GLRT-based detectors for FDA-MIMO radar with training data
Introduction
In recent years, some new radar systems have been proposed, such as frequency diverse array (FDA) radar, multi-input multi-output (MIMO) radar, etc [1], [2], [3], [4], [5]. The FDA radar is obtained by introducing a small frequency increment across adjacent antenna elements, which has attracted a lot of attention due to the range-angle-dependent property [6], [7], [8]. The FDA provides more degrees of freedom (DOFs) than the conventional array, thereby increasing the flexibility of signal processing [9], [10], [11], [12].
The MIMO radar uses multi-channel transmission and multi-channel reception technologies. For MIMO radar, one advantage over phased array radar is the waveform diversity. Waveform diversity means transmitting uncorrelated signals at the transmitting end, which leads to an increase in the DOF of the transmitter [13], [14], [15]. Hence, the MIMO radar can use matched filter banks to obtain more independent observable signals at the receiving end.
In order to separate the transmitting orthogonal waveform of FDA radar and extract the distance information of the target, the combining of FDA and MIMO radar emerged. The FDA-MIMO radar expands the traditional space-time 2-dimensional signal processing to range-space-time 3-dimensional signal processing. Using the advantages of FDA and MIMO radar, the FDA-MIMO radar can suppress the deceptive interference coming from the main lobe of radar beamformer [16], [17]. Moreover, the FDA-MIMO radar can suppress range-dependent clutter.
There are only a few papers addressing the problem of FDA-MIMO radar detection so far. In [18], an adaptive moving target detection approach for FDA radar without training data was proposed in interference environment. To reduce the high complexity of the 3-dimensional search of structured generalized likelihood ratio test (GLRT), an unstructured GLRT and a low-complexity two-stage implementation of the unstructured GLRT were proposed in [18]. In [19], a mainlobe clutter suppression approach for FDA radar blind-Doppler target detection without training data was proposed, by exploiting the Doppler-spreading effect. In [20], a unified framework detector was presented to comparatively analyze the detection performance of FDA-MIMO radar for single- and multiple-coherent pulses in the Neyman-Pearson sense, which does not use training data. In order to detect the target in Gaussian clutter with unknown but stochastic covariance matrix, Bayesian Rao (BRao) detector and Bayesian Wald (BWald) detector without training data were presented in [21], and a Bayesian detector for FDA-MIMO radar moving targets and two detectors without training data based on Bayesian framework were proposed according to the structured GLRT and unstructured GLRT in [22], and these designed Bayesian detectors outperform conventional non-Bayesian counterparts.
In practice, there are a large number of training data, which can be used to improve detection performance. In particular, the GLRT was proposed in [23] and [24] with training data when the position of the target within each range cell was assumed unknown. And the training data are used to estimate spectral characteristics of the interference. In addition, in order to detect the actual target from the noise background while rejecting false targets, reference [25] proposed a range-angle-GLRT detector with unknown covariance matrix, where the training data were also utilized. FDA-MIMO radar was employed in [26] for low-observable moving target detection with the training data, and a 3-dimensional processing method named as space-range-Doppler focus (SRDF) processing was proposed for coherent integration and high-resolution estimation. A signal model with the training data for FDA-MIMO radar based on the distributed source model was built in [27], and the detection performance of the FDA-MIMO radar multi-pulse detector was analyzed for Swerling I and II model. It was demonstrated by simulations that the proposed detector in [27] has better detection performance than the MIMO radar detector at low signal-to-noise ratio (SNR). A nonhomogeneous sample detection method with training data was developed in [28] to obtain the jamming-plus-noise (JNR) covariance matrix with high accuracy.
However, for the problem of FDA-MIMO radar detection with training data, no effective detector was proposed either for the case of unknown target velocity or for the case of known target velocity. To bridge this gap, in this paper we propose adaptive detectors using training data for FDA-MIMO radar detection and derive their statistical performance of the proposed detectors.
The rest of this paper are organized as follows. Section 2 presents the detection problem for FDA-MIMO radar. The detectors with training data in the case of known target velocity and unknown target velocity are proposed in Section 3. Section 4 analyzes the statistical performance of the proposed detectors. Numerical results are provided in Section 5 to assess the detection performance of the proposed detectors. Finally, conclusions are drawn in Section 6.
Section snippets
Problem formulation
We consider a colocated FDA-MIMO radar with M-element uniform linear array (ULA) transmitter and N-element co-located ULA receiver. The FDA-MIMO radar transmits orthogonal waveforms, which is composed of K pulses. The inter-element spacing of transmitting and receiving arrays is d [18], [19], [23]. A frequency increment Δf is introduced element-by-element in the transmitting array. The carrier frequency at the mth element is , , where is the reference carrier frequency,
Proposed detector
Note that the Doppler frequency of the target is usually unknown. There are two basic approaches to deal with the unknown Doppler frequency [18]. One approach is that taking the Doppler frequency as an unknown, and adopting appropriate methods to estimate it. The other approach is performing target detection by discrete grid search.2
The case of unknown
Equation (11) is equivalent to because of . Equation (25) has the same form as the GLRT for conventional phased-array radar detecting a target with multiband [30] or multiple coherent processing intervals (CPIs) in [31], where the statistical performance was given, also summarized in [32]. Hence, we can analogously obtain the statistical distribution of the proposed detector in (25). The
Simulation results
This section will compare the proposed detectors with the detectors in [18]. The radar operates at and the array with inter-element spacing is . The range bin under test is located at , the azimuth angle is 0.3 rad, the velocity of the target is 100 m/s and the pulse repetition period is 10 us, the frequency increment is set to and , and the number of the transmitting pulses is and . To decrease the computation load, the PFA is set to . For
Conclusions
In this paper, using training data we derived two FDA-MIMO detectors for moving target detection in unknown Gaussian noise. It has been shown that the detection performance of the proposed GLRT-kn and GLRT-un is better than detectors without training data. Among the two proposed detectors, the detection performance of the GLRT-kn is much better. The main reason is that coherent accumulation can be used to improve detection performance when the Doppler frequency is known.
CRediT authorship contribution statement
Li Zeng: Conceptualization, Writing – original draft. Yong-Liang Wang: Methodology, Supervision. Weijian Liu: Software, Supervision. Jun Liu: Formal analysis. Lan Lan: Formal analysis.
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 in part by National Natural Science Foundation of China under Contracts 62071482, 61871469 and 62001510, the Youth Innovation Promotion Association CAS (CX2100060053), the Anhui Provincial Natural Science Foundation under Grant 2208085J17.
Li Zeng received her M.S. degree in signal and information processing from Xidian University, Xi'an, China, in 2019. Currently she is a Ph.D. candidate at the Wuhan university. Her research interests include radar signal processing and array signal processing.
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Li Zeng received her M.S. degree in signal and information processing from Xidian University, Xi'an, China, in 2019. Currently she is a Ph.D. candidate at the Wuhan university. Her research interests include radar signal processing and array signal processing.
Yong-Liang Wang received his Ph.D. degree in electrical engineering from Xidian University, Xi'an, China, in 1994. From June 1994 to December 1996, he was a Post-doctoral Fellow with the Department of Electronic Engineering, Tsinghua University, Beijing, China. He has been a full Professor since 1996, and he was the Director of the Key Research Lab, Wuhan Radar Academy, Wuhan, China, from 1997 to 2005. Dr. Wang was the recipient of the China Postdoctoral Award in 2001 and the Out-standing Young Teachers Award of the Ministry of Education, China, in 2001. He has authored or coauthored three books and more than 200 papers. His recent research interests include radar systems, space–time adaptive processing, and array signal processing. Dr. Wang is a member of the Chinese Academy of Sciences and also a Fellow of the Chinese Institute of Electronics.
Weijian Liu received the B.S. degree in information engineering and M.S. degree in signal and information processing, both from Wuhan Radar Academy, Wuhan, China, and the Ph.D. degree in information and communication engineering from National University of Defense Technology, Changsha, China, in 2006, 2009, and 2014, respectively. Now he is an adjunct professor with Wuhan Electronic Information Institute. His current research interests include multichannel signal detection, statistical and array signal processing.
Jun Liu received the B.S. degree in mathematics from the Wuhan University of Technology, Wuhan, China, in 2006, the M.S. degree in mathematics from the Chinese Academy of Sciences, Beijing, China, in 2009, and the Ph.D. degree in electrical engineering from Xidian University, Xi'an, China, in 2012. From July 2012 to December 2012, he was a Post-Doctoral Research Associate with the Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA. From January 2013 to September 2014, he was a Post-Doctoral Research Associate with the Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ, USA. He is currently an Associate Professor with the Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China. His research interests include statistical signal processing, image processing, and machine learning.
Lan Lan received the B.S. degree in electronic engineering, and the Ph.D. degree in signal and information processing from Xidian University, Xi'an, China, in 2015 and 2020, respectively. From July 2019 to July 2020, she was a Visiting Ph.D. Student with the University of Naples Federico II, Naples, Italy. Since 2020, she is currently a Tenure-track Associated Professor with the National Laboratory of Radar Signal Processing, Xidian University. Her research interests include frequency diverse array radar systems, MIMO radar signal processing, target detection, and ECCM.