the Wald test in [17]; the Rao- and Wald-based detectors outperform the GLRT-based ones under certain parameter settings. The principle of invariance is used in [18], [19], [20], [21]: in detail, the cases of HE and PHE are studied in [18], [19], [20] and [21], respectively; one primary data is involved in [18], [21], while multiple primary data are used in [19], [20].
It is important to point out that all the detectors mentioned above are derived under the strong assumption that the signal and interference subspaces are linearly independent. However, those two subspaces are possible to be partially related. For instance, the main-lobe beam pointing of a detection system is overlapped with the range where possible interference sources lie in; the targets of interest and the interference sources share similar Doppler frequencies and/or distances in the view of a detection system, leading to that the signal and interference cannot be completely separated. Hence, urgent attention is required for the case where the signal and interference subspaces are partially related. Fortunately, this case is addressed in this paper.
Considering that the signal and interference may be partially related, first we do singular value decomposition (SVD) to the overall matrix which is composed of the signal and interference subspace matrices, to obtain a slice of a unitary matrix; the columns of this slice matrix are the standard orthogonal basis vectors for the above overall matrix. Second, we recast the signal plus interference as one which lies in the subspace spanned by this slice matrix. Finally, the original detection problem is equivalently reformulated as a new one which can be solved by using the common design techniques. Precisely, we derive the 1S GLRT and 2S GLRT in both HE and PHE. The four new detectors have the constant false alarm rate (CFAR) properties against the NCM (and the scaling factor in PHE) and the capabilities of interference rejection. They degrade to the GLRT-based ones in [13] if the signal and interference subspaces are linearly independent. Therefore, the new detectors are the generalizations of those GLRT-based ones in [13]. When the interference subspace is totally covered by the signal subspace, the proposed 2S-GLRT-based detectors become the 2S-Rao-based ones in [16]. The effectiveness of the four new detectors are demonstrated via several numerical experiments, also in comparison with the Rao-based detectors in [16].
The remainder of this paper is organized as follows. In Sec. 2, the detection problem at hand is formulated as a binary hypothesis. Sec. 3 derives the 1S GLRT and 2S GLRT in both HE and PHE. Several numerical experiments are presented in Sec. 4. Conclusions of this paper are drawn in the final section.
Section snippets
Problem formulation
In this section, we first introduce some useful notations; second, we formulate the detection problem at hand.
Detectors design
In this section, the 1S GLRT and 2S GLRT are derived in Sec. 3.1 and Sec. 3.2, respectively; then, the CFAR properties of the new detectors are proved in Sec. 3.3. The special cases of and are discussed in Sec. 3.4 and Sec. 3.5, respectively.
Simulation results
In this section, the detection performance is assessed through numerical experiments. We resort to the standard Monte Carlo counting technique, to evaluate the detection thresholds and probabilities of detection (PDs) via 106 and 103 independent trials, respectively. Precisely, the test statistic of a detector is calculated 106 times under , to obtain 106 values; then, for a specified PFA, the th largest value is selected as the detection threshold. The test statistic is also
Conclusion
Adaptive detection of distributed targets in structured interference and Gaussian noise was studied in both HE and PHE, for the case where the signal and interference subspaces are partially related. The signal and interference were recast as one. Then, the 1S-GLRT-HE (1S-GLRT-PHE) and 2S-GLRT-HE (2S-GLRT-PHE) were designed in HE (PHE) via the 1S GLRT and 2S GLRT, respectively. If the signal and interference subspaces are linearly independent, the new detectors degrade to the ones in [14]; if
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61601103, 61721001 and 61871083).
Zuozhen Wang received the B.S. degree and M.S. degree in electronic engineering at University of Electronic Science and technology of China (UESTC). Now he is pursuing a Ph.D. degree in the school of information & communication engineering, UESTC. His current research is radar target detection.
References (39)
- et al.
Distributed target detection in subspace interference plus Gaussian noise
Signal Process.
(2014) - et al.
Rao tests for distributed target detection in interference and noise
Signal Process.
(2015) - et al.
Polarization-space-time domain generalized likelihood ratio detection of radar targets
Signal Process.
(1995) - et al.
A polarimetric adaptive matched filter
Signal Process.
(2001) - et al.
Adaptive detection of distributed targets in partially homogeneous environment with Rao and Wald tests
Signal Process.
(2012) - et al.
Multichannel signal detection in interference and noise when signal mismatch happens
Signal Process.
(2020) - et al.
Wald tests for direction detection in noise and interference
Multidimens. Syst. Signal Process.
(2018) - et al.
GLRT-based direction detectors in homogeneous noise and subspace interference
IEEE Trans. Signal Process.
(2007) - et al.
CFAR matched direction detector
IEEE Trans. Signal Process.
(2006) - et al.
Detection of subspace waveforms in subspace interference and noise
Distributed target detection in partially homogeneous environment when signal mismatch occurs
IEEE Trans. Signal Process.
Distributed target detectors with capabilities of mismatched subspace signal rejection
IEEE Trans. Aerosp. Electron. Syst.
Invariant adaptive detection of range-spread targets under structured noise covariance
IEEE Trans. Signal Process.
Detection of a distributed target with direction uncertainty
IET Radar Sonar Navig.
Polarimetric adaptive detection of range-distributed targets
IEEE Trans. Signal Process.
Matched subspace detectors
IEEE Trans. Signal Process.
Blind adaptation of zero forcing projections and oblique pseudo-inverses for subspace detection and estimation when interference dominates noise
IEEE Trans. Signal Process.
Adaptive radar detection of distributed targets in homogeneous and partially homogeneous noise plus subspace interference
IEEE Trans. Signal Process.
False alarm rate of the GLRT for subspace signals in subspace interference plus Gaussian noise
IEEE Trans. Signal Process.
Cited by (2)
Efficient jamming attack against MIMO transceiver
2022, Digital Signal Processing: A Review JournalCitation Excerpt :Jamming strategies involve exploiting weaknesses in legitimate wireless links, particularly the physical layer, through the development of adaptive intelligent attacks while minimizing the resources consumed in these activities. A smart jammer can learn and adapt to the environment, then interact by injecting artificial interference signals based on its ability to extract information about the legitimate link at stake to decrease the jamming power, thus improving the resistance against the anti-jamming systems [4–8]. Interferences can be divided into two major branches: “jammers and spoofers” [9,10].
Persymmetric adaptive detection of range-spread targets in subspace interference plus Gaussian clutter
2023, Science China Information Sciences
Zuozhen Wang received the B.S. degree and M.S. degree in electronic engineering at University of Electronic Science and technology of China (UESTC). Now he is pursuing a Ph.D. degree in the school of information & communication engineering, UESTC. His current research is radar target detection.
Zhiqin Zhao (M'05–SM'05) received the B.S. and M.S. degrees in electronic engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, and the Ph.D. degree in electrical engineering from Oklahoma State University, Stillwater, OK, USA, in 1990, 1993, and 2002, respectively.
From 1996 to 1999, he was with the Department of Electronic Engineering, UESTC. From 2000 to 2002, he researched rough surface scattering as a Research Assistant with the School of Electrical and Computer Engineering, Oklahoma State University. From 2003, he was a Research Associate with the Department of Electrical and Computer Engineering, Duke University, Durham, NC. In 2006, he became a Professor with the School of Electronic Engineering, UESTC. His current research interests include computational electromagnetics, signal processing, et al. He has published over 200 refereed journal papers and conference papers.
Dr. Zhao is a member of Phi Kappa Phi honor society and a senior member of IEEE. In 2016, Zhao was hired as the deputy editor of the IEEE Transactions on Geoscience and Remote Sensing (TGRS).
Chunhui Ren received her master degree in communication and information systems in April 1998 from University of Electronic Science and technology, China. In June 2006, she obtained the Ph.D. degree in communication and information systems at the same university. Now she is work at the same university and focus on signal processing.
Zaiping Nie (M'98–SM'99–F'13) was born in Xi'an, China, in 1946. He received the B.S. degree in radio engineering and the M.S. degree in electromagnetic field and microwave technology from the Chengdu Institute of Radio Engineering (now UESTC: University of Electronic Science and Technology of China), Chengdu, China, in 1968 and 1981, respectively.
From 1987 to 1989, he was a Visiting Scholar with the Electromagnetics Laboratory, University of Illinois, Urbana. Currently, he is a Professor with the Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, China. He has published more than 300 journal papers. His research interests include antenna theory and techniques, fields and waves in inhomogeneous media, computational electromagnetics, electromagnetic scattering and inverse scattering, and signal processing based on physical process.