Adaptive two-step Bayesian MIMO detectors in compound-Gaussian clutter
Introduction
Different from the traditional monostatic radar and phase array radar, the statistical multiple-input multiple-output (MIMO) radar exploits multiple widely separated transmitters and receivers to observe targets from different spatial aspects, which can obtain spatial diversity to improve the radar performance in target detection. The technique of adaptive MIMO radar detection has raised more attention internationally in the research area of radar signal processing [1], [2].
In the cases of MIMO radar detections, there are two factors that have severe influence on the adaptive detection performance of MIMO radar, i.e., clutter model and the availability of secondary clutter data. The configuration of widely separated antennas in MIMO radar commonly causes fluctuations in receiving clutter powers at different observing aspect angles. Compared with traditional Gaussian model, the compound-Gaussian model is better to represent the clutter power fluctuations [3], [4], [5], [6]. Hence, it is more suitable to use compound-Gaussian models to represent clutter returns at different receivers in MIMO radar detections. On the other hand, the utilization of sufficient secondary clutter data will improve the performance of adaptive detectors in overwhelmed clutter environment. The covariance matrix of clutters can be estimated with a set of secondary clutter data, which is assumed to be same with that of primary data in Gaussian environment [7], [8], [9], or the same covariance structure except different power levels (textures)1 in compound-Gaussian environment [10], [11], [12], [13]. The accuracy of estimated clutter covariance matrix is related with the amount of secondary clutter data.
In the recent decades, several classic adaptive estimators and detectors, such as normalized sample covariance matrix (NSCM) [14], [15], sample covariance matrix (SCM) and fixed-point estimate (FPE) [16], [17], [18] have been proposed. They perform well when the secondary data is sufficient2. However, these approaches lead to poor estimators and severe detection loss in the case of limited secondary data. Although some efficient Bayesian detectors exploiting a priori knowledge about the clutter covariance matrix have been derived to handle the adaptive detection with limited secondary data, they can only work for traditional radar [19], [20], [21], [22] or MIMO radar in Gaussian clutter environment [23]. The MIMO radar detectors that suitable for the compound-Gaussian clutter in limited secondary data cases need to be studied.
In this paper, we present Bayesian-based adaptive MIMO detection algorithms to improve the detector performance in compound-Gaussian clutters. We discussed the idea in [24], [25], which are some preliminary conference versions of the work presented here. These algorithms are based on the assumption that the clutter structures have a priori random distribution. For the clutter power levels (textures), we consider two ways to model them at the design stage: unknown deterministic quantities or random variables ruled by certain distribution. Within this framework, we propose three detectors based on the generalized likelihood ratio test (GLRT) and two-step adaptive design procedure. Firstly, we obtain the GLRT by assuming the known covariance matrices. Then, we derive the maximum a posteriori (MAP) estimator of the matrices by exploiting the Bayesian technique, and replace the given covariance matrices in the obtained GLRT with MAP estimates. Note that the Bayesian-based adaptive MIMO detectors for compound-Gaussian clutter have been discussed in [26]. However, the adaptive design procedure of detectors and the way to model the texture considered in [26] are different from those considered in this paper:
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In this paper, the two-step adaptive design procedure is employed, where the clutter covariance matrices are estimated based on the secondary data only. In [26], the one-step adaptive design procedure is considered, where the clutter covariance matrices are estimated based on both the primary data and secondary data.
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In this paper, the integration was performed for the unknown random textures and the MAP estimators were derived for the unknown covariance matrix structures. In [26], the integration was performed for the unknown covariance matrix structures and the MAP estimators were derived for the unknown textures.
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In this paper, two ways are used to model the texture at the design stage: unknown deterministic quantities or random variables ruled by certain distribution. In [26], just one way is used to model the texture at the design stage: random variables ruled by certain distribution.
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In the section of simulation, the results show the proposed detectors in this paper perform better than those in [26].
The rest of this paper is organized as follows. In Section 2, the model of MIMO radar signal in compound-Gaussian clutter environment is given. In Section 3, the new GLRT-based detectors are proposed based on the Bayesian framework. In Section 4, the detection performance of proposed detectors are evaluated via numerical simulations. Finally, the conclusions are drawn in Section 5.
Section snippets
Model formulation
The MIMO radar model with M transmitters and R receivers is considered. All the transmitters and receivers are set far enough away from each other that the target reflections and/or clutters have uncorrelated reflection coefficients at different transceiver pairs. is a N-dimensional complex vector, which denotes the returns from the kth range cell received at the rth receiver, where is the complex field, . Then, the detection problem with MIMO radar can be described
Detector design
Modeling the structures as unknown random variables with inverse complex Wishart distribution, clutter textures τrk, as unknown deterministic quantities or random parameters following the Gamma distribution and inverse Gamma distribution respectively, we design adaptive detectors based on the two-step strategy. Firstly, we obtain the GLRT with the known covariance matrix structure. Then, we derive the MAP estimator of the matrix structure by exploiting the
Performance assessment
Simulation results are provided to verify the proposed adaptive Bayesian detectors AGLRT-DT-MAP, AGLRT-GT-MAP and AGLRT-IGT-MAP. In the procedure of performance analysis, we first analyze the detectors under the design assumptions, then we conduct a study to quantify their sensitivity to possible mismatches between nominal and operating conditions.
Conclusion
The problem of MIMO radar adaptive detection in compound-Gaussian clutter is addressed in this paper. Based on the Bayesian approach, we derived three adaptive GLRTs according to the two-step strategy. Finally, the performance of the GLRTs is evaluated with numerical simulations. The results highlight that the framework of Bayesian is a viable approach to improve adaptive performance. Precisely, the proposed Bayesian GLRTs exhibit acceptable performance losses with respect to the GLRTs with
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grants 61701088 and 61701093, the Chinese Postdoctoral Science Foundation under Grants 2016M600731, 2017T100690, 2017M612943 and 2018T110961, the Fundamental Research Funds for the Central Universities under Grant ZYGX2018J018, the Sichuan Science and Technology Project of China under Grant 2018RZ0063, and the Guangdong Natural Science Foundation of China under Grant 2017A030310637.
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